ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)

GRADO EN INGENIERÍA ELECTROMECÁNICA

Especialidad Mecánica

Measurement of the just-suspended speed in

orbitaly shaken bioreactors with conical

bottoms

Autor: Gabriel Sánchez Arranz

Director: Andrea Ducci

Madrid

Mayo, 2016

(Andrea Ducci)

(José Ignacio Linares)

MEASURMENT OF THE JUST-SUSPENDED SPEED IN ORBITALY SHAKEN BIOREACTORS WITH CONICAL BOTTOMS

Autor: Sánchez Arranz, Gabriel

Directores: Ducci, Andrea

Entidad Colaboradora: UCL - University College of London

1 Introducción

1.1 Microportadores

Los microportadores son pequeñas partículas (10 μm - 5 mm) usadas para contener células que requieren estar adheridas a una superficie para su desarrollo (e.g. células madre), para su cultivo en suspensión en Bioreactores. Poseen muchas ventajas respecto a los cultivos en 2D, y sus aplicaciones son muy diversas, incluyendo la producción a nivel industrial de virus, vectores, antibióticos, y para el cultivo a gran escala de células para ensayos clínicos y aplicaciones médicas.1

Permiten mejorar la productividad, llegando hasta 200 millones de células por mililitro. Además, se consigue un ambiente homogéneo, que reduce el gradiente en el PH y las concentraciones de nutrientes y oxígeno. El proceso es fácilmente escalable, siendo los cultivos desde unos pocos mililitros hasta miles de litros.2

1.2 Reactores de agitación orbital

En el caso de estudio, un reactor de agitación orbital (OSR) es un tanque cilíndrico en el que se introducen los microportadores junto a un líquido con nutrientes. La suspensión de las partículas se consigue agitando el tanque en una trayectoria circular, a una velocidad N[rpm] con un diámetro do[cm]. Esto crea un vórtice en el fluido que empuja a los microportadores hacia arriba desde el fondo del tanque.3

En ensayos de laboratorio y aplicaciones industriales de biotecnología, el cultivo de células se suele realizar en OSRs, porque permiten ensayar varias condiciones distintas en paralelo. Los reactores de agitación mecánica con hélices se suelen usar para producción a gran escala, una vez que el proceso ha sido previamente optimizado en OSRs y escalado. Sin embargo, como la geometría y el modo de agitación son distintos, la distribución de velocidades en el fluido y los niveles de turbulencias son distintos. Para solucionar este problema, se ha diseñado reactores con hélices para pequeña escala, y OSRs para gran escala, hasta 1000L de capacidad.5

Las ventajas de los OSRs incluyen: diseño simple y funcional6, buena eficiencia de mezcla5, buena transferencia de oxígeno7, menor esfuerzo cortante8 y ausencia de burbujas en el líquido.9

1.3 Necesidad de conocer la velocidad de agitación

Es muy importante que los microportadores estén suspendidos para un cultivo apropiado de las células1. No tienen que quedarse en el fondo del tanque, ni ser agitados bruscamente, que dañaría las células. La velocidad de agitación es un factor clave en el la productividad del cultivo de células. Si es muy baja, el esfuerzo cortante en las células es bajo, pero las partículas precipitan en el fondo del tanque, causando gradientes en el PH y la concentración de oxígeno y nutrientes, que afectan muy negativamente al crecimiento de las células.10 Si la velocidad es muy grande, el esfuerzo en las células es muy grande, provocando que se despeguen de los microportadores, además de chocar estos unos contra otros y contra las paredes del tanque.11

2 Estado de la técnica

El parámetro fundamental para estudiar la mecánica de fluidos en un OSRs el el numero de Froude �� = � � �/�, donde d puede ser el diámetro orbital (do) o el del cilindro del tanque (di).

Los principales avances publicados se resumen en:

El flujo en OSRs con fondo plano se caracteriza a bajas velocidades de agitación por un vórtice toroidal que se expande hacia el fondo según aumenta la velocidad de agitación. Cuando Fr=Frc, se convierte en un vórtice precesional.15

Existe una ley que determina el Froude crítico (Frc). Hay dos ecuaciones, dependiendo de la geometría del tanque:15

o Si ℎ/�� /√� /�� �� 0 = �0� ℎ� 0� .5

o Si ℎ/�� /√� /�� �� � = �0�

donde a0w=1.4 para el agua.

En el primer caso la transición ocurre cuando el vórtice toroidal alcanza el fondo del cilindro, y en el segundo antes, sin llegar a alcanzarlo.

La suspensión de los microportadores está asociada a esta transición. Si ℎ/��√� /��,la suspensión ocurre para ��� . �� , y la homogenización de la mezcla

cuando ��~ . �� , mientras que si ℎ/�� √� /�� los valores de Fr crecen. La

velocidad medida es la aquella a la que los microportadores acaban de suspenderse, que se asume que ocurre cuando el 95% de las partículas están en suspensión.18

La concentración de microportadores no tiene una influencia apreciable en la velocidad de suspensión.18

El flujo del líquido para OSRs con fondo cónico es muy similar. Sin embargo, para el mismo volumen de llenado el vórtice alcanza el fondo a velocidades de agitación

menores que en el caso de fondo plano, siendo menores cuando mayor es la altura del cono. A pesar de esto, la transición ocurre para el mismo Fr.20

Por tanto, se espera que la velocidad de suspensión (Ns) de los microportadores sea menos para fondos cónicos que planos.

3 Objetivos

El principal objetivo es estudiar cómo cambia la velocidad de suspensión si el fondo plano se sustituye por un fondo cónico. La velocidad medida será la de homogenización, que es aquella que se usará como velocidad de operación en procesos reales.

La velocidad de suspensión, Ns, fue medida para 36 geometrías distintas, representativas del cultivo de células, que son:

Para di=10cm: o h=4.5-7cm (Altura constante). o do=1.5-2.5-5cm. o Fondo plano, Cono A, Cono B y Cono C.

Para di=7cm: o h=3-5cm (Para fondo plano, Volumen constante) o do=1.5-2.5-5cm. o Fondo plano y Cono C.

En todos los experimentos, el tipo de microportador empleado es Cytodex-3, con una concentración de 1.5g/L. Para di=10cm, las alturas de los fondos cónicos son respectivamente 0.5-1.1.5cm, y para di=7cm, el fondo cónico C fue escalado con respecto al diámetro del cilindro. En el primer caso, la altura del llenado del fluido es constante, y en el segundo lo es el volumen, y por tanto la altura de llenado para el fondo cónico C fue modificada para que el vólumen de llenado fuera el mismo que para fondo plano.

4 Metodología

El tanque se llena con agua destilada, y se introducen los microportadores. El reactor se fija a la mesa de agitación, que permite ajustar el diámetro orbital. Los microportadores se tiñen previamente usando Trypan-Blue,22 durante 12 horas. La cámara se fija también a la mesa, apuntando al reactor. Se incrementa la velocidad de agitación, y para cada velocidad la cámara captura una imagen a cada vuelta, para un ángulo fijo. en total, unas 10-20 imágenes se capturan para cada velocidad, para hacer la media posteriormente. El parámetro que se usa para determinar si los microportadores están suspendidos o no es el brillo de la imagen dentro del cilindro. Debido a que estos están teñidos de azul oscuro y hay un fondo blanco iluminado detrás del cilindro, el brillo tendrá el valor más

alto cuando los microportadores estén todavía en el fondo, mientras que cuando se empiecen a elevar irá disminuyendo. Se usará el Índice de brillo normalizado: �∗ � = �� � − �� ∞�� − �� ∞

donde �� es el brillo medio para la velocidad más baja medida, y �� ∞ para la velocidad más alta, es decir, los microportadores están completamente suspendidos. �∗ � está comprendido entre 0 y 1.

I* se interpola con una curva de ecuación I∗ = +ea x−xo , donde x=Fr/Frc o N. La

velocidad de suspensión se considera alcanzada cuando I*=0.05 (95% de las partículas suspendidas).

Se realizaron dos scripts en Matlab para procesar las imágenes. El primero para generar un vector con el brillo medio de las imágenes para cada velocidad, y el segundo para interpolar y calcular la velocidad de suspensión (Ns), el Froude de suspensión (Frs), el Froude crítico (Frc) y los parámetros de interpolación.

5 Resultados

El cociente Fr/Frc para todos los casos estudiados en el laboratorio se muestra a continuación:

di=10cm

Se demuestra que para la misma geometría, la velocidad de suspensión es menor cuando más alto sea el cono del fondo. En general, hay una tendencia creciente con h/di /√do/di para las 4 curvas, que tienden a converger para los valores más altos de este coeficiente.

Para el cono B, la diferencia respecto al fondo plano es la más constante de los 3. La mayor diferencia se registra, como se esperaba, para el Cono C, en los 2 valores más

pequeños de h/di /√do/di, con un descenso de la velocidad de suspensión de en torno a un 15% en ambos casos. Los valores de Frs/Frc para fondo plano concuerdan con los de los experimentos de

Ducci, estando en torno a 1.2 para los valores más pequeños de h/di /√do/di, e incrementándose para los más altos.

di=7cm

En este caso, la tendencia creciente se puede apreciar para el fondo cónico, pero los valores para fondo plano son ligeramente mayores que lo esperado para los valores más pequeños de h/di /√do/di. Sin embargo, hay una reducción significativa en la velocidad de suspensión en fondo cónico, que es lo que se pretendía demostrar.

6 Conclusión

Queda demostrado que si se sustituye el fondo plano por uno cónico, la velocidad de suspensión reduce, si el resto de parámetros no cambian. De hecho, cuanto más alto el cono, menor la velocidad de suspensión. Además, se aprecia que el fondo cónico tiene una gran influencia en el flujo, mejorando los mecanismos para la elevación de los microportadores, que era lo que se esperaba a raíz de los experimentos de Rodríguez (2015),20 que concluyó que el vórtice toroidal alcanza el fondo cónico a menores velocidades y la vorticidad aumenta.

Estos resultados implican que el cultivo en suspensión se puede mejorar significativamente. El coste de mantener la velocidad de agitación será menor, y las condiciones de cultivo mejorarán también, ya que al ser la velocidad de agitación menor, el esfuerzo cortante disminuirá.

MEASURMENT OF THE JUST-SUSPENDED SPEED IN ORBITALY SHAKEN BIOREACTORS WITH CONICAL BOTTOMS

Author: Sánchez Arranz, Gabriel

Directors: Ducci, Andrea

Collaborating Entity: UCL - University College of London

PROJECT ABSTRACT

1 Introduction

1.1 Microcarriers

Microcarriers are small support matrixes (10 μm - 5 mm) used for containing adherent cells (e.g. stem cells) for their growth in suspension inside bioreactors. They are being increasingly employed in adherent cell applications, because they overcome many of the difficulties of 2D cell culture. Some of the main applications include the production of viruses, vectors, proteins, antibodies at industrial scale, and the culture of large number of cells for clinical trials and routine cell culture.1

They provide an increase in yields, which reach up to 200 million cells per millilitre. They allow the culture in suspension of cells that require a surface to grow, such as stems cells. Furthermore, 3D culture allows for a homogeneous environment, which reduces PH and concentration gradients, and the processes are easily scalable (from a few millilitres to several thousand litres).2

1.2 Orbitaly Shaken Bioreactors

In the case of study, an orbitaly shaken bioreactor (OSR) is a cylindrical vessel in which the Microcarriers are submerged into a liquid with nutrients. The suspension is reached by shaking the vessel, which describes a circular trajectory with a fixed angular speed of N[rpm] and a diameter of do[cm]. This creates vortex in the fluid that lift up the microcarriers. 3

In laboratory trials and industrial biotechnology applications, cells are usually grown in shaken bioreactors because they offer a low power consumption solution to screen several conditions in parallel. Stirred tanks are traditionally used for large-scale production, once the process is optimised in a shaken bioreactor and then scaled up. However, as the geometry and shaking mechanism are different, the fluid velocity field distribution and the turbulence levels change too. To overcome this problem, miniature stirred tanks for bioprocess development have been designed, as well as large scale shaken bioreactors, up to a capacity of 1000 L.5

Some of the advantages of OSRs respect to stirred tanks are: simple and functional design6, good mixing efficiency5, good oxygen transfer,7 lower shear stress8 and lack of damaging bubble bursts.9

1.3 Need for knowing the suspension speed

It is very important that microcarriers are properly suspended for a successful culture of cells, not staying at the bottom of the tank, or being shaken too sharply that the cells get damaged.1 The shaking speed is a key factor in the growth and final yield of cells, due to its influence in the shear forces on cells and mixing of the fluid. If the rate is low, the shear stress is low too, but the microcarriers will settle in the bottom of the reactor, causing gradients in the pH, O2 and nutrient concentrations, which affect very negatively the cell growth.10 If the speed is too high, the shear stress increases, leading to cells dislodging from the microcarriers, as well as increasing the rate of microcarriers colliding against each other and the walls. 11

2 Literature Review

The main parameter to study the fluid mechanics in OSRs is the Froude number: �� = � � �/�, where d can be the orbital diameter (do) or the cylinder diameter (di).

The main findings from the Literature Review are:

The flow in OSRs with flat bottom is dominated at low speeds by a toroidal vortex that expands to the bottom of the reactor as the speed is increased. At Frc it transitions to a preccesional vortex.15

There is a scaling law that establishes the critical Froude (Frc). There are two equations for this, one for each case, depending on the geometry:15

o For ℎ/�� /√� /�� �� 0 = �0� ℎ� 0� .5

o For ℎ/�� /√� /�� �� � = �0�

where a0w=1.4 for water.

In the first case the transition occurs when the vortex reaches the bottom of the tank, and in the second, before.

The suspension of microcarriers is directly associated to this transition. When ℎ/�� √� /��, the suspension occurs at ��� . �� , and the homgenisation of

the mix at ��~ . �� , and when ℎ/�� √� /�� the values drift upwards. The

speed that it is measured is the just-suspended speed, which is considered when 95% of the Microcarriers are lifted.18

The concentration of microcarriers does not have a significant influence in the suspension speed.18

The one-phase flow in conical bottom OSRs is qualitatively very similar. However, for the same filling volume the vortex reaches the bottom at lower speeds the higher the cone is, and the vorticity is higher. Despite this, the transition between the two main flow regimes takes place at the same Fr.20

It is therefore expected that the suspension of microcarriers will be attained at lower shaking speeds, Ns.

3 Objectives

The main objective of this project is to study how the suspension speed changes if the flat bottom of an OSRs is replaced by a conical one. The speed that will be measured is the one at which complete homogenisation is achieved, which will be the one to use as the operating condition in real processes.

In order to carry out this research, Ns is measured for 36 different operating conditions, representative of cell culture, which are:

For di=10cm: o h=4.5-7cm (Constant height). o do=1.5-2.5-5cm. o Flat Bottom, Cone A, Cone B and Cone C.

For di=7cm: o h=3-5cm (For flat bottom, Constant volume) o do=1.5-2.5-5cm. o Flat Bottom and Cone C.

In all the experiments, the microcarrier type used is Cytodex-3, with a concentration of 1.5g/L. For di=10cm, the heights of the cones are respectively 0.5-1-1.5cm, and for di=7cm, Cone C is scaled respect to the cylinder diameter, to 1.05cm. In the first case, the filling height is kept constant, and in the second, the filling volume is constant, and the filling height for Cone C has to be modified so that the fluid volume is the same as in the flat bottom case.

4 Methodology

The reactor containing the corresponding filling volume of distilled water and microcarriers is mounted rigidly on a shaker table, that allows to adjust the orbital diameter. The microcarriers are dyed previously for 12 hours with Trypan Blue. A camera is mounted on the table facing the reactor. The speed is increased, and for each speed the camera captures one image every revolution at a fixed angle. In total, for each speed 10-20 images are taken, to do the average. The variable used to determine if the microcarriers are suspended or not is the brightness of the image within the cylinder. Because the microcarriers are coloured in dark blue and a white illuminated background is placed behind the reactor, the brightness will be the highest when the microcarriers

are settled at the bottom, whereas when the particles start lifting it will decrease. The normalised Brightness Index will be used: �∗ � = �� � − �� ∞�� − �� ∞

where �� is the mean brightness at the lowest measured speed, and �� ∞ is the brightness at the highest speed measured (i.e. microcarriers fully suspended. �∗ � is comprised between 0 and 1.

It is then interpolated to fit into a model of equation I∗ = +ea x−xo , where x=Fr/Frc or

N. The just-suspended speed is considered to be achieved when I*=0.05 (i.e. 95% of the particles suspended).

Two Matlab scripts were written to process the images. One for generating an array with the mean brightness of the images inside the cylinder for each speed, and the other for interpolating and calculating the suspension speed (Ns), suspension Froude (Frs), critical Froude (Frc) and the interpolating parameters.

5 Results

The ratio of Fr/Frc of all the experiments done in the Laboratory are shown below:

di=10cm

It is proved that for the same geometry, the suspension speed is lower the higher the

cone. Overall, there is an increasing trend with h/di /√do/di in the 4 plots, which

tend to converge for the greatest values of the last coefficient. For cone B, the difference respect to Flat Bottom is the most constant of the 3 cones. The biggest difference takes

places, as expected, for Cone C, in the 2 lowest values of h/di /√do/di, with a

decrease in the suspension speed of around 15% in both cases. The values of Frs/Frc for the flat bottom case agree with Ducci's experiments,18 being

around 1.2 for lower values of h/di /√do/di, and drifting upwards for the highest.

di=7cm

In this case, the increasing trend can be seen as well for the conical bottom, but the values for Flat Bottom are a little higher than expected for the lowest values of h/di /√do/di. However, there is a reduction in the suspension speed for the conical bottom,

which is what it was being expected to prove.

6 Conclusion

From the experiments it was proved that if the commonly used Flat Bottom was replaced by a conical one, the suspension speed would reduce, if the other parameters remained unvaried. Indeed, the higher the cone, the lower the suspension speed. Therefore, it is shown that the cone has a high influence in the flow, improving the lifting mechanisms of the flow on the Microcarriers. This could be expected from the findings of Rodriguez (2015),20 that concluded that the toroidal vortex reaches the conical bottom at lower speeds, and the vorticity is higher.

These results mean that suspension culture can be significantly improved. The cost of maintaining the shaking speed will be lower, as this will be lower. The culture conditions for adherent-dependent will improve as well because as the agitation speed is lower, the shear stress on the cells will be lower.

University College London, Torrington Place, LONDON WC1E 7JE

DEPARTMENT OF MECHANICAL ENGINEERING

MECH 3002 THIRD YEAR PROJECT

2015/16 Session

Student Name : Gabriel Sánchez Arranz

Title of Project : Measurement of the just-suspended speed in orbitaly shaken bioreactors with conical bottoms.

Project Supervisor : Andrea Ducci

University College London, Torrington Place, LONDON WC1E 7JE

1

DEPARTMENT OF MECHANICAL ENGINEERING

MECH 3002 PROJECT

2015/2016

DECLARATION FINAL REPORT

I, Gabriel Sánchez Arranz ,

confirm that this work submitted for assessment is my own and is

expressed in my own words. Any uses made within it of the works

of other authors in any form (ideas, equations, figures, text, tables,

programs, etc.) are properly acknowledged at the point of their use.

A full list of the references employed is included.

Signed: ...........………………………………………………

Date: ..........……………………….………………………

2

3

Abstract

The objective of this Thesis is to study how the suspension speed of Microcarriers in a

cylindrical orbitaly shaken bioreactor changes if the widely used flat bottom is replaced by a

conical one. The speed that is measured is the one at which complete homogenisation is

achieved, which will be the one to use as the operating condition in real processes.

2 sets of experiments were done: the first using a flat bottom and 3 cones, and the second

with only one cone. 3 different orbital diameters and 2 heights were evaluated for these cases.

A visual based technique has been developed to provide a systematic approach to analyse the

images taken at increasing speed, which are processed using a Matlab algorithm.

Overall, it was concluded that using a conical bottom reduces the suspension speed for the

same employed geometry, and particularly, it diminishes more the higher the cone.

4

5

Table of Contents

Nomenclature ........................................................................................................................... 7

1. Introduction ................................................................................................................. 9

1.1 Microcarriers ............................................................................................................. 9

1.2 Orbitaly Shaken Bioreactors .................................................................................... 11

1.3 Motivation. Need for knowing the suspension speed ............................................ 12

2. Recent developments in OSRs .................................................................................... 15

3. Literature Review ....................................................................................................... 17

3.1 One-phase flow characterization in flat bottom cylindrical OSRs........................... 17

3.2 Suspension speed in shaken flasks and cylinders ................................................... 23

3.3 One-phase flow in OSRs with conical Bottom ......................................................... 33

4. Objectives .................................................................................................................. 35

5. Methodology ............................................................................................................. 37

5.1 Summary of procedure ........................................................................................... 37

5.2 Geometry of the OSRs of study ............................................................................... 38

5.3 Preparing the microcarriers .................................................................................... 39

5.4 Experimental Set-up ................................................................................................ 42

5.5 Analysing images ..................................................................................................... 43

6. Experimental results................................................................................................... 47

6.1 Cylinder diameter, di=10cm .................................................................................... 47

6.2 Cylinder diameter, di=7cm ...................................................................................... 51

6.3 Discussion of results ................................................................................................ 55

7. Conclusion ................................................................................................................. 57

8. Bibliography ............................................................................................................... 59

Appendix A. Algorithm....................................................................................................... 61

Image Brightness Measure ...................................................................................................... 61

6

Interpolate to obtain Ns and Frs .............................................................................................. 64

Appendix B. Laboratory Results ......................................................................................... 69

Cylinder diameter, di=10cm .................................................................................................... 71

Cylinder diameter, di=7cm .................................................................................................... 101

Appendix C. Plans of Reactor with di=10cm ...................................................................... 125

Appendix D. Plans of Cone C for di=7cm ........................................................................... 137

7

Nomenclature

N: Shaking speed.

Ns: Suspension speed.

Nc: Critical speed.

Fr: Froude number.

Frs: Suspension Froude.

Frc: Critical Froude.

Vf: Filling volume.

mmc: Mass of Microcarriers.

cmc: Concentration of Microcarriers.

h: Filling height of fluid.

d: Diameter.

do: Orbital diameter

di: Cylinder diameter

aow: Flow scaling constant for water.

g: Gravity acceleration.

: Density.

a: Decay coefficient of interpolation.

x0: Displacement coefficient of interpolation.

8

9

1. Introduction

1.1 Microcarriers

Mi ro arriers are s all support atri es ( - 5 mm) used for containing adherent cells

(e.g. stem cells) for their growth in suspension inside bioreactors1. However, for good mixing it

is showed that the ideal size is between 100 - 3 . The spe ifi de sit related to ater is

between 1.02 -1.04, to ensure proper suspension at low speeds. They are being increasingly

employed in adherent cell applications, because they overcome many of the difficulties of 2D

cell culture.

They have a wide variety of applications, as it is shown by the more than 600 publications in

the literature concerning them. The main ones are:

a) High-yield production of cells, viruses or cell products:

Viruses and vectors: The majority of producers in Europe use microcarriers to produce

vaccines for human use.

Natural proteins: through the culture of diploid cells.

Antibodies.

b) In vitro cell studies: The large number of cells required for clinical trials (millions of cells per

kg of body weight) requires a fast expansion procedure, and microcarrier culture demonstrates

its advantages compared to 2D culture2.

c) Routine cell culture techniques: microcarriers can be employed for harvesting a large

number of cells. Cultures can often be initiated with 105 cells/mL or less and at the harvesting

stage the yield is usually more than 106 cells/mL.

1

Some of the main advantages of microcarriers are:1

They provide the required surfaces that are needed for the culture of certain cells,

which could not be grown is suspension without being attached to a surface.

Great increase in productivity The use of microcarriers in 3D suspension culture, result

in yields of up to 200 million cells per millilitre.

Reduce of labour requirements.

3D culture results in a homogenous culture system. This allows the reduction of PH

and nutrient gradients, which are a detrimental for obtaining a quality yield.

10

The process is easily scalable to different bioreactor sizes. culture. The volumes of the

bioreactor employed vary from a few millilitres to several thousand litres.

Reduction of shear and chemical stress in the case of porous microcarriers.

Save in space, due to the large surface to volume ratio. This allows a reduction in space

for storage, production and waste-handling.

Inexpensive (in terms of price/m2)

The main types of microcarriers are:1

In the first type, the cells are only found in the surface of the microcarrier, whereas in the

other two, they are contained in pores inside the microcarrier. This arrangement has the

advantage of mitigating the shear stress on the cells from the movement of the microcarrier in

the fluid, by providing an isolated environment for the growth of the cells.

In microcarrier culture, cells grow as monolayers on the surface of the microcarriers, which

have a spherical shape, or as multilayers in the pores of the macroporous ones.

11

1.2 Orbitaly Shaken Bioreactors

A bioreactor is a device used for supporting a bioprocess. In the case of study, an orbitaly

shaken bioreactor (OSR) is a cylindrical vessel in which the Microcarriers (used for supporting

cells) are submerged into a liquid with nutrients. It is very important that microcarriers are

properly suspended for a successful culture of cells, not staying at the bottom of the tank, or

being shaken too sharply that the cells get damaged. The suspension is reached by shaking the

vessel, which describes a circular trajectory with a fixed angular speed of N[rpm] and a

diameter of do[cm]. This creates vortex in the fluid that lift up the microcarriers.

They have some advantages compared to stirred tanks. It is estimated that more than 90% of

the culture experiments in biotechnology are performed in shaken bioreactors, however there

are surprisingly very few publications dealing with them, less than 2%.3

In the case of laboratory trials and industrial biotechnology applications, cells are usually

grown in shaken bioreactors because they offer a low power consumption solution to screen

several conditions in parallel.

OSR with Erlenmeyer Flasks4

Stirred tanks are traditionally used for large-scale production, once the process is optimised in

a shaken bioreactor and then scaled up. However, as the geometry and shaking mechanism

are different, the fluid velocity field distribution and the turbulence levels change too. To

overcome this problem, miniature stirred tanks for bioprocess development have been

designed, as well as large scale shaken bioreactors, up to a capacity of 1000 L.5

However, the number of publications addressing scaling aspects of shaken bioreactors is still

very limited. The optimal medium components, types of microcarriers and other culture

conditions in general have been thoroughly investigated, but the number of publications

12

relating to the engineering aspects, such the fluid dynamics and the suspension conditions are

still very limited.

Some of the advantages of OSRs are:

Simple and functional design available for screening bioprocesses. It provides a low-

cost solution for screening a large number of bioprocesses in parallel.6

Good mixing efficiency: mixing performance for liquids with water-like viscosity in

shaken reactors is better than for stirred tanks. 5

Good oxygen transfer: OSRs have a suitable oxygen transfer capacity to support

mammalian cell cultivation at high cell densities up to volumes of 2000 L. This is greatly

due to the circular movement, which generates a dynamic free-surface.7

Lower shear stress: for the same volumetric power consumption, the maximum energy

dissipation rate in shaken reactors is around ten times lower than in stirred-tank

reactors, which results in much lower shear stress on cells.8

Lack of damaging bubble bursts: stirred tanks have complications with oxygen

transfer. In bubble aerated bioreactors, changing concentrations will generally

influence the oxygen solubility. Surface aeration in shaken reactors eliminates the

uncertain complications of the action and changing behaviour of the bubbles.9

1.3 Motivation. Need for knowing the suspension speed

The shaking speed is a key factor in the growth and final yield of cells, due to its influence in

the shear forces on cells and mixing of the fluid. If the rate is low, the shear stress is low too,

but the microcarriers will settle in the bottom of the reactor, causing gradients in the pH, O2

and nutrient concentrations, which affect very negatively the cell growth10

. If the speed is too

high, the shear stress increases, leading to cells dislodging from the microcarriers, as well as

increasing the rate of microcarriers colliding against each other and the walls11

. The following

graph represents how the growth of cells change with the stirring speed in a STR. It is shown

that there is an optimum speed of 90rpm for the successful culture of cells in this case:1

13

Particle suspension is a complex mechanism, influenced by turbulent eddies, forces on

particles (gravity, buoyancy, drag) and particle-particle and wall-particle interactions.

In order to create a suitable mixing procedure for microcarrier culture, the critical agitation

rate for complete suspension (or just-suspended rate), Nc has to be quantified. It was first

defined by Zwietering in 1958 as the minimum agitation rate at which particles achieve

complete suspension.12

14

For mechanically stirred bioreactors with a central impeller rotating around a vertical axis, the

critical agitation speed Nc can be estimated with the Zwietering equation, knowing the

impeller diameter D, the ki e ati is osit L a d de sit L of the liquid, the particle

diameter dp and de sit p, mass concentration of particles X, and S, which is a constant

depending on the geometry of the vessel and the impeller:12

� = �. ν . . [g(ρ − ρL)ρL ] . . X . . d . . D− .

However, the studies of Ibrahim and Niewon (2004) show that if the particulates that are

suspended are microcarriers, the previous equation overestimates Nc up to 50%, due to the

great similarity in density of the fluid and the microcarriers.13

Collignon et al. (2010), in Axial

impeller selection for anchorage dependent animal cell culture in stirred bioreactors, provided

insight in microcarrier suspension in stirred tanks by means of PIV measurements.14

15

2. Recent developments in OSRs

As it has been stated, most of large-scale mammalian cell culture is currently performed in

stirred-tank bioreactors. However, Zhang et al. (2009 and 2010), from the results they

obtained in the studies about mixing efficiency in orbitaly shaken bioreactors, believe that

suspension cell culture using will become an attractive option at scales up to 1000 L5 (the value

up to which oxygen transfer has been proved adequate) because of better functionality and

lower costs. To test this principles they designed a prototype of a cylindrical OSR of 2000 L,

with a filling capacity of 1000 L, which is fitted with disposable cultivation bags. The results

obtained7 for the mixing of oxygen indicate that it is suitable for successful cell growth.

Furthermore, it also fulfils the criteria of mixing by agitation with low shear stress on cells,

which can damage the most sensitive ones, sufficient gas transfer capacity and facility in

scaling-up and process control. Although operating conditions in large-scale shaken

bioreactors require further research, as it has been mentioned, the data obtained proves that

this simple design of bioreactor can have useful applications in large-scale high-density

mammalian cell cultivation.8

16

Despite that single-use disposable arrangements are widely used in many processes, including

filtration and sterile liquid handling, the typical equipment for cell cultivation is non-

disposable. With stainless steel bioreactors, the material most employed, each new production

start must follow a long testing procedure after sterilization. The same applies during

changeover and cleaning of the reactor. Such demand of time decrease overall productivity. To

overcome the disadvantages present in stainless steel reactors, single-use cultivation systems

are being developed. The first of these kind of reactors developed were small-scale shaken

devices with the corresponding disposable flasks or cylinder containers. They were proved to

be reliable for cell culture applications. For large-scale production, subsequently OSRs

containing single use vessels were developed. In 1998 Wave Biotech was the first company to

commercialize a completely disposable cell cultivation system. The system is used for many

different applications at scales of up to 500 L, the main one being mammalian cell culture.

Other designs based in stirred tanks and air-lift technology quickly followed, due to the success

of disposable bioreactor culture.8

Orbitaly shaken vessels, have been the most widely used bioreactor system for over half a

century in laboratory scale applications in the case of microbial cultures. Due to the high

oxygen consumption rate of microbial hosts, the working volume of these shaken bioreactors

is limited to 10–20% of the nominal volume. However, mammalian cells have a relatively low

demand of oxygen, and in their lab Zhang et al. (2009 and 2010) successfully achieved the

culture of cells in a large-scale of 1000 L.

17

3. Literature Review

3.1 One-phase flow characterization in flat bottom cylindrical

OSRs

It is logical to assume that microcarrier suspension is linked to the physical phenomena

occurring in the liquid as a consequence of the velocity field generated through agitation15

. The

work of Weheliye et. al (2012) provided a thorough characterization of the flow characteristics

and dynamics in a cylindrical OSR, by using a phased-resolved PIV (Particle Image Velocimeter),

which allows to obtain the vorticity and velocity distribution at different conditions:

N[rpm]: shaking speed.

d0[cm]: orbital diameter.

di[cm]: cylinder diameter.

h[cm]: filling height of the liquid.

The results obtained only apply for liquids with the same viscosity as water, which are the

majority of fluids used as a culture media for the growth of mammalian and microbial cells. In

the experiments carried out for this thesis, the only employed liquid is distilled water. The fluid

dynamics of more viscous fluids were studied by Ducci et al. (2014), but it is not relevant for

these experiments.16

Apart from the work of Weheliye there are very few articles related to the flow in shaken

bioreactors, and none of them are experimental, but CFD (computational fluid dynamics)17

.

The Froude number, which is the ratio between the characteristic velocity of the fluid and the

wave propagation velocity, is defined hereinafter with the equation �� = � /�, with d

being either the orbital or the cylinder diameter.

The experiments were carried out by Weheliye for inner diameters di = 10 cm and 13 cm, and

for fluid heights, orbital diameters and shaking speeds in the ranges of h = 3–7 cm, do = 1.5–5

cm and N = 60–140 rpm respectively, which are very similar conditions to the ones in the

experiments of Ducci et. al (2015) for the study of the suspension speed in flat bottom orbital

shaken bioreactors and the ones in this thesis.18

18

3.1.1 Types of flow

For low viscosity fluids, which is the case of water, the fluid used in this study, at low speeds

(low Froude number) the flow is characterised by a toroidal vortex, whereas at high speeds it

becomes a preccesional vortex. This transition occurs when the Froude number reaches a

critical value and is associated to the suspension of the microcarriers.

3.1.1.1 In-phase flow

At low Fr the free surface has an elliptical shape in phase with the shaker table orbital

movement and it remains mainly two-dimensional. As the shaking speed is increased, two

counter rotating toroidal vortexes are generated near the surface, and progressively expand

towards the bottom of the tank. For a low shaking speed there are two different zones in the

fluid easily distinguishable: zone A, where the mixing takes place mostly by convection, and

zone B, where it does by diffusion.

19

3.1.1.2 Out-of-phase flow

At higher rotational speeds, the free surface is not longer in phase with the movement of the

table. The profile is no longer two-dimensional, but three-dimensional, and as the following

figure shows, the intersection with the vertical plane shows a wavy profile. The toroidal vortex

becomes a processional vortex, which has a vertical axis, and it is formed on the side of the

bioreactor opposite to the highest side of the free surface.

20

The following figure shows the transition between the two regimes:

21

3.1.2 Transition between flows and scaling law

The free surface motion is the flow driving mechanism of the shaken bioreactor, and its

maximum inclination �, is related to the non-dimensional wave amplitude ∆ℎ/ , according to

the equation:

tan � = ∆ℎ ∝ �� = �� = ��

The linear relationship is more consistent at lower Fr (lower shaking speeds), when the free

surface in 2D and in phase with the shaking table, whereas at higher Fr, the data obtained in

the experiments is more scattered around the interpolation line due to the wavy 3D shape

nature of the free surface characteristic for out-of-phase conditions. In this case, � is the

average inclination calculated across the free surface.

22

The constant a0 is 1.4 in the case of water, as shown in the figure. From the data obtained it

was concluded that the transition between the two regimes occurs at a critical Froude number

Frc, which can be predicted following the next equations:

For ℎ/ √ / �� 0 = �0� ℎ� 0� .

For ℎ/ √ / �� � = �0�

In the first case, the transition occurs after the toroidal vortex reaches the bottom of the

vessel, whereas in the second, the transition takes place without the toroidal vortex reaching

the reactors bottom.

23

3.2 Suspension speed in shaken flasks and cylinders

3.2.1 Work of Olmos et. al. (2014)

The suspension speed is studied in shaking bioreactors, both in Erlenmeyer flasks and in

cylindrical geometries (with flat bottom).19

They carried out 220 experiments representative of

animal cell culture conditions, varying the bioreactor size and geometry, microcarrier type (i.e.

density and diameter), liquid viscosity, orbital diameter and filling height. A dimensional

analysis was performed to obtain a correlation between the suspension speed Nc and other 4

non-dimensional variables. The resulting equation after this analysis and the data obtained in

the laboratory is:

��√�/ = √ ��� = �. ( )− . . (ℎ�) . . ∗ . . − .

Where g is the gravity acceleration, d is the characteristic diameter (cylinder diameter di in

that case), A is a constant which is 0.12 for Erlenmeyer flasks and 1.39 for cylindrical flasks, do

the orbital diameter, hL the filling height, ∗ = / � is the relative density between

microcarriers and fluid, and the diameter of the microcarriers.

It has a relative error of 5.7% for Erlenmeyer flasks and 10.2% for cylinders, so it is not enough

to establish the operating speed of a bioreactor, and more measurements are required.

From a fluid mechanics point of view, it is logical to assume that in the case of cylindrical

vessels, microcarrier suspension should take place at the transition between the two regimes

described by Weheliye (2012), i.e. when the two counter-rotating vortices reach the bioreactor

bottom. The experimental suspension speeds are compared to the transition shaking speed in

the following graph, and it shows that this is the case:

24

Also, direct comparison of the equation obtained by Olmos with the first equation of Weheliye

shows that the critical Froude number, Frc, associated to the flow transition is related to the

just-suspended Froude number, Frs, obtained with the non-dimensional analysis, because the

fluid height-cylinder diameter ratio, h/di and orbital to cylinder diameter ratio, do/di, terms

have the same exponents.

The technique used is similar to the one in this thesis regarding that the microcarriers where

dyed with Trypan-blue to assess the suspension, and measures of the vertical plane were

taken. However, the suspension speed was determined by observation, and an algorithm was

not developed, so it does not establish a methodology to employ in further studies.

25

3.2.2 Work of Ducci et. al. (2015)

This research was the first to analyse the two-phase flow dynamics occurring in a cylindrical

shaken bioreactor when microcarriers are employed in suspension under real process

conditions.18

In this study the just-suspended speed was calculated through measures of the light scattered

by the microcarriers that remain at the bottom of the vessel, for an increasing shaking-speed,

when a laser is directed to the bottom plane of the cylinder. Furthermore, the homogeneity of

the mix of the microcarriers in the fluid was assessed taking vertical plane measures, similar to

the ones in this study, and a Particle Image Velocimetry was used to study the flow and mixing

dynamics in the presence of microcarriers (Two-phase flow), and to assess how their

concentration affects the mean flow characteristics.

3.2.2.1 Suspension Speed

The set up for measuring the suspension speed is the next:

It can't be used in this research because the bottom is conical, not flat, so the microcarriers

settle following a conical pattern, and therefore vertical measures will be used instead. The

images taken in both cases are at a fixed angle (phase-locked).

The just-suspended speed is obtained from the brightness of the images taken on the

horizontal measurement plane, which is directly proportional to the amount of microcarriers

settled at the bottom of the cylinder. The image brightness, IB(N), for a shaking speed, N, is

calculated by adding the pixel greyscale, pij , across the area delimited by the bioreactor walls:

26

�� = ∑ �����

where Ntot is the total number of pixels in the area.

To analyse the data, instead, the normalised brightness index is used:

�∗ � = �� � − �� ∞�� − �� ∞

where �� is the brightness at zero-speed, and �� ∞ is the brightness at the highest speed

at which measured (i.e. particulates fully suspended). �∗ � values will therefore be comprised

between 0 and 1.

It is then fitted into a curve of the form:

I∗ = + ea x−x

where x can be either Fr/Frc or N.

The just-suspended speed is considered to be attained when 95% of the particles are

suspended, i.e. when the plot crosses the 0.05 line.

The reactor diameter for all the experiments was di=7cm, and the microcarriers employed

were Cytodex-3, the same as in the experiments in this research. The results for the

interpolated sets of data taken are shown in the following table:

The coefficients a and x0 can be used for determining Ns and Frs: Frs/Frc = log(19)/a + x0 for 95%

suspension. It can be noted that in most cases the decay coefficient, a, when ℎ/ √ /

(7 < a < 14.3) is lower than when ℎ/ √ / (14 < a < 17.8). This means that for the

second situation suspension occurs more sharply with increasing speed.

27

From the following image, it can be observed that suspension starts taking place when the

particles at the bottom arrange in a spiral pattern and a drop in the images' brightness occurs.

The concentration of microcarriers doesn't affect to a large extent the suspension speed, at

least within the range of concentrations considered in this experiments, which include those

commonly employed in the bioprocess industry, as it is shown in these graphs:

28

In the first case, Ns increases with the concentration, whereas in the second, it decreases. The

possible variation with the concentration is within the range of error, which is set to 2RPM,

and will not be taken into consideration.

On the contrary, h and do have a great influence, with N decreasing with h and increasing with

do:

29

The measurements of the just-suspended speed and Frs/Frc differ when the transition between

the main 2 flow regimes takes place when the vortex reaches the bottom (i.e. ℎ/√ / ), and when it does not (i.e. ℎ/ /√ / . In the following graph, it is shown that

for the first case, the 95% suspension takes place for Frs/Frc . , which proves that the

suspension of the particles is directly associated to the flow transition, whereas for the second

case the values drift away to higher ratios:

30

3.2.2.2 Homogeneity

The dispersion of the microcarriers across the vertical plane was measured using a similar

technique, taking measures of the brightness across the vertical plane, instead of the

horizontal. The normalised brightness index used in this case changes:

�∗ � = �� � − ���� ∞ − ��

The 95% dispersion is attained for the first case at Fr~ . Frc for the first case, slightly larger

than for suspension, as it is shown in the next graph:

The operating condition for shaken bioreactors has to be this, as microcarriers not only need

to be lifted, but also properly mixed. In these experiments, as the measures are taken in the

vertical plane, instead of at a the horizontal at the bottom, this will be the N and Fr measured.

3.2.2.3 Two-phase flow dynamics

The constant a0 depends on the fluid used, and its value is 1.4 for water, and lower for fluids

with higher viscosity. In the following graph, ∆ℎ/ is plotted against Fr, for different

concentrations. The points are close to the reference line for single-phase flow (slope 1.4),

which means that the microcarriers do not have a significant influence in the fluid dynamics of

31

the liquid (the free surface is the flow driving mechanism). However, the points corresponding

to higher concentrations are the ones with the lowest ∆ℎ/ , which corresponds to the

behaviour of higher viscosity fluids.14

PIV phase-resolved measures were used to assess the velocity and vorticity fields of the two-

phase flow:

32

The mean flows of the liquid and the particles are found to be qualitatively very similar, both

for in-phase (a,b) and out-of-phase conditions (c,d). Quantitatively they are slightly different.

In the in-phase cases, the vorticity of the toroidal region is higher for the particles, and in the

out-of-phase condition, the velocity of the particles is higher than the fluid. The axial speed

velocity was calculated for this case: |��� − ���| < . � , which is equivalent to (0-6mm/s) for the case in the figure. It is

worth noticing that this measure is comparable in magnitude to the average and maximum

velocities of the liquid phase over the plane of measurement, 0.033 and 0.10 Ndo,

respectively.

33

3.3 One-phase flow in OSRs with conical Bottom

G. Rodriguez et. al. studied the flow dynamics inside an OSR when the flat bottom is replaced

by a conical one, by means of PIV measurements20

. The 3 cases that were considered are:

Note: These two cones are also used in the experiments for this research.

The volume is the same for the 3 cases, corresponding to Vf=393ml, and h is calculated from

that.

The PIV measurements show that the flow is qualitatively similar to the one present in flat

bottom reactors, described by Weheliye (2012), with two toroidal vortices expanding towards

the bottom as N is increased. It was found that the speed at which the toroidal vortex reaches

the bottom is lower the bigger the cone is. However, the Froude value, Frc, at which the

transition to preccesional vortex occurs does not change. This could happen because the cone

influences the toroidal vortices, pushing them against the cylinder walls, and away from each

other, making difficult the interaction at the centre.

The space-averaged shear rate is similar for all geometries at the same Fr, although it is slightly

higher in the highest cone. The vorticity levels are higher in the conical configurations,

especially in cone B.

From the next images it can be extracted that the vortex reaches the bottom at N=115rpm for

flat bottom, N=110rpm for cone A, and N=100rpm for cone B.

34

Therefore, the conical configurations allow the fluid to have similar flow dynamics conditions

at lower shaking speeds N than the flat bottom one As the vorticity is higher, the suspension

will be better because the lifting forces are higher, and they prevent the accumulation of the

particles in the centre of the cylinder. It is therefore expected that the suspension speed for

particles will be lower, resulting in lower shear rates, which is very beneficial for adherent

dependent cells.

35

4. Objectives

The main findings from the Literature Review are:

There is a scaling law for cylindrical OSRs with flat bottom that establishes the Frc at which

the flow changes from a toroidal vortex to a preccesional one. There are two equations for

this, one for each case, depending on the geometry.15

The suspension of microcarriers is directly associated to this transition. When ℎ/√ / , the suspension occurs at ��� . �� , and the homgenisation of the mix at ��~ . �� , and when ℎ/ √ / the values are higher.18

The concentration of microcarriers does not have a significant influence in the suspension

speed.18

The one-phase flow in conical bottom OSRs is qualitatively very similar. However, for the

same filling volume the vortex reaches the bottom at lower speeds the higher the cone is,

and the vorticity is higher. Despite this, the transition between the two main flow regimes

takes place at the same Fr.20

It is therefore expected that the suspension of microcarriers will be attained at lower shaking

speeds, N.

The main objective of this Thesis is to study how the suspension speed changes if the flat

bottom of an OSRs is replaced by a conical one. The speed that will be measured is the one at

which complete homogenisation is achieved, which will be the one to use as the operating

condition in real processes.

In order to carry out this research, Ns will be measured for 36 different operating conditions,

representative of cell culture, which are:

For di=10cm:

o h=4.5-7cm (Constant height).

o do=1.5-2.5-5cm.

o Flat Bottom, Cone A, Cone B and Cone C.

For di=7cm:

o h=3-5cm (For flat bottom, Constant volume)

o do=1.5-2.5-5cm.

36

o Flat Bottom and Cone C.

In all the experiments, the microcarrier type used is Cytodex-3, with a concentration of 1.5g/L.

For di=10cm, the heights of the cones are respectively 0.5-1-1.5cm, and for di=7cm, Cone C is

scaled respect to the cylinder diameter, to 1.05cm. In the first case, the filling height is kept

constant, and in the second, the filling volume is constant, and the filling height for Cone C has

to be modified so that the fluid volume is the same as in the flat bottom case.

37

5. Methodology

5.1 Summary of procedure

The steps followed in this research can be summarised in:

Outline of technique: because the flat bottom is replaced by conical bottoms, the

technique used in Ducci's research, a laser going through the bottom horizontal plane of

the cylinder, cannot be used. Instead, a similar approach to Olmos' experiments19

was

employed. The microcarriers were dyed with Trypan-Blue for 12 hours, and the camera

was placed attached onto the shaker table, on which the cylinder is placed, taking a picture

of the vertical plane of the vessel every revolution at a fixed angle. The parameter used to

assess the suspension is the brightness of the fluid, which is interpolated with the shaking

speed, N, and the Froude number, Fr, corresponding to each different geometry.

Suspension is considered to be achieved when the curve crosses the 5% reference line.

Preliminary experiments: in order to test the technique proposed, 3 experiments with flat

bottom were carried out, in which the geometries were h=3-4-6cm,do=2cm,di=7,c=1.5g/L.

The microcarrier type used was Cytodex-1. The technique for capturing the images,

obtaining the brightness, and the interpolated function to yield the suspension speed and

Froude, Ns and Frs was proved successful, as the suspended speed obtained from the

algorithm corresponded to the one observed. However, the values of Frs diverged

significantly from the ones in Ducci's research, because the microcarriers agglomerated,

sticking to each other, which is likely to be due to that this type of microcarriers, Cytodex-1

are charged, to facilitate that the cells attach to them, so the speed required to lift them

increases. The type of microcarriers selected for the experiments in this Thesis was then

Cytodex-3, in which this does not happen.

Development of Algorithm: two code scripts were developed in Matlab to process the

images, which can be found in Appendix A. The first one, from a folder containing the

folders named after the suspension speed in RPM, in which the images are stored,

generated an array with the mean Normalised Brightness for each speed. The second one

interpolates it with N and Fr, and obtains Ns and Frs. It also calculates the parameters of

the interpolated function, a and x0, the critical Froude, Frc, and the standard deviation of

the interpolated functions respect to the experimental data.

38

First set of experiments: All the cases corresponding to di=10cm. The results of Suspension

Speed and Froude can be found in the Results section. Appendix B contains the graphs of

all experiments for N and Frs, as well as the interpolating parameters.

Manufacturing of Cone C for di=7cm: this type of cone was not among the available ones in

the laboratory, so it had to be manufactured. The plan was developed using CAD Software,

and the cone was built in one of UCL's workshops. The plan can be found in Appendix D.

Second set of experiments: All the cases corresponding to di=7cm.

5.2 Geometry of the OSRs of study

The figure below represents a front view of the reactor of study, when a conical bottom of

height hcone is placed. h is the filling height and do and di the orbital and cylinder diameters

respectively.

39

5.3 Preparing the microcarriers

5.3.1 Microcarrier caracteristics

The type of microcarriers employed is Cytodex-3 for all experiments, with a fixed

concentration of c=1.5g/L. The main characteristics of this type are summarised in the

following table:21

Cytodex microcarriers have been designed for the culture of a great variety of animal cells.

They can be used in a wide range of volumes, from a few millilitres to more than 6000 litres. In

3D suspension culture, the yields obtained are of the order of a million cells per millilitre.

They have a great variety of applications, including the production of large quantities of cells,

viruses and cell products (e.g. enzymes, nucleic acids, hormones). They can be employed as

well for microscopy studies, membrane studies, and for harvesting mitotic cells. They facilitate

the isolation, storage and transport of cells.

Because they are mostly used for suspension culture, the size and density are optimized to

achieve a good growth and a high final yield for the variety of cells for which can be used. The

matrix is biologically inert, and strong, necessary for shaking cultures, but not rigid, which

would be detrimental. The microcarriers are transparent, which allows for easy microscopic

examinations of the attached cells.

40

The matrix is made of cross-linked dextran, which is covalently bonded to a surface layer of

denaturated collagen, in contrast with other microcarrier surfaces, like the one in Cytodex-1

which are charged to provide cell adhesion.

5.3.2 Mass calculation

The mass of microcarriers to be used in each experiment varies with h and di, and can be

calculated with the equation:

�� = � . �� = � . ℎ . . ( )

The mass needed for each set of experiments is then:

di=10cm

o h=4.5cm: mmc=0.5301g

o h=7.0cm: mmc=0.8247g

di=7cm

o h=3.0cm: mmc=0.1732g

o h=5.0cm: mmc=0.2886g

5.3.3 Filling height for di=7cm and Cone C

The filling volumes have to be the same as in the flat bottom cases in this set of experiments,

and it can be calculated with the equation:

�� = ℎ . . ( )

For flat bottom, when h=3cm, Vf=115.45ml, and when h=5cm, Vf=192.42ml. Knowing that the

volume of the cone is �� = . ℎ . . � , then the fluid heights need to be h=3.35cm and

h=5.35cm respectively for the conical bottom cases.

5.3.4 Filtering

The visual-based technique for analysing the experiments relies on the microcarriers being

easily distinguished from the fluid (distilled water). That is why they were coloured with

Trypan-Blue solution, which is a vital stain (can colour cells without killing them) derived from

Toluene. It is commonly used for cell-counting and assessment of tissue viability.

41

In order to colour the microcarriers, the given mass needed for a experiment is mixed with

10ml of Trypan-Blue22

, and left for 12 hours. After that it is filtered. The filter employed in this

experiments as Fisher ra d™ Cell Strainers, of 40µm of filtering diameter23

, which is lower

than the minimum diameter of Cytodex-3, but of the same order of magnitude, so the filter

does not get blocked.

It is worth mentioning that the liquid resulting from the filtering was completely clear, which

means that the microcarriers absorbed all of the dyeing pigment.

42

Picture of the set-up in the Laboratory.

5.4 Experimental Set-up

The shaker table used is Lab LS-X Kühner,24

which can rotate at up to 300rpm at 5.0cm of

orbital diameter. The speed is regulated in intervals of 1rpm, with an accuracy of ±0.1rpm.

The bioreactor is mounted rigidly on the table. The plans for the one with a cylinder diameter

of 10cm can be found in Appendix C, which contains the plans of the 3 cones as well. The cone

used for di=7cm is scaled from the biggest cone in the first case, to have the same angle, and

its plan can be found in Appendix D.

The cylinder is contained in a square acrylic, and the gap between them is filled with distilled

water. This is done to minimise refraction at the cylinder curved wall.

The camera used is a Net I-Cube, and it was equipped with a macro lens with a shallow depth-

of-field, that allows to capture any small variation of the image brightness. It is placed also

fixed to the shaker table, pointing at the reactor. A white illuminated background is located at

the back of the reactor.

The camera and the computer are connected to an encoder, which generates a signal every

time the shaking table completes a revolution. The camera captures an image every time the

angle of rotation (phase) is 180º. This is known as a phase-locked approach.

The number of images taken at every speed is approximately 10-20. Every time the speed is

increased, it is needed around 1 minute to reach stationary fluid condition. When a new

experiment with the same conditions but different orbital diameter is to be started, the

waiting time for the microcarriers to settle at the bottom of the reactor is around 5 minutes.

43

5.5 Analysing images

The variable used to determine if the microcarriers are suspended or not is the brightness of

the image within the cylinder. Because the microcarriers are coloured in dark blue and a white

illuminated background is placed behind the reactor, the brightness will be the highest when

the microcarriers are settled at the bottom, whereas when the particles start lifting it will

decrease. The normalised Brightness Index will be used:

�∗ � = �� � − �� ∞�� − �� ∞

where �� is the mean brightness at the lowest measured speed, and �� ∞ is the

brightness at the highest speed measured (i.e. microcarriers fully suspended). �∗ � is

comprised between 0 and 1.

The values of the brightness I* together with the images to which they correspond, for one of

the cases analysed in this study (di=10cm, h=4.5cm, do=2.5cm, Cone B) , are showed below:

N=80rpm. The particles are still fully settled. It can be seen that the free surface is flat, so

the flow is in-phase.

44

I*(80)=1

N=105rpm. The particles have started to lift in a spiral pattern at the centre of the vessel.

The brightness intensity of the pixels in this part of the image is lower, so the mean

brightness of the images at this speed decrease.

I*(105)=0.8664

N=108rpm. More particles start lifting into the spiral at the centre, as well as from other

parts of the bottom. The brightness of the images decreases also because some particles

are scattered all over the fluid.

I*(108)=0.6197

45

N=110rpm. Full suspension is about to be achieved. The spiral has grown and many

particles are dispersed and suspended around the liquid.

I*(110)=0.1629

N=114. Full suspension and homogenisation has been achieved. The fluid is completely

dark blue. The surface is not seen from the camera as a straight line anymore because the

fluid has transitioned from in-phase to out-of-phase.

I*(114)=0.0015

I* is interpolated into a curve of the form:

I∗ = + ea x−x

where x can be either Fr/Frc or N, a is the decay coefficient, which is higher when the

steepness of the curve is higher (i.e. the suspension is achieved more sharply), and x0

measures the displacement across the x-axis.

46

When I*=0.05 (i.e. the interpolated curve crosses the 5% reference line), it will be considered

that the particles have achieved the suspension speed and are homogenised. The Froude for

just-suspended speed can be calculated with the equation: ���/�� = �og 9 /� + � (for 95% suspension)

Two Matlab code scripts, which can be found in Appendix A, are used for obtaining the mean

normalised brightness of the images at different speeds. The first one generates a vector with

I* for each speed N. The second one interpolates I* with N and Fr, and obtains Ns and Frs. It

also returns the values of the parameters of the interpolated function, a and x0, the critical

Froude, Frc, and the standard deviation of the interpolated functions respect to the

experimental data.

It is worth noting that in some of the cases analysed, one or two points were not considered

for interpolating, because in the first analysis they displaced the interpolated function to the

right, making the calculated suspended speed, which corresponds to point of the interpolated

curve that crosses the reference line of 5%, higher than the speed for some observed values

that were very close to it. This points are still plotted in the resulting graph, but in red colour.

47

6. Experimental results

6.1 Cylinder diameter, di=10cm

6.1.1 Suspension Speed

The tables below show the just suspended (95% of particles suspended) Ns for all the cases

done for a cylinder diameter di=10cm, in which Cytodex-3 microcarriers are used. The

precision of the obtained speeds is ±0.1rpm, which is the precision of the shaker table. The

heights of cones (hc) A, B and C are 0.5, 1.0 and 1.5cm respectively.

h=4.5cm

Ns[rpm] Flat Bottom Cone A Cone B Cone C

do=1.5cm 126.7 124.5 122.3 116.3

do=2.5cm 118.4 111.7 111.4 100.6

do=5.0cm 98.3 98.4 95.2 84.0

h=7.0cm

Ns[rpm] Flat Bottom Cone A Cone B Cone C

do=1.5cm 128.2 127.9 126.4 124.1

do=2.5cm 127.9 124.2 122.2 121.7

do=5.0cm 102.1 103.2 102.1 101.0

6.1.2 Suspension Froude number

The ratio between the suspension Froude number, Frs, and the critical Froude, Frc is shown

below. The last one is calculated using the equations from Weheliye, depending if /� /√��/� is higher or lower than 1.

h=4.5cm

Frs/Frc Flat Bottom Cone A Cone B Cone C /� /√��/�

do=1.5cm 1.2561 1.2120 1.1701 1.0580 1.1619

do=2.5cm 1.2197 1.0840 1.0786 0.8807 0.9000

do=5.0cm 1.1893 1.1904 1.1137 0.8680 0.6364

h=7.0cm

48

Frs/Frc Flat Bottom Cone A Cone B Cone C /� /√��/�

do=1.5cm 1.2855 1.2797 1.2510 1.2043 1.8074

do=2.5cm 1.2809 1.2065 1.1681 1.1591 1.4000

do=5.0cm 0.8239 0.8426 0.8233 0.8067 0.9899

49

6.1.3 Graphs

Ns[rpm] for h=4.5cm

Ns[rpm] for h=7.0cm

50

Combined graph for all cases with di=10cm

51

6.2 Cylinder diameter, di=7cm

6.2.1 Suspension Speed

The following tables show Ns for all the cases studied for a cylinder diameter di=7cm. Cytodex-

3 microcarriers are also used in these experiments. The precision of the obtained speeds is

±0.1rpm as well. The filling volume is the same for flat bottom and conical bottom, and it is

calculated bellow.

h=3cm h=3.35cm

Ns[rpm] Flat Bottom Cone C

do=1.5cm 140.8 132.2

do=2.5cm 128.4 118.7

do=5.0cm 110.0 98.3

h=5cm h=5.35cm

Ns[rpm] Flat Bottom Cone C

do=1.5cm 153.3 150.2

do=2.5cm 141.6 138.8

do=5.0cm 119.8 115.7

6.2.2 Suspension Froude number

The ratio between the suspension Froude number, Frs, and the critical Froude, Frc is shown

below. The last one is calculated using the equations from Weheliye, depending if /� /√��/� is higher or lower than 1, where h is the filling height, which is different for the same

filling volume when the flat bottom is replaced by a conical one. This makes that the

coefficient is lower than 1 in the case of h=3cm, and higher when h=3.35cm for the same

orbital diameter do=1.5cm.

h=3cm h=3.35cm

Frs/Frc Flat Bottom /� /√��/� Cone C /� /√��/�

do=1.5cm 1.1729 0.9258 0.9575 1.0338

do=2.5cm 1.2592 0.7171 0.9638 0.8008

do=5.0cm 1.3069 0.5071 0.9346 0.5663

52

h=5cm h=5.35cm

Frs/Frc Flat Bottom /� /√��/� Cone C /� /√��/�

do=1.5cm 1.2866 1.5430 1.2351 1.6510

do=2.5cm 1.0979 1.1952 1.0553 1.2789

do=5.0cm 0.9297 0.8452 0.8683 0.9043

53

6.2.3 Graphs

Ns[rpm] for Vf=115.45ml.

h=3cm (flat bottom), h=3.35cm(Cone C)

Ns[rpm] for Vf=192.42ml.

h=5cm (flat bottom), h=5.35cm(Cone C)

54

Combined graph for all cases with di=7cm

55

6.3 Discussion of results

From the results obtained in the first set of laboratory experiments, shown in the first 3 graphs

of this section, it can be concluded that for the same geometry (i.e. same orbital and cylinder

diameter, and fluid height), the suspension speed (Ns) is lower the higher the cone. In

particular, the highest difference in Ns and in the ratio of suspension Froude (Frs) and critical

Froude (Frc), calculated as in the flat bottom case with Weheliye equations, takes place in the

highest cone of the 3, cone C, which has a height of hc=1.5cm for di=10cm.

For cone B, the difference in Frs/Frc, plotted versus the coefficient h/di /√d /di, respect to

the flat bottom case is the most constant of the 3 cases, only decreasing for the highest value

of the coefficient, in which the 4 plots, for the 4 different bottoms, converge. For Cone A, the

difference increases with h/di /√d /di, but then decreases.

The biggest difference of all cases in this set of experiments can be observed at the two lowest

values of h/di /√d /di, where the difference in suspension speed is quite notable. These

corresponds to h=4.5cm and do=2.5cm and 5cm. In the first case there is a decrease in Ns of

15.0%, and in the second of 14.6%.

The measurements for the flat bottom cases agree with Ducci's experiments.18

When h/di /√d /di < Frs/Frc is around 1.2, and when h/di /√d /di > it drifts upwards, up

to 1.29. Overall, there is an increasing trend for the 4 bottoms with respect to this coefficient.

In the second set of experiments (di=7cm), the only conical bottom studied was cone C,

because it gave the greatest difference in Ns. The filling height (h) was scaled respect to di to

provide similar values of the coefficient h/di /√d /di . The values of Frs/Frc in the flat

bottom case differ from expected, being 1.3 for the lowest value of the coefficient, and 1.1 for

one value in which h/di /√d /di > . Despite this, Ns and Frs/Frc are lower for all the cases

studied, which is what was expected, and the plot for cone C is increasing, as in the first set. It

can be noted as well that the values of Frs/Frc increase from around 0.9 to 1.2 with h/di /√d /di as in the first set, so it can be concluded that using the variables Frs/Frc and h/di /√d /di to normalise for bioreactors with different sizes and geometries is a good

method.

56

It is also worth mentioning that there is an outlier in both sets of experiments, for the third

lowest value of h/di /√d /di, the one closest to 1. Frs/Frc is very similar in the 4 cases for

the first set and the 2 for the second one, and all differ a lot downwards from the main trend.

The experiments were done twice in these cases, but the results were the same. In the images

taken it could be seen that the suspension took place without the fluid going out of phase (the

surface could be seen as a straight line), unlike in all the other cases.

The interpolation of the data is very precise, with the highest value of the standard deviation

being 0.074 of all cases, in which in the majority this value is not higher than 0.02. Special care

was taken to eliminate the points that modified the interpolating curve, moving it sideways to

the right and giving a suspension speed that did not correspond to the one observed. Because

of this, the precision of the values of N[rpm] can be assumed to be the precision of the shaker

table: ±0.1rpm.

57

7. Conclusion

In this research, 2 sets of experiments for different fluid heights, orbital and cylindrical

diameters and different bottoms were done in the laboratory. In total, there were 36, with 24

in the first set and 12 in the second. Images were taken using a camera that for each speed

captured images at a determined angle (phase-locked), and then they were processed using

two Matlab scripts.

The main objective was to prove that replacing the commonly used flat bottom in orbitaly

shaken reactors for a conical one would reduce the agitation speed needed for the suspension

of Microcarriers. From the laboratory results it was proved that this hypothesis was right, and

the higher the cone, the lower the suspension, considering that the other geometrical

parameters remain unvaried. Therefore, it is shown that the cone has a high influence in the

flow, improving the lifting mechanisms of the flow on the Microcarriers. This could be

expected from the findings of Rodriguez et. al (2015)20

, that concluded that the toroidal vortex

reaches the conical bottom at lower speeds, and the vorticity is higher.

These results mean that suspension culture can be significantly improved. The cost of

maintaining the shaking speed will be lower, as this will be lower. The culture conditions for

adherent-dependent will improve as well because as the agitation speed is lower, the shear

stress on the cells will be lower.

Further research would include doing more experiments for different geometries, and for

more types of microcarriers. Cytodex-3 is one of the most used, and its density is quite

representative, but other sizes and densities should be evaluated as well to see how the

suspension speed changes.

In order to find the reasons for the improvement of the suspension in conical bottoms, a

complete fluid appraisal like the one in Weheliye (2013)15

should be done, as well as deriving a

scaling law. Rodriguez's experiments provided some insight, but a further research is needed.

The algorithm used for processing the images could be improved too. From the graphs

obtained, it shows that it detects the changes in brightness related to the suspension of the

Microcarriers appropriately, and the calculated suspension speed corresponds accurately to

the one observed. However, the brightness is measured in the whole cylinder, not only in fluid,

and this might create some errors in the graph. A surface detection algorithm would solve this

58

problem. It should detect the free surface and the borders of the cylinder and calculate the

brightness in just this region of the images.

59

8. Bibliography

1. GE Healthcare. Microcarrier Cell Culture. Principles and Methods (2013).

http://www.gelifesciences.com/file_source/GELS/Service%20and%20Support/Documents

%20and%20Downloads/Handbooks/pdfs/Microcarrier%20Cell%20Culture.pdf

2. Storm, M.P et al (2010). Three-dimensional culture systems for the expansion of

pluripotent embryonic stem cells.

3. J. Büchs (2001). Introduction to advantages and problems of shaken cultures.

4. Bioprocess Online. http://www.bioprocessonline.com/doc/sfr-shake-flask-reader-oxygen-

and-ph-0001 [24-02-2016]

5. Zhang et. Al. (2009). Efficient oxygen transfer by surface aeration in shaken cylindrical

containers for mammalian cell cultivation at volumetric scales up to 1000 L.

6. Ferrari et al. (2012). Limiting cell aggregation during mesenchymal stem cell expansion on

microcarriers.

7. J.Büchs et al (2012). Advances in Shaking Technologies.

8. Zhang et. Al. (2010). Use of Orbital Shaken Disposable Bioreactors for Mammalian Cell

Cultures from the Millilitre-Scale to the 1,000-Liter Scale.

9. A.W. Niewon (2006).Cytotechnology. Reactor engineering in large scale animal cell culture.

10. A.R. Lara (2006). Living with heterogeneities in bioreactors: understanding the effects of

environmental gradients on cells. Molecular biotechnology.

11. R. Cherry et al. (1988). Physical mechanisms of cell damage in microcarrier cell culture

bioreactors. Biotechnology and Bioengineering.

12. Zwietering (1958). Suspending of solid particles in liquid by agitators. Chemical Engineering

Science.

13. S. Ibrahim, A. Niewon (2004). Suspension of microcarriers for cell culture with axial flow

impellers.

14. Collingnon et al. (2010) Axial impeller selection for anchorage dependent animal cell

culture in stirred bioreactors. Methodology based on impeller comparison at just-

suspended speed of rotation. Chemical Engineering Science.

60

15. Weheliye et. Al. (2012). On the Fluid Dynamics of Shaken Bioreactors. Flow

Characterization and Transition.

16. Ducci and Weheliye (2014). Orbitally Shaken Bioreactors. Viscosity Effects on Flow

Characteristics.

17. Zhang et al. (2005). Computational fluid-dynamics (CFD) analysis of mixing and gas-liquid

mass transfer in shake flasks. Biotechnology and applied biochemistry.

18. A. Ducci et al. (2015). Microcarriers' suspension and flow dynamics in orbitally shaken

bioreactors.

19. E. Olmos et al. Critical agitation for microcarrier suspension in orbital shaken bioreactors:

experimental study and dimensional analysis. Chemical Engineering Science.

20. G. Rodriguez et. al. (2015). Appraisal of fluid flow in a shaken bioreactor with conical

bottom at different operating conditions.

21. Cytodex-3 product details. GE Healthcare (2013).

http://www.gelifesciences.com/webapp/wcs/stores/servlet/ProductDisplay?categoryId=1

1694&catalogId=10101&productId=21214&storeId=12751&langId=-1

22. Trypan Blue Characteristics. Thermofisher.

https://www.thermofisher.com/order/catalog/product/15250061

23. Fisher ra d™ Cell Strainers. Fisher Cientific.

https://www.fishersci.com/shop/products/fisherbrand-cell-strainers-4/p-3599344

24. Lab LS-X Kühner. Product detalis.

http://www.kuhner.com/en/downloads.html?file=tl_files/kuhner/product/shaker/LS-

X/Flyer%20LS-X%20(en).pdf

61

Appendix A. Algorithm

Image Brightness Measure

%It obtains an array with the Normalised Brightness Index (I*)

for each speed at which images are taken.

%The current folder has to be the one in which there are several

folders, whose names need to be the value of the speed at which

measured in rpm, containing the corresponding images for those

speeds.

List_of_speeds = dir; %Generates a list of the folders contained

in the main folder.

number_of_speeds = numel(List_of_speeds)-2; %Number of speeds at

which images are taken.

for k = 1:number_of_speeds

speed_k = List_of_speeds(k+2);

speed_name_k = speed_k.name;

speeds(k) = str2num(speed_name_k);

end

speeds=sort(speeds); %A vector with the values of the speeds at

which images are taken is obtained.

mean_brightness=[]; %Vector with the mean Brightness Index for

each speed.

brightness=[]; %Matrix where in each row, the brightness of each

of the images for a speed is stored.

for k=1:number_of_speeds

cd(num2str(speeds(k))); %Jumps to a subfolder for a

determined speed.

List_of_images = dir('*.jpg'); %List of the images found in the folder for a speed.

Number_of_images = numel(List_of_images); %Number of

images in the folder being analysed.

62

for j = 1:Number_of_images %Measures the brightness of the

images of a folder.

img_j = List_of_images(j);

img_name = img_j.name;

img = imread(img_name); %current image

being analysed.

%Points that delimit the area of the image in which

the brightness is measured. They need to be changed

if the camera is placed at a different distance for

different experiments. In this case, it is the set

used for h=7cm and di=10cm.

A=[266,708]; %Bottom-left corner of the cylinder.

B=[1023,708]; %Bottom-right corner.

C=[A(1),1]; %Top-left corner.

D=[B(1),C(2)]; %Top-right corner.

[rows columns colours] = size(img); %Obtains the size

of the image.

img=im2double(img); %Converts the image to double

format.

img=rgb2gray(img); %Turns it to gray scale.

n=0; Counts number of pixels analysed.

b=0; Adds up the brightness of the pixels.

for x=A(1):B(1)

for y=C(2):A(2)

b=b+img(y,x);

end

n=n+1;

end

mean_brightness_image=b/n; %Brightness of the

image analysed.

63

brightness(k,j) = mean_brightness_image; %Places

it into the matrix of brightness.

end

mean_brightness(k)=mean(brightness(k,:)); Calculates the

Mean Brightness for a determined speed.

cd ..; %returns to the main folder.

end

mean_brightness_zero=mean_brightness(1); %sets I(0) to the value

of the brightness at the lowest speed.

mean_brightness_infinite=mean_brightness(number_of_speeds);

%sets I(∞) to the value of the brightness at the highest speed.

normalised_brightness=(mean_brightness-

mean_brightness_infinite)./(mean_brightness_zero-

mean_brightness_infinite);

%Calculates the Normalised Brightness Index for each speed.

figure;

hold all;

scatter(speeds,normalised_brightness);

grid;

xlabel('N(rpm)');

ylabel('I*');

%Plots I* vs N(rpm)

64

Interpolate to obtain Ns and Frs

%Interpolate to fit data into a function of the form

I*=1/(1+e^(a(x-xo)),where x can be either Fr/Frc or N(rpm)

%Define the geometrical parameters. They are divided by 100 to

convert to meters. Different for each case assessed.

h=4.5/100; %Filling height.

di=10/100; %Cylinder diameter.

do=5/100; %Orbital diameter.

%Define fluid proportionality factor(water in all the cases in

this thesis)

awo=1.4;

%Obtains interpolated graph for speeds first.

x=speeds;

y=normalised_brightness;

%Close values (for starting interpolating)

% a_speed=1

% xo_speed=80-120

beta0=[1;80]; %initial values of the parameters to iterate.

modelfun=@(b,x)(1./(1+exp(b(1)*(x-b(2))))); %defines the type of

function to which adjust the data from the experiments.

[beta,R,J,COVB,MSE]=nlinfit(x,y,modelfun,beta0);

a_speed=beta(1) %decay coefficient

xo_speed=beta(2) %expresses the displacement of the curve

across the x axis.

std_deviation_speed=sqrt(mean(R.^2)) %standard deviation of the

regression

65

x2=[0:0.01:150]; %Values of N(rpm) to plot the interpolated

function(small intervals to make it detailed)

I_int_speed=1./(1+exp(a_speed*(x2-xo_speed))); %Evaluates the

interpolated function.

%Plots the data and the fitted curve together.

figure

hold all

scatter(speeds,normalised_brightness);

plot(x2,I_int_speed,'b');

xlabel('N(rpm)');

ylabel('I*');

grid;

set(gca,'XTick',[0:20:160])

set(gca,'YTick',[0:0.2:1.4])

%Plots the reference line of 5% for Just-suspended Speed.

ref_line=0.05+0*x2;

plot(x2,ref_line,'k--');

%Obtain interpolated graph for Fr

%Calculate critical Froude number, Frc

if((h/di)<=sqrt(do/di)) %Transition between toroidal and

precessional vortex occurs when the vortex reaches the bottom of

the cylinder

Frc=(1/awo)*(h/di)*(do/di)^(1/2)

else Transition occurs before

Frc=1/awo

end

66

%Obtains Fr from geometry and measured speeds

if((h/di)<=sqrt(do/di))

Fr=((speeds/60).^2)*2*pi^2*do/9.81;

else

Fr=((speeds/60).^2)*2*pi^2*di/9.81;

end

%Interpolates Fr

x=Fr/Frc;

y=normalised_brightness;

beta0=[1;1]; %Starting values

modelfun=@(b,x)(1./(1+exp(b(1)*(x-b(2)))));

[beta,R,J,COVB,MSE]=nlinfit(x,y,modelfun,beta0);

a_Fr=beta(1)

xo_Fr=beta(2)

std_deviation_Fr=sqrt(mean(R.^2))

%Interpolated function

x3=[0:0.01:1.6];

I_int=1./(1+exp(a_Fr*(x3-xo_Fr)));

%Plot interpolated function for Fr divided by Frc, and measured

data together

figure;

hold all;

grid;

67

scatter(x,normalised_brightness);

plot(x3,I_int,'b');

ref_line=0.05+0*x3;

plot(x3,ref_line,'k--');

xlabel('Fr/Frc');

ylabel('I*');

set(gca,'XTick',[0:0.2:1.8])

set(gca,'YTick',[0:0.2:1.4])

%Froude for just-suspended speed

Frs=Frc*(log(19)/a_Fr+xo_Fr)

%Just-suspended speed

if((h/di)<=sqrt(do/di))

Njs=sqrt(Frs*9.81/2/pi^2/do);

else

Njs=sqrt(Frs*9.81/2/pi^2/di);

end

%in rps

Njs=60*Njs %in rpm

68

69

Appendix B. Laboratory results

In this section, for each experiment carried out in the laboratory, the mean Normalised

Brightness Index (I*) is plotted versus the speed at which measured (N) and the ratio between

the Froude number at that speed (Fr) and the critical Froude (Frc), at which transition occurs.

Both functions are interpolated to a curve of the form I∗ = +ea x−xo where x is Fr/Frc or N,

depending on the graph. The points that are not used because they cause a bad interpolation,

giving a suspension speed that does not correspond to the one observed are plotted in red.

The calculated values that are showed are the suspension speed (Ns), the suspension Froude

(Frs), the critical Froude (Frc) and the interpolating coefficients a and x0 and the standard

deviation for both curves. The Froude number is referred in all cases to the orbital diameter

(do): �� = � � ��/� and Frc is calculated with the equations from Weheliye, depending on

the geometry.

Contents 1 Cylinder diameter, di=10cm ........................................................................................ 71

1.1 h=4.5cm, do=1.5cm ..................................................................................................... 71

1.1.1 Flat bottom .......................................................................................................... 71

1.1.2 Cone A ................................................................................................................. 73

1.1.3 Cone B ................................................................................................................. 74

1.1.4 Cone C ................................................................................................................. 75

1.2 h=4.5cm, do=2.5cm ..................................................................................................... 76

1.2.1 Flat Bottom .......................................................................................................... 76

1.2.2 Cone A ................................................................................................................. 78

1.2.3 Cone B ................................................................................................................. 79

1.2.4 Cone C ................................................................................................................. 80

1.3 h=4.5cm, do=5cm ........................................................................................................ 81

1.3.1 Flat Bottom .......................................................................................................... 81

1.3.2 Cone A ................................................................................................................. 83

1.3.3 Cone B ................................................................................................................. 84

1.3.4 Cone C ................................................................................................................. 85

1.4 h=7cm, do=1.5cm ........................................................................................................ 86

1.4.1 Flat Bottom .......................................................................................................... 86

70

1.4.2 Cone A ................................................................................................................. 88

1.4.3 Cone B ................................................................................................................. 89

1.4.4 Cone C ................................................................................................................. 90

1.5 h=7cm, do=2.5cm ........................................................................................................ 91

1.5.1 Flat Bottom .......................................................................................................... 91

1.5.2 Cone A ................................................................................................................. 93

1.5.3 Cone B ................................................................................................................. 94

1.5.4 Cone C ................................................................................................................. 95

1.6 h=7cm, do=5cm ........................................................................................................... 96

1.6.1 Flat Bottom .......................................................................................................... 96

1.6.2 Cone A ................................................................................................................. 98

1.6.3 Cone B ................................................................................................................. 99

1.6.4 Cone C ............................................................................................................... 100

2 Cylinder diameter, di=7cm ........................................................................................ 101

2.1 Vf=115.45ml .............................................................................................................. 101

2.1.1 h=3cm, do=1.5cm. Flat Bottom ......................................................................... 101

2.1.2 h=3.35cm, do=1.5cm. Cone C............................................................................ 103

2.1.3 h=3cm,do=2.5cm. Flat Bottom .......................................................................... 105

2.1.4 h=3.35cm, do=2.5cm. Cone C............................................................................ 107

2.1.5 h=3cm, do=5cm. Flat Bottom ............................................................................ 109

2.1.6 h=3.35cm, do=5cm. Cone C ............................................................................... 111

2.2 Vf=192.4ml ................................................................................................................ 113

2.2.1 h=5cm, do=1.5cm. Flat Bottom ......................................................................... 113

2.2.2 h=5.35cm, do=1.5cm. Cone C............................................................................ 115

2.2.3 h=5cm, do=2.5cm. Flat Bottom ......................................................................... 117

2.2.4 h=5.35cm, do=2.5cm. Cone C............................................................................ 119

2.2.5 h=5cm, do=5cm. Flat Bottom ............................................................................ 121

2.2.6 h=5.35cm, do=5cm. Cone C ............................................................................... 123

71

1 Cylinder diameter, di=10cm

The height of the cones are 0.5-1-1.5cm for Cones A, B, C respectively.

1.1 h=4.5cm, do=1.5cm ℎ/��/√��/�� = . >

Transition between toroidal and preccesional vortex occurs before the toroidal vortex reaches

the bottom of the vessel.

1.1.1 Flat bottom

Ns(rpm) a_N xo_N Std_dev_N

126.7 1.25 124.36 0.0085

72

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1346 0.1071 1.2561 64.0624 1.2102 0.00854

73

1.1.2 Cone A

Ns(rpm) a_N xo_N Std_dev_N

124.5 0.9235 121.2448 0.0158

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1299 0.1071 1.2120 48.0883 1.1507 0.01570

74

1.1.3 Cone B

Ns(rpm) a_N xo_N Std_dev_N

122.3 1.1428 119.7325 0.0166

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1254 0.1071 1.1701 60.9975 1.1219 0.01608

75

1.1.4 Cone C

Ns(rpm) a_N xo_N Std_dev_N

116.3 2.6933 115.1841 0.0148

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1134 0.1071 1.0580 149.0580 1.0382 0.01490

76

1.2 h=4.5cm, do=2.5cm ℎ/��/√��/�� = . <

Transition between toroidal and preccesional vortex occurs when the toroidal vortex reaches

the bottom of the vessel.

1.2.1 Flat Bottom

Ns(rpm) a_N xo_N Std_dev_N

118.4 0.6127 113.7077 0.0145

77

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1960 0.1607 1.2197 30.9591 1.1245 0.01340

78

1.2.2 Cone A

Ns(rpm) a_N xo_N Std_dev_N

111.7 2.8220 110.6086 0.0107

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1742 0.1607 1.0840 146.2314 1.0638 0.01072

79

1.2.3 Cone B

Ns(rpm) a_N xo_N Std_dev_N

111.4 0.9814 108.3776 0.0353

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1733 0.1607 1.0786 51.4488 1.0212 0.03462

80

1.2.4 Cone C

Ns(rpm) a_N xo_N Std_dev_N

100.6 1.3301 98.4200 0.0005

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1415 0.1607 0.8807 75.7389 0.8417 0.00055

81

1.3 h=4.5cm, do=5cm ℎ/��/√��/�� = . <

Transition between toroidal and preccesional vortex occurs when the toroidal vortex reaches

the bottom of the vessel.

1.3.1 Flat Bottom

Ns(rpm) a_N xo_N Std_dev_N

98.3 0.5169 92.7329 0.0167

82

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2703 0.2273 1.1893 22.5053 1.0584 0.01500

83

1.3.2 Cone A

Ns(rpm) a_N xo_N Std_dev_N

98.4 1.3134 96.1681 0.0344

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2706 0.2273 1.1904 55.3697 1.1372 0.03382

84

1.3.3 Cone B

Ns(rpm) a_N xo_N Std_dev_N

95.2 0.6781 90.9070 0.0287

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2531 0.2273 1.1137 30.2927 1.0165 0.02758

85

1.3.4 Cone C

Ns(rpm) a_N xo_N Std_dev_N

84.0 2.1147 82.6431 0.0493

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1973 0.2273 0.8680 104.3935 0.8398 0.04955

86

1.4 h=7cm, do=1.5cm ℎ/��/√��/�� = . >

Transition between toroidal and preccesional vortex occurs before the toroidal vortex reaches

the bottom of the vessel.

1.4.1 Flat Bottom

Ns(rpm) a_N xo_N Std_dev_N

128.2 0.6800 123.9128 0.0033

87

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1377 0.1071 1.2855 35.1676 1.2018 0.00309

88

1.4.2 Cone A

Ns(rpm) a_N xo_N Std_dev_N

127.8 2.1115 126.4885 0.0157

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1371 0.1071 1.2797 105.8311 1.2519 0.01567

89

1.4.3 Cone B

Ns(rpm) a_N xo_N Std_dev_N

126.4 2.9318 125.4333 0.0147

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1340 0.1071 1.2510 148.6871 1.2312 0.01470

90

1.4.4 Cone C

Ns(rpm) a_N xo_N Std_dev_N

124.1 1.9011 122.5396 0.0129

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1290 0.1071 1.2043 101.3714 1.1757 0.01290

91

1.5 h=7cm, do=2.5cm ℎ/��/√��/�� = . >

Transition between toroidal and preccesional vortex occurs before the toroidal vortex reaches

the bottom of the vessel.

1.5.1 Flat Bottom

Ns(rpm) a_N xo_N Std_dev_N

127.9 0.3617 119.9756 0.0376

92

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2287 0.1786 1.2809 19.1222 1.1269 0.03571

93

1.5.2 Cone A

Ns(rpm) a_N xo_N Std_dev_N

124.2 1.1204 121.5441 0.0740

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2155 0.1786 1.2065 58.6281 1.1563 0.07401

94

1.5.3 Cone B

Ns(rpm) a_N xo_N Std_dev_N

122.2 3.9411 121.4360 0.0194

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2086 0.1786 1.1681 209.2759 1.1541 0.01946

95

1.5.4 Cone C

Ns(rpm) a_N xo_N Std_dev_N

121.7 0.7702 117.9166 0.01080

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2070 0.1786 1.1591 41.7388 1.0885 0.01120

96

1.6 h=7cm, do=5cm ℎ/��/√��/�� = . <

Transition between toroidal and preccesional vortex occurs when the toroidal vortex reaches

the bottom of the vessel.

1.6.1 Flat Bottom

Ns(rpm) a_N xo_N Std_dev_N

102.1 0.7375 97.9905 0.0100

97

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2913 0.3536 0.8239 46.6119 0.7606 0.00970

98

1.6.2 Cone A

Ns(rpm) a_N xo_N Std_dev_N

103.2 3.1234 102.2933 0.0130

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2979 0.3536 0.8426 191.8830 0.8272 0.01300

99

1.6.3 Cone B

Ns(rpm) a_N xo_N Std_dev_N

102.1 1.3130 99.8410 0.0238

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2911 0.3536 0.8233 83.3016 0.7880 0.02428

100

1.6.4 Cone C

Ns(rpm) a_N xo_N Std_dev_N

101.0 0.4685 94.8696 0.05220

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2852 0.3536 0.8067 31.0373 0.7118 0.05358

101

2 Cylinder diameter, di=7cm

2.1 Vf=115.45ml

2.1.1 h=3cm, do=1.5cm. Flat Bottom ℎ/��/√��/�� = . <

Transition between toroidal and preccesional vortex occurs when the toroidal vortex reaches

the bottom of the vessel.

Ns(rpm) a_N xo_N Std_dev_N

140.8 3.2241 139.8814 0.0025

102

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1662 0.1417 1.1729 196.0293 1.1577 0.00250

103

2.1.2 h=3.35cm, do=1.5cm. Cone C ℎ/��/√��/�� = . >

Transition between toroidal and preccesional vortex occurs before the toroidal vortex reaches

the bottom of the vessel.

Ns(rpm) a_N xo_N Std_dev_N

132.2 1.6568 130.4481 0.0145

104

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1466 0.1531 0.9575 116.0123 0.9321 0.01430

105

2.1.3 h=3cm,do=2.5cm. Flat Bottom ℎ/��/√��/�� = . <

Transition between toroidal and preccesional vortex occurs when the toroidal vortex reaches

the bottom of the vessel.

Ns(rpm) a_N xo_N Std_dev_N

128.4 2.4026 127.1556 0.0127

106

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2303 0.1829 1.2592 123.8521 1.2350 0.01270

107

2.1.4 h=3.35cm, do=2.5cm. Cone C ℎ/��/√��/�� = . <

Transition between toroidal and preccesional vortex occurs when the toroidal vortex reaches

the bottom of the vessel.

Ns(rpm) a_N xo_N Std_dev_N

118.7 1.7125 116.9863 0.0120

108

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1969 0.2043 0.9638 107.3309 0.9362 0.01200

109

2.1.5 h=3cm, do=5cm. Flat Bottom ℎ/��/√��/�� = . <

Transition between toroidal and preccesional vortex occurs when the toroidal vortex reaches

the bottom of the vessel.

Ns(rpm) a_N xo_N Std_dev_N

110.0 0.9421 106.9143 0.0198

110

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.3381 0.2587 1.3069 40.8805 1.2348 0.01940

111

2.1.6 h=3.35cm, do=5cm. Cone C ℎ/��/√��/�� = . <

Transition between toroidal and preccesional vortex occurs when the toroidal vortex reaches

the bottom of the vessel.

Ns(rpm) a_N xo_N Std_dev_N

98.3 0.9137 95.1158 0.0107

112

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2700 0.2889 0.9346 49.7943 0.8753 0.01150

113

2.2 Vf=192.4ml

2.2.1 h=5cm, do=1.5cm. Flat Bottom ℎ/��/√��/�� = . >

Transition between toroidal and preccesional vortex occurs before the toroidal vortex reaches

the bottom of the vessel.

Ns(rpm) a_N xo_N Std_dev_N

153.3 1.5465 151.3882 0.0159

114

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1969 0.1531 1.2866 94.0045 1.2553 0.01600

115

2.2.2 h=5.35cm, do=1.5cm. Cone C ℎ/��/√��/�� = . >

Transition between toroidal and preccesional vortex occurs before the toroidal vortex reaches

the bottom of the vessel.

Ns(rpm) a_N xo_N Std_dev_N

150.1 1.5678 148.2840 0.0251

116

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.1890 0.1531 1.2351 95.9930 1.2044 0.02510

117

2.2.3 h=5cm, do=2.5cm. Flat Bottom ℎ/��/√��/�� = . >

Transition between toroidal and preccesional vortex occurs before the toroidal vortex reaches

the bottom of the vessel.

Ns(rpm) a_N xo_N Std_dev_N

141.6 1.3162 139.3607 0.0091

118

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2801 0.2551 1.0979 86.4037 1.0639 0.00940

119

2.2.4 h=5.35cm, do=2.5cm. Cone C ℎ/��/√��/�� = . >

Transition between toroidal and preccesional vortex occurs before the toroidal vortex reaches

the bottom of the vessel.

Ns(rpm) a_N xo_N Std_dev_N

138.8 2.0077 137.3509 0.0034

120

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.2692 0.2551 1.0553 134.2169 1.0334 0.00340

121

2.2.5 h=5cm, do=5cm. Flat Bottom ℎ/��/√��/�� = . <

Transition between toroidal and preccesional vortex occurs when the toroidal vortex reaches

the bottom of the vessel.

Ns(rpm) a_N xo_N Std_dev_N

119.8 0.9766 116.7913 0.0154

122

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.4009 0.4312 0.9297 64.5249 0.8841 0.01590

123

2.2.6 h=5.35cm, do=5cm. Cone C ℎ/��/√��/�� = . <

Transition between toroidal and preccesional vortex occurs when the toroidal vortex reaches

the bottom of the vessel.

Ns(rpm) a_N xo_N Std_dev_N

115.7 6.6087 115.2800 0.0057

124

Frs Frc Frs/Frc a_Fr xo_Fr Std_dev_Fr/Frc

0.3744 0.4312 0.8683 464.4998 0.8050 0.01590

Exploded view wholeWEIGHT:

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180

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77.500

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49.497

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SECTION A-A SCALE 1 : 2

10 5 5

100

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118

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A A

Bottom plate

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15

45

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105

135

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28 x 2.500 THRU ALL

M3x0.5 - 6H 5

8 x 2.500 6.500

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8 x 2.500 6.500

240

240

100

77.500

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77.50077.500

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EDGES

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50 140 50

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100

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135

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195

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B B

SECTION B-B SCALE 1 : 2

105

5

5

5cm Conical Bottom

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SECTION C-C SCALE 1 : 2

4.900

3R60

77.500

6.300 X 90°

8 x 3.400 THRU ALL

77.500

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6.34°

200

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SECTION D-D SCALE 1 : 2

3

4.900

25

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100

51525

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R60

77.500D D

15cm Conical Bottom

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SURFACE FINISH:

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SECTION E-E SCALE 1 : 2

3

4.900

15

5

200

100

51530

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120129.800

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Perspex wall

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Pillars

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ITEM NO. PART NUMBER DESCRIPTION QTY.1 Top_plate Top Plate 12 Cylinder Glass Cylinder 13 Glass_wall Perspex wall 44 Pillars Pillars 45 Bottom_plate Bottom plate 16 Cyl_bottom 17 ISO 4762 M5 x 25 --- 25N 48 ISO 10642 - M5 x 20 --- 20N 49 O-ring 109x3.55-A-ISO 3601-1 110 ISO 10642 - M3 x 12 --- 12N 8

4.90

F

F

18.43°

10.

50

7

130 103.40 83 70

53

7

70

13

0

4.9

0 6.

60

83

103

.40

10.50

20

SECTION F-F

Cyl_bottom_withconeWEIGHT:

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FINISH:UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES: LINEAR: ANGULAR:

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