effect of rotor–stator distance and rotor radius on the rate of gas–liquid mass

G

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Contents lists available at ScienceDirect

Chemical Engineering and Processing:Process Intensification

jo u rn al hom epage: www.elsev ier .com/ locate /cep

ffect of rotor–stator distance and rotor radius on the rate of gas–liquid massransfer in a rotor–stator spinning disc reactor

arco Meeuwse1, Edwin Hamming, John van der Schaaf, Jaap C. Schouten ∗

aboratory of Chemical Reactor Engineering, Department of Chemical Engineering & Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

r t i c l e i n f o

rticle history:eceived 5 November 2010eceived in revised form 29 April 2011ccepted 30 May 2011vailable online xxx

eywords:pinning disc reactor

a b s t r a c t

This paper describes the effect of rotor radius, rotor–stator distance, liquid flow rate and rotationaldisc speed on the rate of gas–liquid mass transfer in a rotor–stator spinning disc reactor. A rotorradius of 0.135 m is studied with rotor–stator distances of 1, 2 and 5 mm, at rotational disc speedsup to 209 rad s−1, and compared with a rotor radius of 0.066 m. At rotational disc speeds lower than70 rad s−1, elongated gas bubbles are formed, that are larger than the rotor–stator distance. At rota-tional disc speeds above 100 rad s−1, spherical gas bubbles are formed that are smaller than therotor–stator distance. The volumetric gas–liquid mass transfer coefficient increases with increasing

otor–statorass transferultiphase reactorsas holdup

rotational disc speed and decreases with increasing liquid flow rate. This decrease is larger than pre-dicted by the Wallis drift flux model because of the complex two-phase flow pattern. The rate ofgas–liquid mass transfer per unit of reactor volume increases with decreasing rotor–stator distance.The maximum observed volumetric mass transfer coefficient in case of the 0.135 m rotor is a fac-tor 3 higher than in case of the 0.066 m rotor, while the rate of energy dissipation is a factor 15higher.

© 2011 Elsevier B.V. All rights reserved.

. Introduction

The rotor–stator spinning disc reactor is a novel type of mul-iphase reactor, which is shown to have high gas–liquid andiquid–solid mass transfer rates compared to conventional reactorquipment [1–3]. The spinning disc reactor consists of a rotatingisc (rotor) and a reactor wall (stator) on both sides of the disc (seeig. 1), with a small gap in between. Liquid is injected to the reactorhrough the top stator, gas is injected via a gas inlet in the bottomtator, near the rim of the disc. The high rotational disc speed cre-tes a large shear force between the rotor and the stator, therebyreaking up gas bubbles. This results in a high gas–liquid inter-acial area, aGL. The turbulence induced in the system due to theotation results in high values of the gas–liquid mass transfer coeffi-

Please cite this article in press as: M. Meeuwse, et al., Effect of rotor–statorrotor–stator spinning disc reactor. Chem. Eng. Process. (2011), doi:10.1016

ient, kGL. The combination gives a high volumetric gas–liquid massransfer coefficient, for example, kGLaGL = 0.43 mL

3 mR−3 s−1 with a

otor radius of 0.066 m and a rotational disc speed of 179 rad s−1.

∗ Corresponding author. Tel.: +31 40 247 2850; fax +31 40 244 6653.E-mail addresses: [email protected] (M. Meeuwse),

[email protected] (J. van der Schaaf), [email protected] (J.C. Schouten).URL: http://www.chem.tue.nl/scr (J.C. Schouten).

1 Present address: DSM Research, Advanced Chemical Engineering Solutions, P.O.ox 18, 6160 MD Geleen, The Netherlands.

255-2701/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.cep.2011.05.022

This is a factor 3 higher than in conventional reactors like bubblecolumns and stirred tanks, in spite of the low gas holdup, which isless than 2% [1]. The gas holdup, and thus the efficiency of the reac-tor is increased by using multiple gas inlets. However, this may notbe preferable if the reactor has to be scaled up to a multiple discsystem, since a (re)distribution of the gas is then needed. If gas andliquid are fed together through the inlet in the top of the reactor,a liquid film will form on top of the rotor. Small gas bubbles willbe sheared off at the rim of the rotor, the gas–liquid dispersion willfill the rest of the reactor, i.e. the region surrounding the rim ofthe disc, and the region between the rotor and the bottom stator.The reactor volume is used more efficiently in this configuration,and therefore gives rise to a significant increase in gas–liquid masstransfer [2].

The aforementioned results were all obtained using an exper-imental setup with a rotor radius of 0.066 m and a rotor–statordistance of 1 mm. The gas bubble diameter, and therefore also thegas–liquid interfacial area, is mainly determined by the gas flowrate and the shear force between the rotor and the stator at the gasinlet. The magnitude of the velocity gradient, and thus the shearforce, depends on the rotor–stator distance, and on the tangential

distance and rotor radius on the rate of gas–liquid mass transfer in a/j.cep.2011.05.022

velocity of the rotor, which is the product of the radius and therotational disc speed. The gas–liquid interfacial area is thereforeexpected to increase with increasing rotor radius and decreas-ing rotor–stator distance. The gas–liquid mass transfer coefficient

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Nomenclature

aGL gas–liquid interfacial area (mi2 mR

−3)C concentration (mol mL

−3)CD drag force coefficientCm torque coefficientD liquid phase diffusion coefficient (mL

2 s−1)db gas bubble diameter (mG)Ed rate of energy dissipation (J mR

−3 s−1)G gap ratio G = h/RD

H Henry coefficient (mL3 Pa mol−1)

h rotor–stator distance (mR)HD rotor thickness (mR)kGL gas–liquid mass transfer coefficient (mL

3 mi−2 s−1)

kGLaGL volumetric gas–liquid mass transfer coefficient(mL

3 mR−3 s−1)

kLS liquid–solid mass transfer coefficient (mL3 mi

−2 s−1)kLSaLS volumetric liquid–solid mass transfer coefficient

(mL3 mR

−3 s−1)Lb bubble length (m)n empirical coefficient Richardson and Zaki modelR gas constant (mG

3 mol−1 K−1)r radial position (m)Rb bubble radius (mG)RD rotor radius (mR)Re Reynolds number, Re = ωR2

D/�T temperature (K)t time (s)tc contact time between gas and liquid (s)vr radial velocity (m s−1)vs slip velocity between gas and liquid phase (m s−1)v∞ terminal velocity of gas bubble in stationary liquid

(m s−1)v� tangential velocity (m s−1)vG,i interstitial velocity gas phase (m s−1)vG,s superficial velocity gas phase, vG,s = �G/2�rh

(m s−1)vL,i interstitial velocity liquid phase (m s−1)vL,s superficial velocity liquid phase, vL,s = �L/2�rh

(m s−1)VR reactor volume (mR

3)Vvessel volume storage vessel (mR

3)w distance between the rim of the rotor and the reac-

tor wall (m)

Greek symbolsεG gas holdup (mG

3 mR−3)

�L liquid viscosity (Pa s)� kinematic viscosity (mL

2 s−1)G gas density (kg mG

−3)L liquid density (kg mL

−3) torque (Nm)�G gas flow rate (mG

3 s−1)�L liquid flow rate (mL

3 s−1)ω rotational disc speed (rad s−1)

SubscriptsG gas phasei interfacein inletL liquid phaseout outlet

Fig. 1. Schematic representation of the rotor–stator spinning disc reactor with agas inlet in the bottom stator. The reactor consists of a rotating disc in a cylindricalhousing. Liquid is fed to the reactor from the top inlet, near the rotating axis. Gas isinjected through an orifice in the bottom stator. Gas bubbles are sheared off due tothe high velocity gradient in between the rotor and the stator. The surface renewalrate near the gas bubbles is large due to the turbulence induced by the rotationof the disc, which leads to a high gas–liquid mass transfer coefficient. The samemechanism causes a high rate of mass transfer from the bulk of the liquid to the
rotor and the stator. More information about the dimensions of the reactor used inthis study is shown in Fig. 3, photographs of the gas–liquid dispersion between therotor and the stator are shown in Figs. 5 and 7.
depends on the energy input in the system per unit of reactorvolume, which is also strongly affected by the rotor–stator dis-tance and the rotor radius. An increase in the gas–liquid masstransfer coefficient is thus expected with increasing rotor radiusand decreasing rotor–stator distance. As a result, the volumetricgas–liquid mass transfer coefficient is also expected to increasewith increasing rotor radius and decreasing rotor–stator distance.This paper describes the influence of the rotor radius and therotor–stator distance on the gas–liquid mass transfer rate in thespinning disc reactor, using a single gas inlet in the bottom sta-tor. The influence of the gas flow rate, the liquid flow rate, andthe rotational disc speed are also investigated. Additionally, mod-els for the gas–liquid mass transfer coefficient and the gas holdupare proposed, which are used to explain the effects observed in theexperiments.

For an industrial application of the rotor–stator spinning discreactor in a given process, the mass transfer of the reactor at a cer-tain flow rate is most often the determining factor. In this study it istherefore chosen to compare the different reactor configurations atconstant liquid and gas flow rates. The conditions used for the com-parison of the rotor–stator distances used in this paper are: a liquidflow rate of 3 × 10−5 m3 s−1 and a gas flow rate of 1.5 × 10−5 m3 s−1.

2. Theory

In the next section, a short summary of literature on single phaseflow in rotor–stator systems is presented; in particular those refer-ences will be considered that are relevant for the work presentedin this paper. Data on two-phase flow in rotor–stator systems isscarce and the gas–liquid flow in between a rotor and a stator isnot yet well understood. Here we will present a simplified model,based on the Wallis drift flux model, that we will apply as a toolin the explanation of the experimental data obtained. Additionally,models for the gas–liquid mass transfer coefficient are presented.

2.1. Single phase flow in rotor–stator systems


Single phase flow in rotor–stator systems has been researchedextensively in the past decades. Four different flow regimes can bedistinguished, two laminar regimes and two turbulent regimes. The

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v = r

rotor

stator

v = r

rotor

stator

rotor

stator

rotor

stator

r

r

Fig. 2. Schematic representation of the mean tangential (left) and radial (right) velocities in a rotor–stator system with a large rotor–stator distance (top) and a smallrotor–stator distance (bottom). In the case of a large rotor–stator distance two separate boundary layers are formed, at the rotor and the stator, separated by a region rotatingat a constant tangential velocity, approximately 0.3–0.45 times the velocity of the rotor [4,5]. No radial velocity is present in this region. The size of this region decreases withd ndary[ drawm in the

mitp

aspsibaridp1tdttsrreab

ltict

ecreasing rotor–stator distance. Below a certain rotor–stator distance the two bou6–8]. The transition between the two flow regimes occurs at GRe1/5 ≈ 0.5 [9]. The

erged boundary layers nor accurate experimental or numerical results are found

ean velocity profiles of the two turbulent regimes have approx-mately the same shape as the two laminar regimes. Only theurbulent regimes are described here, since all the experimentserformed in the present study are in these regimes.

Fig. 2 shows a schematic representation of the mean tangentialnd radial velocities in the case of single phase flow in a rotor–statorystem. At a large rotor–stator distance, two boundary layers areresent, one at the stator and one at the rotor. These layers areeparated by a core of liquid in which no tangential or radial veloc-ty gradient is present, which thus rotates as a solid body. In theoundary layer at the stator an inward radial velocity is present,t the rotor the radial velocity is directed outwards. The maximumadial velocity is approximately 10–20% of the tangential veloc-ty of the rotor [10–12,5,13]. The thickness of the boundary layersepends on the rotational disc speed and the rotor radius, and isroportional to the Reynolds number (Re = ωR2

D/�) to the power/5 [9,14]. When the rotor–stator distance is decreased, the cen-ral core decreases in size, until it vanishes. At a lower rotor–statoristance the boundary layers merge; no region without a tangen-ial velocity gradient is present anymore. The transition betweenhe two flow regimes occurs at GRe1/5 ≈ 0.5 [9]. The experimentaletup as used in this study operates in the regime with the sepa-ate boundary layers (as shown in the top part of Fig. 2) at 5 mmotor–stator distance and a disc radius of 0.135 m. In the rest of thexperiments, i.e. h = 1 mm and h = 2 mm at RD = 0.135 and h = 1 mmt RD = 0.066 m, the boundary layers are merged, as indicated in theottom part of Fig. 2.

The velocity profiles in Fig. 2 are without a net throughflow ofiquid. In the case of an inward flow, the thickness and velocity of


he stator boundary layer increase, while these quantities decreasen the rotor boundary layer. A large increase in centripetal flowan lead to an inward flow in the rotor boundary layer. The tangen-ial velocity in the core region increases with increasing centripetal

layers merge, resulting in a continuous variation in tangential and radial velocityings are schematic representations of the velocity profiles; in the region with the

literature.

flow rate. This can even lead to a tangential velocity of the liquid inthis core region which is higher than the tangential velocity of therotor [4,15], although this happens at conditions which are, in thepresent study, only reached very close to the axis. Therefore thiseffect is neglected in the derivation of the holdup model presentedin the next section.

2.2. Two phase flow and gas–liquid mass transfer

The rate of gas–liquid mass transfer depends on the productof the gas–liquid interfacial area, aGL, and the mass transfer coeffi-cient, kGL. The gas–liquid interfacial area depends on the gas holdupand the gas bubble diameter. The mass transfer coefficient is deter-mined by the energy dissipation rate in the system, or by therelative velocity of the gas bubbles and the liquid.

2.3. Gas bubble size, gas holdup and gas–liquid interfacial area

The gas–liquid interfacial area depends on the gas bubble sizeand the gas holdup in the reactor. The gas bubbles are formed atthe gas inlet, the bubble size is determined by the shear force at thegas inlet. Duhar and Colin [16] and Terasaka et al. [17] studied thebubble detachment from an orifice in a shear flow, but only at lowshear rates, in the order of 10 s−1, which is 3 orders of magnitudelower than in the rotor–stator spinning disc reactor. The gas bub-bles size decreases with increasing shear rate [16,17]. This is alsoobserved in the rotor–stator spinning disc reactor, where the gasbubble size decreases with increasing rotational disc speed [1]. Nobubble breakup and coalescence is observed, only at 0.02 m from


the center of the reactor the bubbles coalesce to larger gas bubbles.The gas bubbles in the rotor–stator spinning disc reactor are split

in two categories. At low rotational disc speeds (typically below70 rad s−1), large gas bubbles are formed, with a diameter which

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s larger than the rotor–stator distance. At higher rotational discpeeds (commonly above 100 rad s−1), the gas bubbles are smallerhan the rotor–stator distance. The gas holdup and the gas–liquid

ass transfer mechanism are different for the two types of bubbles.The gas holdup depends on the inward radial velocity of the gas

ubbles. The radial velocity is determined by the drag force andhe centrifugal force. The flow rate of liquid, which is directed radi-lly inwards, has an influence on the inward gas bubble velocity.ear the center of the reactor the area perpendicular to the flowecreases. The influence of the two phase flow rate, i.e. the gas flownd liquid flow rate together, on the radial velocity of the gas bubbleill thus increase near the axis. A common method to incorporate

he effect of the two phase flux on the gas holdup is by using theallis drift flux model [18]. This model combines the slip velocity

etween the phases with the two phase flux.In the Wallis drift flux model it is assumed that the flow is one-

imensional, i.e. that only flow in the radial direction is taken intoccount. The liquid and gas are assumed to have the same tangentialelocity, which only depends on the radial position in the reac-or, and there is no axial variation in tangential and radial velocity.his is in contradiction with the flow regimes as observed in singlehase rotor–stator systems (see, e.g. Fig. 2). However, in the case of

arge gas bubbles, with a diameter which is much larger than theotor–stator distance (see, e.g. Fig. 13 at 1 and 2 mm rotor–statoristance), the complete axial distance is filled with the gas bubble.he influence of the presence of this gas bubble on the radial andangential velocity profiles is unknown. Due to the large scale ofhe bubble, however, it is assumed that these gradients do not con-ribute to a large extent to the radial velocity of the gas bubble. Thene-dimensional flow can thus be used to estimate the gas holdupn the rotor–stator spinning disc reactor for large (i.e. db � h) gasubbles.

The slip velocity as used in the Wallis drift flux model is theifference in interstitial velocities, which can be expressed as aunction of the superficial velocities and the gas holdup:

s ≡ vG,i − vL,i = vG,s

εG− vL,s

1 − εG(1)

The velocities can be divided by the terminal velocity in a stag-ant liquid (v∞), leading to:

G(1 − εG)vs

v∞= (1 − εG)

vG,s

v∞− εG

vL,s

v∞(2)

The slip velocity can be expressed as a function of the gas holdup,sing the empirical relation of Richardson and Zaki [19]:

vs

v∞= (1 − εG)n−1 (3)

he parameter n is a function of the Reynolds number based on theerminal velocity of a single gas bubble in a stationary liquid, ands in this case 2.39. Combining Eqs. (2) and (3) leads to:

G(1 − εG)n = (1 − εG)vG,s

v∞− εG

vL,s

v∞(4)

his relation is used to get an estimate of the gas holdup as a func-ion of the gas flow rate and liquid flow rate, based on the terminalelocity of a single gas bubble in a stationary liquid. This veloc-ty follows from a force balance between the centrifugal force andhe drag force. Gas bubbles larger than the rotor–stator distancere assumed to behave as solid cylinders. The terminal velocity ofylindrical gas bubbles is calculated, using CD = 1.2 [20]:

∞ =√

�RbL − G ((1/2)ω)2r

(5)


L CD

Experimental observations with a high speed camera show thathe gas bubbles have a tangential velocity which is approximatelyalf the velocity of the rotor [21]. The bubbles are assumed to be

PRESS and Processing xxx (2011) xxx– xxx

uniform in size. Eqs. (4) and (5) are used in Section 4.2 to get anestimate of the gas holdup, which is used in the discussion aboutthe influence of the liquid flow rate on the gas–liquid mass transfer.

The same procedure can be used to estimate the gas holdup inthe case of spherical bubbles (where db < h), which behave as solidspheres [22,23]. The terminal gas bubble velocity in a stationaryliquid, also assuming the gas bubbles have a tangential velocitywhich is half of the tangential velocity of the rotor, is different,however [22]:

v∞ = 0.46

((1/8)(ω2r)

2(L − G)2

L�L

)1/3

Rb (6)

The estimation of the gas holdup using Eqs. (4) and (6) is based onthe assumption of one-dimensional flow, with no axial velocity gra-dient, and the same tangential velocity of the gas bubbles and theliquid. For spherical gas bubbles, especially if db � h, however, thediameter of the gas bubbles is in the same order, or even smaller, asthe thickness of the boundary layer. The foregoing analysis is thusnot valid for small gas bubbles (i.e. db � h). In this case the axialposition of the gas bubble is important. If the gas bubble is locatedin the rotor boundary layer, which is centrifugal, the inward radialvelocity is decreased, due to the drag force which acts outwards.In the stator boundary layer, the flow is centripetal, leading to ahigher radial velocity than expected based on the centrifugal force.The radial velocity of a gas bubble is thus a strong function of theaxial position of the gas bubble. It is therefore not possible to obtaina realistic estimate of the gas holdup in this case, since no informa-tion about the axial position of the gas bubbles is available. Thequantitative results are thus only used when the gas bubbles arepresent in the core region, in the case of the flow regime presentedin the top part of Fig. 2. An example of this is shown in Section 4.2.This method is not applicable in case the gas bubbles are present inone of the boundary layers.

2.4. Mass transfer coefficient

The magnitude of the mass transfer coefficient, kGL, dependson the rate of refreshment of the liquid surrounding the gas bub-bles. Two different mass transfer mechanisms play a role in therotor–stator spinning disc reactor, depending on the size of the gasbubbles. At low rotational disc speed large gas bubbles are present,which fill the whole reactor height between the bottom and thestator (see, e.g. Fig. 7 at ω = 26 rad s−1). Most of the gas–liquid inter-facial area is in this case present as a liquid film between the rotor orstator and the gas bubble. Most of the mass transfer will thereforetake place from the gas bubble to this liquid film. This liquid filmis not present with the small spherical bubbles, which are smallerthan the rotor–stator distance (see, e.g. Fig. 7 at ω = 131 rad s−1).The rate of gas–liquid mass transfer is in this case based on the rateof surface renewal at the gas–liquid interface by turbulent eddiesin the liquid.

The rate of mass transfer between a large gas bubble and theliquid film can be estimated using the Higbie penetration theory,which is based on the time of contact between the gas and theliquid, before the liquid in the film is mixed with the bulk liquid[24]:

kGL = 2

√D

�tc(7)


As mentioned before, the gas bubbles appear to have a tangentialvelocity of 0.5 times the velocity of the rotor. The liquid films atthe rotor and the stator are assumed to have the same velocitiesas the rotor (v� = ωr) and the stator (v� = 0). The contact times for

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bb

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F

k

Tpgrtgb

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Egrtdrtcsitr

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V

Twa

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3

saiTuat(oriLbr



oth liquid films can thus be calculated using the length of the gasubble perpendicular to the velocity:

c = Lb

ω/2(8)

rom this contact time the value of kGL follows:

GL =√

2Dωr

�Lb(9)

he value of kGL as calculated with Eq. (9) depends on the radialosition of the gas bubble, since this position determines the tan-ential velocity. This value of kGL has to be averaged over the wholeeactor volume taking part in mass transfer, i.e. the region betweenhe rotor and the bottom stator, based on the assumption that theas bubbles are evenly distributed over this region, and that theubble length is independent of the radial position.

¯GL =∫ VR

0kGL dV∫ VR

0dV

=∫ h

0dz

∫ 2�

0d�

∫ RD

0kGLr dr∫ h

0dz

∫ 2�

0d�

∫ RD

0r dr

= 45

√2DωRD

�Lb(10)

q. 10 is used as an estimate of the mass transfer in case of largeas bubbles, thus at low rotational disc speeds. In case of higherotational disc speeds (commonly larger than 100 rad s−1), most ofhe gas bubbles are spherical, and smaller than the rotor–statoristance. At these conditions the liquid is turbulent. The surfaceefreshment rate for the small gas bubbles, is now determined byhe velocity and size of the turbulent eddies. The mass transferoefficient is therefore determined by the energy dissipated in theystem, commonly to the power 1/4 [25]. The energy dissipations a function of the rotational disc speed and the rotor–stator dis-ance (Eqs. (16)–(18), [6]). kGL depends on the rotational disc speed,otor–stator distance and disc radius as follows:

GL ∝ E1/4d

, Ed ∝ ω11/4R14/3D h−(1/6)

VR⇒ kGL ∝ ω11/16R7/6

D

h1/2V1/4R

(11)

The reactor volume depends on the disc radius, the distanceetween the rim of the rotor and the reactor wall (w) andotor–stator distance:

R = �(2hR2D + 4wRDh + 2wRDHD + 2hw2 + HDw2) (12)

he dependency of kGL on the rotor–stator distance and disc radiushich follows from Eqs. (11) and (12) is used in Section 4.3 in the

nalysis of the experimental results.

. Experimental

.1. Experimental setup

The rotor–stator spinning disc reactor, as shown in Fig. 3, con-ists of a stainless steel rotating disc of 0.135 m radius, in between

top stator (stainless steel) and a bottom stator (PMMA). The max-mum rotational disc speed of the rotor is 209 rad s−1 (=2000 rpm).he rotor–stator distances can be adjusted by shifting the statorsp and down. In this study the rotor–stator distances on the topnd the bottom are 1, 2 and 5 mm. Liquid is fed to the reactor athe top, near the rotating axis. Gas is injected through a gas inlet0.5 mm inner diameter) in the bottom stator, at a radial position


f 0.130 m, near the rim of the disc. The gas and the liquid leave theeactor via an outlet in the center of the bottom stator. The liquids recirculated via a 5 dm3 s torage vessel, which is cooled using aauda WKL 1200 circulation chiller, to remove the heat generatedy the rotating disc. Gas–liquid mass transfer coefficients for a discadius of 0.066 m were obtained in previous work [1].

PRESS and Processing xxx (2011) xxx– xxx 5

3.2. Gas–liquid mass transfer measurement

The volumetric gas–liquid mass transfer coefficient is deter-mined with two different methods, a steady state method and atransient method. The steady state method uses the difference inoxygen concentration in the liquid phase between the inlet andthe outlet to calculate the gas–liquid mass transfer coefficient. Thetransient method uses the decrease in oxygen concentration in thestorage vessel, which is in a recirculation loop with the reactor, todetermine the gas–liquid mass transfer coefficient.

The oxygen concentration is measured in the liquid phase at thereactor inlet and, in case of the steady state method, at the reactoroutlet, using Ocean Optics FOXY-R fiber optic oxygen sensors. Thetemperature is measured at the same position. The oxygen sensorsare calibrated in oxygen-free and oxygen-rich conditions over thewhole temperature range used (5–30 ◦C).

In the steady state method, air is fed to the storage vessel, toincrease the oxygen concentration. Nitrogen is used as the gasphase in the reactor, to strip the oxygen from the liquid. The vol-umetric gas–liquid mass transfer coefficient is calculated from thedifference in the oxygen concentrations in the liquid at the inletand outlet of the reactor:

kGLaGL = �G

VR

H

RTln

[(RT/H)C in

G − CoutL

(RT/H)CoutG − Cout

L

](13)

This equation is based on an ideally mixed liquid phase, and a gasphase as plug flow [1]. The oxygen concentration in the gas phaseat the outlet follows from a mole balance:

CoutG = C in

G + �L

�G(C in

L − CoutL ) (14)

The rate of gas–liquid mass transfer depends on the difference inoxygen concentration between the gas phase and the liquid phase.If the volumetric mass transfer coefficient is high, the driving force,(RT/H)Cout

G − CoutL , will be low at the exit. A small error in the oxygen

concentration measurement will then have a large influence on thevalue of kGLaGL as calculated by Eq. (13). This situation occurs whenkGLaGL is high, in combination with low gas and/or liquid flow rates.Under these circumstances the steady state method will not giveaccurate results.

In the transient method the whole liquid system is saturatedwith oxygen from air, at the start of the experiment. No air is fed tothe storage vessel during the experiment. Nitrogen is again the gasphase in the spinning disc reactor, leading to a liquid outlet oxygenconcentration which is lower than the inlet oxygen concentration.The liquid is recirculated, the oxygen concentration in the storagevessel will therefore decrease with time. This decrease is a measurefor the rate of gas–liquid mass transfer. The liquid vessel is assumedto be ideally mixed, the oxygen concentration at the reactor inletas a function of time is then:

C inL = C in

L,t=0e

⎛⎝ �L

Vvessel

⎡⎣ RT�L

H�G

RT�LH�G

+1−e

(−kGLaGL

RTVRH�G

) −1

⎤⎦

⎞⎠t

(15)

The decrease in oxygen concentration is fitted, with kGLaGL asfitting parameter. An example of a measurement, and the corre-sponding fit, is shown in Fig. 4. This method can be used when thesteady state method is not applicable. Measurements performedunder the same conditions with the two methods showed that thekGLaGL values obtained were within 20% of each other, with thehighest mass transfer rates, near the edge of applicability of Eq.


(13). This difference is smaller for the cases where the gas–liquidmass transfer is lower. In both cases it is of the same magnitudeas the experimental error of the measurements, which is generallybetween 10 and 20%.

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F 2 or 5r

3

Etwic

E

tmt

C

Frso(s

ig. 3. Schematic drawing of experimental setup. The rotor–stator distance h is 1,espectively.

.3. Torque measurement

The motor used for the rotation of the spinning disc is a SEWurodrive CFM71M. The current, which is proportional to theorque applied by the motor, is measured. The torque appliedithout a rotating disc, i.e. when the engine is running on idle,

s subtracted. The energy dissipation rate is calculated using theorrected torque:

d = ω

VR(16)

A comparison is made in this paper with the gas–liquid massransfer in a system with a disc radius of 0.066 m [1]. No torque

easurements are available for this configuration. The torque forhis case is therefore calculated using the following correlation [6]:

= Cm1

ω2R5 (17)


2 D

m = 0.08(

h

R

)−(1/6)

Re−(1/4) (18)

0 500 10000

0.1

0.2

0.3

0.4

0.5

time(s)

Con

cent

ratio

n (m

ol m

−3 )

CLin data

CLin fit

CLout data

CLout fit

RT/H CGout

ig. 4. A typical transient oxygen measurement at the inlet and the outlet of theeactor (see Fig. 3). The liquid concentration at the inlet of the reactor (C in

L ) is mea-ured, and fitted with Eq. (15) using the value of kGLaGL as fitting parameter. Theutlet concentration (Cout

L ) is measured as well; the value of CoutL calculated with Eq.

13), based on the inlet concentration and the kGLaGL that gave the best fit, is alsohown in the picture.

mm. The reactor volumes are 1.67 × 10−4 m3, 2.99 × 10−4 m3 and 6.96 × 10−4 m3,

The applicability of this equation is checked with the torque mea-surements with the disc of 0.135 m radius, with 1 and 2 mmrotor–stator distance, which is also in the range where this cor-relation is applicable [9]. All the measurements are within 40% ofthe values obtained by this correlation. Eq. 17 is only used for thecomparison between the 0.066 m disc and the 0.135 m disc. As canbe seen in Fig. 17, this error has no influence on the conclusions,since the difference in performance between the two disc sizes ismuch larger than this error of (maximum) 40 %.

3.4. Image acquisition

Pictures of the gas–liquid dispersion between the rotor and thetransparent bottom stator are made via a mirror, which is adjustedat 45◦. The shutter time of the Canon EOS 400D camera is 0.1 s. Dueto a stroboscope flash, the exposure time of the image is only 10 �s.In spite of this short exposure time, the bubbles on the picture areblurred at rotational disc speeds above 130 rad s−1, due to the highvelocity at the rim of the disc. Additionally, the bubbles on the pic-ture sometimes overlap each other, at a rotor–stator distance ofmore than 1 mm; accurate determination of the bubble size is thennot possible. The image analysis method as described in Meeuwseet al. [1] can therefore not be used to determine the gas holdupand the gas–liquid interfacial area in this study. Only a qualitativeanalysis of the gas–liquid dispersion is made in this paper. An exam-ple of a picture of the gas–liquid dispersion is shown in Fig. 5; theposition of the detail cuts for Figs. 7 and 13 is indicated.

4. Results and discussion

The following sections describe the effect of rotational discspeed, liquid flow rate, rotor–stator distance, and rotor radius onthe volumetric gas–liquid mass transfer coefficient. The models forthe gas holdup and the gas–liquid mass transfer coefficient pre-sented in Section 2 are used as a tool for the explanation of theexperimental results.

4.1. Rotational disc speed

The volumetric mass transfer coefficient, at 1 mm rotor–statordistance, as a function of the rotational disc speed, is shown inFig. 6. It increases with increasing rotational disc speed and increas-ing gas flow rate. These trends are similar to those observedwith a disc radius of 0.066 m [1]. The values however, which are


up to 2 mL3 mR

−3 s−1, are significantly higher than the highestvalue obtained with RD = 0.066 m, which is 0.43 mL

3 mR−3 s−1 at

179 rad s−1 and �G = 7.3 × 10−6 m3 s−1. The volumetric gas–liquidmass transfer coefficient increases slowly with increasing rota-

dx.doi.org/10.1016/j.cep.2011.05.022




Fig. 5. Photograph of the gas–liquid dispersion between the rotor and the bottomstator, at ω = 105 rad s−1, �G = 1.5 × 10−5 m3 s−1, �L = 3 × 10−5 m3 s−1, and h = 1 mm.The black rectangle, which is 5.8 cm by 5.8 cm in size, indicates the position of thed

tif5at1gt

0 50 100 150 200 2500

0.5

1

1.5

2

2.5

Rotational disc speed, ω (rad s−1 )

k GLa G

L (

m3 L m

−3

R s

−1 )

φG

= 1.8 10−6 m3 s−1

φG

= 3.6 10−6 m3 s−1

φG

= 7.3 10−6 m3 s−1

φG

= 1.5 10−5 m3 s−1

the trends observed, using the models presented before.The volumetric gas–liquid mass transfer coefficient as a func-

Fda

etail cuts in Figs. 7 and 13.

ional disc speed up to 100 rad s−1, at higher rotational disc speedst increases more rapidly. In Fig. 7 images of the gas bubbles at dif-erent rotational speeds are shown. At a rotational disc speed of2 rad s−1 or lower, the gas is present as large gas bubbles, whichre squeezed in between the rotor and the stator. At 79 rad s−1,he first small gas bubbles, which have a diameter smaller than

mm, appear. At 131 rad s−1 and higher rotational disc speeds, the


as is mainly present in the form of small gas bubbles, which fur-her decrease in size with increasing rotational disc speed. The

ig. 7. Gas bubbles in the rotor–stator spinning disc reactor at various rotational disc specreases with increasing rotational disc speed. The position of the images in the reactorre not shown, since the gas bubbles move during the exposure time of the camera (≈ 10

Fig. 6. Volumetric mass transfer coefficient at RD = 0.135, h = 1 mm and�L = 3 × 10−5 m3 s−1. The gas–liquid mass transfer increases with increasing rota-tional disc speed and gas flow rate.

gas–liquid interfacial area, aGL, will thus increase rapidly at rota-tional disc speeds of 100 rad s−1 and higher.

4.2. Liquid flow rate

The liquid flow rate is expected to influence the gas holdup, andthus the gas–liquid mass transfer coefficient, as described in Section2.3. This section describes the experimental results, and discusses


tion of liquid flow rate for a rotor–stator distance of 5 mm isshown in Fig. 8. The gas–liquid mass transfer coefficient decreases

eeds, at �G = 1.5 × 10−5 m3 s−1, �L = 3 × 10−5 m3 s−1, h = 1 mm. The gas bubble size is indicated in Fig. 5. The photographs at rotational disc speeds above 157 rad s−1

�s), resulting in a blurred image.

dx.doi.org/10.1016/j.cep.2011.05.022

ARTICLE ING Model


8 M. Meeuwse et al. / Chemical Engineering

0 1 2 3 4

x 10−5

0

0.01

0.02

0.03

0.04

0.05

0.06

Liquid flow rate (m3 s−1)

k GLa G

L (

m3 L m

−3

R s

−1 )

φG

= 7.3 10−6 m3 s−1

φG

= 1.5 10−5 m3 s−1

Fig. 8. Volumetric mass transfer coefficient at RD = 0.135, h = 5 mm and ω =1ir

suorFlatbtibFFtofi

Fal

05 rad s−1. The volumetric gas–liquid mass transfer coefficient decreases withncreasing liquid flow rate, but the effect is less pronounced than at 1 mmotor–stator distance.

ignificantly, by approximately a factor 2, with an increase in liq-id flow rate, at higher liquid flow rates this effect seems to levelff. This effect was not investigated in the experiments with a discadius of 0.066 m. An image of the flow at 105 rad s−1 is shown inig. 9a, where a bimodal distribution in gas bubbles is observed. Thearge gas bubbles, which have an average gas bubble diameter ofpproximately 2 mm, flow in a spiral pattern towards the center ofhe reactor. The effect of liquid flow on the gas holdup of these bub-les is expected to be very small, only a decrease of 2.5% accordingo Eqs. (4) and (6). The small gas bubbles (db≈ 0.5 mm), are presentn the rest of the reactor, which operates in the regime where theoundary layers are separated by a core rotating as a solid body (seeig. 2, top drawing). The shadows behind the small gas bubbles (seeig. 9b) indicate that most of them are located near the rotor, thus in


he boundary layer which is directed outwards. The residence timef these small gas bubbles will thus be significantly higher thanor the large gas bubbles. The liquid flow rate is known to have annfluence on the velocity and thickness of the rotor boundary layer,

ig. 9. (a) Image of the gas liquid flow at RD = 0.135, h = 5 mm, ω = 105 rad s−1 and �L = × 10t an angle of approximately 45◦ . The position of the shadows gives an indication of theocated to the rotor.


and will thus decrease the residence time. The boundary layer atthe stator will increase in thickness and velocity, thereby increasingthe radial velocity of gas bubbles located in this layer. An increasein liquid flow rate will thus lead to a decrease in gas holdup, whichexplains the decrease of gas–liquid mass transfer. Unfortunately,the drift flux model as presented in Section 2, cannot be used topredict the gas holdup in this configuration, due to the fact that thegas bubbles are much smaller than the rotor–stator distance.

The decrease in gas–liquid mass transfer as a function of rota-tional disc speed is even larger in case of a rotor–stator distanceof 1 mm and a rotational disc speed of 52 rad s−1, as shown inFig. 11a. The liquid flow rate is expected to have an influence onthe inward radial velocity, and thus the gas holdup and gas–liquidinterfacial area, as described in Section 2. The estimated gas holdup,for a rotor–stator distance of 1 mm, and a rotational disc speed of52 rad s−1 is shown in Fig. 10. An increase in liquid flow rate ofa factor 6 decreases the overall gas holdup by 16 %. The effect ofthe liquid flow rate on the gas holdup is only observed at a radialposition below 0.05 m (Fig. 10b), while most of the gas–liquid masstransfer is expected to take place near the rim of the disc. No effectof the liquid flow on the size of the gas bubbles is observed, as wasexpected, since the influence of the liquid flow rate on the shearforce near the gas inlet is negligible.

The volumetric gas–liquid mass transfer coefficient is calcu-lated using the assumption that the liquid phase is ideally mixed.This assumption is based on the velocity profiles in single phaserotor–stator systems, as described in Section 2. The influence ofthe presence of gas bubbles on the flow pattern is unknown. Thepresence of the gas bubbles could have a significant influence onthe formation of the boundary layers at the rotor and the stator,and thus on the mixing in the reactor. In the absence of mixing,the liquid is in plug flow, which affects the values of the volumetricmass transfer coefficient obtained from experiments, as shown inFig. 11b. The volumetric mass transfer coefficient is then lower, butstill the effect of liquid flow rate is observed. Although it is possiblethat the presence of gas bubbles affects the boundary layers, it isimprobable that this would result in complete plug flow behaviourof the liquid phase. This effect, if present, thus does not explain theliquid flow dependency observed.


The volumetric mass transfer coefficients are obtained using twodifferent measurement methods, as described in Section 3. Bothmethods give the same liquid flow dependency, so it is improbablethat the liquid flow dependency is the result of an experimental

−5 m3 s−1. (b) Detail cut from (a) of 1.5 cm by 1 cm. The stroboscope lamb is adjusted position of the gas bubble: the closer the shadow is, the closer the gas bubble is

dx.doi.org/10.1016/j.cep.2011.05.022




0 1 2 3

x 10−5

0

0.002

0.004

0.006

0.008

0.01

0.012a b

ε G (

mG3

mR−

3 )

Liquid flow rate (mL3 s−1)

φG

= 7.3 10−6 m3 s−1

φG

= 1.5 10−5 m3 s−1

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

0.4

0.5

0.6

radial position, r (m)

ε G (

mG3

mR−

3 )

φL = 0.5 10−5 m3 s−1

φL = 1 10−5 m3 s−1

φL = 1.5 10−5 m3 s−1

φL = 2 10−5 m3 s−1

φL = 2.5 10−5 m3 s−1

φL = 3 10−5 m3 s−1

Fig. 10. (a) The gas holdup estimated using the Wallis drift flux model, combined with the slip velocity relation of Richardson and Zaki [18,19], and Eq. 5 at h = 1 mm, ω =5 −1

is, res −6 3 −1 −5 3 −1

( �G = 1p

ewflsatiiim

vmkmmTtE

M

Ffl

2 rad s . The gas bubble radius used is taken from images of the gas bubbles, andb) The gas holdup as a function of the radial position in the spinning disc reactor, atositions, typically below 0.05 m.

rror. The inlet concentration is measured with a fiberoptic sensor,hich is located in the inlet tube of the reactor. An increasing liquidow rate will increase the pressure in this tube, which could pos-ibly affect the measurements. However, calibration of the sensort different flow rates, and thus pressures, showed no influence onhe volumetric mass transfer coefficient. The pressure in the reactortself does not depend on the liquid flow rate, since the outlet tubes relatively large, and therefore only has a small pressure drop. Thiss thus not the source of the influence of the liquid flow rate on the

ass transfer coefficient.An estimate of kGL is made using Eq. (10), leading to a

alue of 5 × 10−4 mL3 mi

−2 s−1. With a gas holdup of 0.07 (esti-ated from the images for �G = 1.5 × 10−5 m3 s−1), this leads to

GLaGL = 0.06 mL3 mR

−3 s−1. The measured value of kGLaGL = 0.16L

3 mR−3 s−1, which is thus more than a factor two higher, which

eans that Eq. (10) underestimates the mass transfer coefficient.o obtain the value of kGLaGL at the lowest rotational disc speed,


he kGL has to be an order of magnitude higher than predicted byq. (10), which indicates that other effects play a role.

The cause of the liquid flow rate dependency is thus not clear.ore information has to be available about the local gas and liquid

0 1 2 3

x 10−5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8a


k GLa G

L (

m3 L m

−3

R s

−1 )

φG

= 7.3 10−6 m3 s−1

φG

= 1.5 10−5 m3 s−1

3−

3−

1

ig. 11. Volumetric mass transfer coefficient at RD = 0.135, h = 1 mm and ω = 52 rad s−1. Tow rate. (a) Calculated assuming the liquid phase to be ideally mixed. (b) Calculated usi

pectively, 6.5 mm and 10 mm at �G = 7.3 × 10 m s and �G = 1.5 × 10 m s ..5 × 10−5 m3 s−1. The influence of the liquid flow rate is only observed at low radial

velocities in the rotor stator spinning disc reactor, which is out ofscope of this paper, but part of future research. All the other mea-surements presented in this paper are therefore performed at thesame liquid flow rate (3 × 10−5 m3 s−1), where the mass transfercoefficient reaches a constant value.

4.3. Rotor–stator distance

The volumetric mass transfer coefficient increases with decreas-ing rotor–stator distance, as is shown in Fig. 12a. The product ofthe volumetric mass transfer coefficient and the reactor volume isshown in Fig. 12b; this quantity represents the overall mass trans-fer rate, divided by the driving force. kGLaGLVR is a factor 2 higher at1 mm rotor–stator distance than at 2 mm for rotational disc speedsbelow 70 rad s−1. In this flow regime all the gas is present as flat gasbubbles (see Fig. 7), where the main gas–liquid mass transfer willtake place from the gas bubble to the liquid film on the rotor and


the stator. The gas–liquid interfacial area per unit reactor volumeof this liquid film will approximately double when the rotor–statordistance decreases from 2 mm to 1 mm. The liquid film at 2 mmrotor–stator distance, however, shows a different behaviour than

b

0 1 2 3

x 10−5

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16


k GLa G

L (

mL m

R s

)

φG

= 7.3 10−6 m3 s−1

φG

= 1.5 10−5 m3 s−1

he volumetric gas–liquid mass transfer coefficient decreases with increasing liquidng the assumption that the liquid phase behaves as plug flow.

dx.doi.org/10.1016/j.cep.2011.05.022




0 50 100 150 200 2500

0.5

1

1.5

2

2.5


k GLa G

L (

m3 L m

−3

R s

−1 )

RD

= 0.135 m, h = 1 mm

RD

= 0.135 m, h = 2 mm

RD

= 0.135 m, h = 5 mm

0 50 100 150 200 2500

0.5

1

1.5

2

2.5

3

3.5bax 10

−4


k GLa G

LVR (

m3 L s

−1 )

RD

= 0.135 m, h = 1 mm

RD

= 0.135 m, h = 2 mm

RD

= 0.135 m, h = 5 mm

Fig. 12. (a) Volumetric mass transfer coefficient at RD = 0.135, �L = 3 × 10−5 m3 s−1, and �G = 1.5 × 10−5 m3 s−1. kGLaGL increases with decreasing rotor–stator distance. (b)V �L = 3

t rad s−

i

aumtTnraFl

fitdrb(bTg

a

Fti

olumetric mass transfer coefficient multiplied by the reactor volume at RD = 0.135,

he mass transfer at 1 mm rotor–stator distance is twice as high as at 2 mm; above 70s lower in the whole range of rotational disc speeds.

t 1 mm, as can be seen in Fig. 13. Ripples are observed in the liq-id film, which are not present at 1 mm. No effect of this on theass transfer rate is observed, however, only the decrease by a fac-

or of 2, due to the factor 2 decrease in gas–liquid interfacial area.he gas–liquid mass transfer at 5 mm rotor–stator distance is sig-ificantly lower than at 1 and 2 mm. The large gas bubbles, at lowotational disc speeds, do fill a large part of the whole reactor heightt 5 mm, but no film layer at the stator is present, as can be seen inig. 13. The rate of mass transfer is therefore less than a factor of 5ower than at 1 mm rotor–stator distance.

Suprisingly, the product of the volumetric mass transfer coef-cient and the reactor volume at rotational disc speeds higherhan 70 rad s−1, is approximately equal for 1 and 2 mm rotor–statoristance. The total rate of mass transfer is independent of theotor–stator distance in this region, which is unexpected. The bub-les are smaller than the rotor–stator distance in both cases, Eq.11) is therefore applied to get an estimate of the gas holdup ratioetween the experiments at 1 and 2 mm rotor–stator distance.he bubbles are assumed to be spherical and uniform in size, theas–liquid interfacial area is then:


GL = 6εG

db(19)

ig. 13. Gas bubbles at 1, 2 and 5 mm rotor–stator distance, at �G = 1.5 × 10−6 m3 s−1, �L =o the situation with 1 mm rotor–stator distance. At 5 mm rotor–stator distance, the gas bun the reactor is indicated in Fig. 5.

× 10−5 m3 s−1, and �G = 1.5 × 10−5 m3 s−1. At rotational disc speeds below 70 rad s−1,1 the mass transfer rates are equal. The mass transfer at 5 mm rotor–stator distance

Combined with Eq. (11), this leads to the following relation for thevolumetric mass transfer coefficient:

kGLaGL ∝ ω(11/16)

h(1/24)V (1/4)R

εG

db(20)

The product of the reactor volume and the volumetric masstransfer coefficient for 1 and 2 mm rotor–stator distance is equal:

[kGLaGLVR]h=1 = [kGLaGLVR]h=2 (21)

The ratio of the gas holdups is therefore:

[εG]h=1

[εG]h=2= [h1/24db]h=1

[h1/24db]h=2

[V3/4R ]h=2

[V3/4R ]h=1

(22)

The ratio of reactor volumes is known, the ratio of bubble diam-eters can be estimated from the images of the gas–liquid flow (e.g.Fig. 7). At 157 rad s−1, the average gas bubble diameter at 1 and2 mm rotor–stator distance is 0.6 and 0.9 mm, respectively. Thisleads to:


[εG]h=1

[εG]h=2= 0.6

0.9× 0.97 × 1.55 = 1.0 (23)

The gas holdup is thus equal for the two rotor–stator distances,in spite of the change in reactor volume, which means that the total

3 × 10−5 m3 s−1 and ω = 26 rad s−1. Liquid ripples are observed at 2 mm, in contrarybbles are not squeezed in between the rotor and stator. The position of the pictures

dx.doi.org/10.1016/j.cep.2011.05.022




0 1 2 3

x 10−5

0

0.005

0.01

0.015

0.02ε G

(m

G3 m

R−3 )

Liquid flow rate (mL3 s−1)

h = 1mmh = 2 mm

Fig. 14. The gas holdup estimated using the Wallis drift flux model, combined withthe slip velocity relation of Richardson and Zaki [18,19] and Eq. (6), at ω = 157 rad s−1

agd

ahflifladattraTbbpflfivdtd

stlrrIfwTttfdi

a

0 1 2 3 4 5 60

0.5

1

1.5

2

2.5

Energy dissipation rate (MW mR−3)

k GLa G

L (

m3 L m

−3

R s

−1 )

RD

= 0.135 m, h = 1 mm

RD

= 0.135 m, h = 2 mm

RD

= 0.135 m, h = 5 mm

Fig. 15. Volumetric mass transfer coefficient as function of the energy dissipationrate at RD = 0.135, �L = 3 × 10−5 m3 s−1, and �G = 1.5 × 10−5 m3 s−1. For 1 and 2 mmrotor–stator distance the rates of mass transfer per unit of energy dissipation are

nd �G = 1.5 × 10−5 m3 s−1. The gas bubble radius used is taken from images of theas bubbles, and is, respectively, 0.3 mm and 0.45 mm for 1 and 2 mm rotor–statoristance.

mount of gas in the case of 2 mm rotor–stator distance is 1.8 timesigher than for 1 mm. This is not expected based on the Wallis driftux model, as shown in Fig. 14, where the difference in gas holdup

s more than a factor 2. As mentioned in Section 2, the Wallis driftux model is not valid in the case of small gas bubbles in the bound-ry layers, since the residence time of the gas bubbles is stronglyependent on the axial position. Gas bubbles in the rotor bound-ry layer have a lower inward radial velocity, while gas bubbles inhe stator boundary layer have an increased radial velocity due tohe centripetal boundary layer. An increase in liquid flow rate willesult in a thinner rotor boundary layer with a lower radial velocitynd a thicker stator boundary layer with a higher radial velocity.his will decrease the residence time, and thus the gas holdup, foroth the gas bubbles in the rotor boundary layer and the statoroundary layer. The area perpendicular to the liquid flow is pro-ortional to the rotor–stator distance; the influence of the liquidow rate will thus be higher for 1 mm rotor–stator distance than

or 2 mm rotor–stator distance. The increase in thickness and veloc-ty of the stator boundary layer and the decrease in thickness andelocity of the rotor boundary layer is apparently large enough toecrease the gas holdup for 1 mm rotor–stator distance, and thushe gas–liquid mass transfer, to the value obtained at a rotor–statoristance of 2 mm.

In the case of a rotor–stator distance of 5 mm, at rotational discpeeds above 100 rad s−1, the gas bubbles are approximately a fac-or 2–3 larger than at 1 mm rotor–stator distance, which results in aower gas–liquid interfacial area, and thus in a lower mass transferate. The difference in gas bubble size is due to the change in flowegime, when increasing the rotor–stator distance from 2 to 5 mm.n the case of 5 mm rotor–stator distance two boundary layers areormed, one at the rotor and one at the stator, separated by a regionith a constant tangential velocity, as shown in the top part of Fig. 2.

hese boundary layers are merged at 1 and 2 mm rotor stator dis-ance, as shown in the bottom part of Fig. 2. The shear force, causinghe break off of the gas bubbles at the gas inlet, is thus much loweror 5 mm rotor–stator distance than for 1 and 2 mm rotor–stator


istance, resulting in larger gas bubbles, and thus a lower gas–liquidnterfacial area and volumetric mass transfer coefficient.

Fig. 15 shows the volumetric gas–liquid mass transfer coefficients a function of the rate of energy dissipation in the system. The

equal. However, a higher rate of energy dissipation, and thus of mass transfer, can bereached with 1 mm rotor–stator distance. The volumetric mass transfer coefficientfor 5 mm is significantly lower.

values for 1 and 2 mm rotor–stator distance are on the same line, theenergy dissipation thus determines the mass transfer rate. Highermass transfer rates can be reached with a rotor–stator distance of1 mm, though, since the energy dissipation rate per unit volume ishigher at the same rotational disc speed. The values of kGLaGL inthe small bubble region are fitted with a power law model, withthe energy dissipation rate as independent variable, resulting inan exponent of 0.75 ± 0.08. The surface renewal rate is determinedby the size and the velocity of the turbulent eddies, the value ofkGL thus depends on the energy dissipation rate to the power 1/4,as shown in Eq. (11). The following dependency of the gas–liquidinterfacial area on the energy dissipation rates is therefore found:

kGLaGL ∝ E0.75d , kGL ∝ E1/4

d⇒ aGL ∝ E0.5

d ,

Ed ∝ ω11/4h−(1/6)

VR⇒ aGL ∝ ω1.4

h0.08V0.5R

(24)

The gas–liquid interfacial area is, in this regime, thus a functionof the rotational disc speed to the power 1.4 ± 0.2. The gas–liquidinterfacial area is a combination of the gas holdup and the gas bub-ble size (see Eq. (19)). Meeuwse et al. [1] showed that, for the discwith 0.066 m radius, the gas holdup increases with increasing rota-tional disc speed. The gas–liquid interfacial area increases morerapidly, due to the decreasing gas bubble size. The same thus holdsfor the rotor–stator with a disc of 0.135 m radius. The gas–liquidmass transfer per unit of energy dissipation at 5 mm rotor–statordistance is much lower. This decrease is probably due to the signif-icantly lower gas–liquid interfacial area, which is a result from thetransition from the regime with a merged boundary layer to theregime with the separated boundary layers.

4.4. Rotor radius

The volumetric gas–liquid mass transfer coefficient as a func-


tion of rotational disc speed, for two rotor diameters, is shown inFig. 16. At rotational disc speeds above 100 rad s−1, the volumet-ric gas–liquid mass transfer coefficient for the disc with a radiusof 0.135 m is higher than for the 0.066 m disc. Below 100 rad s−1,

dx.doi.org/10.1016/j.cep.2011.05.022

ARTICLE ING Model


12 M. Meeuwse et al. / Chemical Engineering

0 50 100 150 200 2500

0.2

0.4

0.6

0.8

1

1.2

1.4


k GLa G

L (

m3 L m

−3

R s

−1 )

RD

= 0.135 m, h = 1 mm

RD

= 0.066 m, h = 1 mm

Fig. 16. Volumetric mass transfer coefficient at h = 1 mm, and �G = 7.3 × 10−6 m3 s−1.�L = 3 × 10−5 m3 s−1 at RD = 0.135 m, and �L = 6.7 × 10−6 m3 s−1 at RD = 0.066 m. At ar −1

ti

ht3lwtilatt

td

Fd�d

otational disc speed below 100 rad s , the volumetric mass transfer coefficient forhe 0.135 m disc is smaller than for the 0.066 m disc, at higher rotational disc speedst is higher.

owever, the volumetric gas–liquid mass transfer coefficient forhe 0.066 m disc is higher. The reactor volume differs by a factor.4, therefore the overall mass transfer, kGLaGLVR, is at 80 rad s−1

arger for RD = 0.135 m. At 52 rad s−1, both have the same value,hich is unexpected, since the gas bubbles have a longer path to

ravel in the case of RD = 0.135 m. The liquid flow rate does have annfluence, since it is more than four times higher at RD = 0.135 m,eading to a decrease in gas holdup and thus in gas–liquid interfacialrea. Additionally, smaller gas bubbles are formed at RD = 0.066 m;his decreases the contact time of the gas with the liquid film onhe rotor and the stator, thereby increasing kGL.


Fig. 17 shows the gas–liquid mass transfer coefficient as a func-ion of the rate energy dissipation, for the two disc radii, and theifferent rotor–stator distances used. The gas–liquid mass trans-

0 0.2 0.4 0.6 0.8 1 1.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Energy dissipation rate (MW mR−3)

k GLa G

L (

m3 L m

−3

R s

−1 )

RD

= 0.135 m, h = 1 mm

RD

= 0.066 m, h = 1 mm

ig. 17. Volumetric mass transfer coefficient as a function of the rate of energyissipation, at �G = 7.3 × 10−6 m3 s−1. �L = 3 × 10−5 m3 s−1 at RD = 0.135 m, andL = 6.7 × 10−6 m3 s−1 at RD = 0.066 m. The rate of mass transfer per unit of energyissipation is higher for the 0.066 m disc than for the 0.135 m disc.


fer, at equal energy dissipation rate, is higher for the disc with RD

= 0.066 m than for the reactor with RD = 0.135 m. The rotationaldisc speed is much larger with the small disc at the same energydissipation rate, therefore the small disc system is filled with smallbubbles with surface renewal due to turbulent eddies, while thelarge disc system has the large gas bubbles with the mass transferoccurring in the liquid film at the rotor and at the stator. The energydissipation rate in the large disc system can be increased tremen-dously, up to 6 MW m−3, compared to 0.4 MW m−3 in the small discsystem. This 15-fold increase in energy dissipation rate leads to a3-fold (0.43 mL

3 mR−3 s−1 with RD = 0.066 m to 1.36 mL

3 mR−3 s−1

with RD = 0.135 m) increase in gas–liquid mass transfer rate. Themass transfer per unit of energy dissipation ((kGLaGL/Ed)) for thedisc with a radius of 0.066 m is 1.1 mL

3 MJ−1, while it is 0.3 mL3

MJ−1 for the 0.135 m disc at the same gas flow rate.The choice of the disc radius in an industrial scale spinning disc

reactor depends on the process itself. When high mass transfercoefficients are needed, e.g. to obtain a higher selectivity, or todecrease the reactor volume for safety purposes, it is beneficial touse a larger disc size. However, the energy dissipation rate, and thusthe operational costs, are higher than in the case of a larger num-ber of smaller discs. For processes where the energy costs duringoperation play an important role in the overall cost of the process,the use of smaller discs is preferred.

5. Conclusions

5.1. Liquid flow rate

The volumetric mass transfer coefficient decreases with increas-ing liquid flow rate. A model for the gas holdup, based on theWallis drift flux, predicts a decrease in gas holdup, and thus in masstransfer, but the effect observed experimentally is much larger. Themodel does not incorporate the complex flow pattern in the two-phase rotor–stator spinning disc reactor. More has to be knownabout the local velocities to accurately describe the effects of theliquid flow rate on the gas–liquid mass transfer in the spinning discreactor.

5.2. Rotor–stator distance

The volumetric gas–liquid mass transfer coefficient in thespinning disc reactor with a disc radius of 0.135 m increaseswith increasing rotational disc speed, increasing gas flow rate,and decreasing liquid flow rate. At rotational disc speedsbelow 70 rad s−1, the total gas–liquid mass transfer with 1 mmrotor–stator distance is twice as high as for 2 mm rotor–statordistance, since the mass transfer mainly occurs at the liquid filmbetween large bubbles and the rotor/stator. At rotational discspeeds above 100 rad s−1, the gas is dispersed as small spheri-cal bubbles. The total gas–liquid mass transfer for 1 and 2 mmrotor–stator distance is equal in this case, for 5 mm it is much lower.The volumetric gas–liquid mass transfer coefficient as a function ofenergy dissipation rate is also equal for 1 and 2 mm rotor–statordistance. At 1 mm, however, higher values of the energy dissipa-tion rate, and thus the volumetric gas–liquid mass coefficient, canbe obtained.

5.3. Rotor radius

The volumetric gas–liquid mass transfer coefficient of the disc


with 0.135 m radius is lower than with the 0.066 m disc below100 rad s−1. Above this rotational disc speed it is significantlyhigher. The gas–liquid mass transfer per unit of energy dissipa-tion (kGLaGL/Ed) is around 0.3 mL

3 MJ−1 at 0.135 m radius, while

dx.doi.org/10.1016/j.cep.2011.05.022

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t is 1.1 mL3 MJ−1 at a radius of 0.066 m. The maximum vol-

metric gas–liquid mass transfer coefficient obtained with the.135 m disc is 2.5 mL

3 mR−3 s−1, at �L = 1.5 × 10−5 m3 s−1, and

G = 1.5 × 10−5 m3 s−1 and a rotational disc speed of 209 rad s−1.he maximum volumetric mass transfer coefficient thus increasesith increasing disc radius, but from energetic point of view scalingp by increasing the number of rotors is preferred above scaling up

n rotor size.

cknowledgement

The authors gratefully acknowledge the financial support by theutch Technology Foundation STW.

eferences

[1] M. Meeuwse, J. van der Schaaf, B.F.M. Kuster, J.C. Schouten, Gas–liquid masstransfer in a rotor–stator spinning disc reactor, Chem. Eng. Sci. 65 (2010)466–471.

[2] M. Meeuwse, J. van der Schaaf, J.C. Schouten, Mass transfer in a rotor–statorspinning disk reactor with cofeeding of gas and liquid, Ind. Eng. Chem. Res. 49(2010) 1605–1610.

[3] M. Meeuwse, S. Lempers, J. van der Schaaf, J.C. Schouten, Liquid–solid masstransfer and reaction in a rotor–stator spinning disc reactor, Ind. Eng. Chem.Res. 49 (2010) 10751–10757.

[4] S. Poncet, M.P. Chauve, R. Schiestel, Batchelor versus Stewartson flow structuresin a rotor–stator cavity with throughflow, Phys. Fluids 17 (2005) 075110.

[5] M. Itoh, Y. Yamada, S. Imao, M. Gonda, Experiments on turbulent flow due toan enclosed rotating disk, Exp. Therm. Fluid Sci. 5 (1992) 359–368.


[6] J.W. Daily, R.E. Nece, Chamber dimension effects on induced flow and fric-tional resistance of enclosed rotating discs, J. Basic Eng. Trans. ASME 82 (1960)217–232.

[7] L. Schouveiler, P. le Gal, M.P. Chauve, Instabilities of the flow between a rotatingand a stationary disk, J. Fluid Mech. 443 (2001) 329–350.

[

[

PRESS and Processing xxx (2011) xxx– xxx 13

[8] D. Dijkstra, G.J.F. van, Heijst, The flow between two finite rotating disks enclosedby a cylinder, J. Fluid Mech. 128 (1983) 123–154.

[9] M. Djaoui, A. Dyment, R. Debuchy, Heat transfer in a rotor–stator system witha radial inflow, Eur. J. Mech. B: Fluids 20 (2001) 371–398.

10] S. Poncet, R. Schiestel, M.P. Chauve, Centrifugal flow in a rotor–stator cavity, J.Fluids Eng. 127 (2005) 787–794.

11] A. Randriamampianina, L. Elena, J.P. Fontaine, R. Schiestel, Numerical predictionof laminar, transitional and turbulent flows in shrouded rotor–stator systems,Phys. Fluids 9 (1997) 1696–1713.

12] H. Iacovides, I.P. Theofanopoulos, Turbulence modeling of axisymmetric flowinside rotating cavities, Int. J. Heat Fluid Flow 12 (1991) 2–11.

13] G.K. Batchelor, Note on a class of solutions of the Navier–Stokes equations rep-resenting steady rotationally-symmetric flow, Q. J. Mech. Appl. Math. 4 (1951)29–41.

14] J.M. Owen, R.H. Rogers, Flow and Heat Transfer in Rotating-Disc Systems. Vol.1. Rotor–Stator Systems, Research Studies Press, Taunton, 1989.

15] S. Poncet, M.P. Chauve, P. Gal le, Turbulent rotating disk flow with inwardthroughflow, J. Fluid Mech. 522 (2005) 253–262.

16] G. Duhar, C. Colin, Dynamics of bubble growth and detachment in a viscousshear flow, Phys. Fluids 18 (2006) 077101.

17] K. Terasaka, S. Murata, K. Tsutsumino, Bubble distribution in shear of flow ofhighly viscous liquids, Can. J. Chem. Eng. 81 (2003) 470–475.

18] G.B. Wallis, One-dimensional Two-phase Flow, 1st ed., McGraw-Hill, New York,1969.

19] J.F. Richardson, W.N. Zaki, The sedimentation of a suspension of uniformspheres under conditions of viscous flow, Chem. Eng. Sci. 3 (1954) 65–73.

20] L.P.B.M. Janssen, M.M.C.G. Warmoeskerken, Transport Phenomena Data Com-panion, 3rd ed., Delft University Press, Delft, 2001.

21] J.B.M. Schoenmaekers, Gas hold-up, bubble behaviour and mass transfer inthe spinning disk reactor, M.Sc. Thesis, Eindhoven University of Technology,2007.

22] J.A. Wesselingh, The velocity of particles, drops and bubbles, Chem. Eng. Pro-cess. 21 (1987) 9–14.

23] R. Clift, J.R. Grace, M.E. Weber, Bubbles, Drops and Particles, 1st ed., Academic


Press, New York, 1978.24] R. Higbie, The rate of absorption of a pure gas into a still liquid during short

periods of exposure, Trans. Am. Inst. Chem. Eng. 31 (1935) 365–389.25] J.C. Lamont, D.S. Scott, An eddy cell model of mass transfer into the surface of

a turbulent liquid, AIChE J. 16 (1970) 513–519.

dx.doi.org/10.1016/j.cep.2011.05.022

effect of rotor–stator distance and rotor radius on the rate of gas–liquid mass

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