shaping of gelling biopolymer drops in an elongation flow
TRANSCRIPT
Journal of Colloid and Interface Science 252, 297–308 (2002)doi:10.1006/jcis.2002.8511
Shaping of Gelling Biopolymer Drops in an Elongation Flow
Lars Hamberg, Pernilla Walkenstrom, and Anne-Marie Hermansson1
SIK, The Swedish Institute for Food and Biotechnology, P.O. Box 5401, SE-402 29 Goteborg, Sweden
Received November 6, 2001; accepted May 22, 2002; published online July 22, 2002
Shaping, defined as deformation in combination with gel forma-tion of gelatine and κ-carrageenan drops in an elongation flow, wasstudied. The focus was to investigate the possibility of shaping andfixating small drops in the diameter range 20 to 229 µm. In theshaping progress and the influence of experimental properties, theviscosity, temperature, and flow of the deforming fluid were exam-ined on the final drop shape. In the experiments a hot emulsion ofan aqueous biopolymer solution in silicone oil was injected into coldsilicone oil where a deforming elongation flow field existed. Afterinjection, a temperature decrease in the drops resulted in a gel for-mation of the biopolymer and a fixation of the deformed drop inthe flow. The shape was measured and the effect on the drop aspectratio was determined by image analysis. Over the total drop diame-ter range, κ-carrageenan was more ellipsoid-shaped than gelatine,with a maximum aspect ratio of 6 compared to 4 for gelatine. Forsmall drops, around 22 µm, it is possible to shape κ-carrageenan,but for gelatine small drops tend to be unaffected. An increase inviscosity, temperature, and flow resulted in an increase in the fi-nal fixated shape of the drops. The differences in drop deformationbetween the biopolymers were explained by drop–viscosity/oil dif-ferences and differences in the kinetics of gel formation. The differ-ent gel formation kinetics resulted in a short, well-defined, shapingprocess for κ-carrageenan, while for gelatine the process was morecomplex, with both deformation and relaxation present at differentstages. C© 2002 Elsevier Science (USA)
Key Words: shaping; elongation; flow; shape; deformation; κ-carrageenan; gelatine; drop; size.
INTRODUCTION
The deformation of a drop during flow has been studied for along time, but the use of a specific drop shape and its functional-ity is a poorly developed area. In order to use shape functionality,the deformation has to be permanent and fixated. The fixationand deformation processes often interact and affect one anotherand could therefore be treated as one process, shaping. Shap-ing is therefore defined here as the deformation of the drop andthe preservation of the shape when the desirable shape has beenaccomplished.
In this work the shaping of gelatine and κ-carrageenan emul-sion drops was studied. The deformation was achieved by
1 To whom correspondence should be addressed. Fax: +46 31 83 37 82.E-mail: [email protected].
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exposing the drops to drag forces in an extensional flow, therebyaccomplishing the formation of ellipsoid-shaped drops. At thesame time, introducing a gel formation of the biopolymer in thedrop preserves the shape by the solidification of the drop content.
Liquid drop deformation is a subject that has been studied fora long time and has been extensionally reviewed (1–3). Defor-mation of drops of Newtonian fluids in shear has been treatedboth theoretically and in practice. The theoretical treatmentsmostly involve the capillary number, Ca, in combination withthe viscosity ratio between the discontinuous drop phase and thecontinuous phase. Taylor started with a first-order expansion forsmall deformation in shear as early as the 1930s (4, 5), andnumerous successors have presented theoretical work for bothhigher order solutions and solutions for other types of flow (3).For hyperbolic flow the first-order equation for the deformation,D, is expressed as
D = a − b
a + b= 19λ + 16
16λ + 16Ca [1]
with the viscosity ratio, λ, as
λ = ηd
ηc[2]
and the capillary number, Ca, as
Ca = ηca0ε
σ. [3]
In the equations a is the longest axis within the drop, a0 is thediameter of the undeformed spherical drop, b is the shortest axison the deformed drop, µc the viscosity of the continuous phase,µd is the viscosity of the drop phase, σ the surface tension, andthe extensional rate is denoted ε. This theoretical description hasproved to be in good agreement with experimental data (6, 7).
Although earlier work dealt with deformation created in shearflow, more and more focus has shifted to other flow types, suchas extensional flow. It has been proved that extensional flow issuperior to shear flow in terms of creating an interfacial areaat the same imposed strain as well as the amount of energy re-quired for deforming a drop (8). Khayat et al., among others,have studied the deformation of drops in extensional flow bothby numerical simulation and with experiments (9). They inves-tigated the effects of elongation stress, viscosity ratio, drop size,
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298 HAMBERG, WALKENSTRinterfacial tension, and the elasticity of the dispersed and am-bient phases. The deformation process follows the behavior ofEq. [1].
When superimposing gel formation on deformation, the in-crease in the drop viscosity makes the theoretical treatment ofthe deformation strongly dependent on the gel formation. Com-mon to the two biopolymers used in this paper, gelatine andκ-carrageenan, is that they are cold-set, e.g., that they are in so-lution at temperatures over Tgel and form a gel at temperaturesbelow Tgel. The viscosity of the biopolymer solution, above Tgel,is strongly temperature-dependent and rises drastically just be-fore Tgel.
According to Djabouroav et al. (10, 11), the temperature-induced viscosity increase and the gel formation for gelatinewhen exposed to shear are related to the coil–helix conversionand then the percolation between the microgels formed. If thebiopolymer is exposed to high shear during the process, the gelformation is delayed until the shear is low again, and it will resultin a more fragile gel. In commercial gelatine, the Tgel and otherproperties, such as gel strength have large variations, and thevariation even exists within the same sample. The result could bethat the drop gel transition from solution to rigid will be extendedboth in time and in temperature and could be experienced asslow (12).
The gel formation properties of carrageenan (13–16) arestrongly dependent on the type of carrageenan and the coun-terions present in the solution. The ion-dependence makes itpossible to choose a suitable Tgel by introducing the proper ionsand ion strength with the solution. To ensure a fast and well-defined gel transition from solution to rigid, carrageenan of typekappa, κ , is favorable.
For large drops of gelatine, the combination gel formation anddeformation has been studied by Walther et al. (17). They foundthat rather complex shapes could be generated in a hyperbolicflow and that the shapes could be related to the specific area in theflow process where the final shape was achieved. They namedthese areas fixation zones and explained the shaping mecha-nism in terms of elongation, relaxation, and gel formation. Thelength of the drops was about 2 mm, and the shapes created had asurprisingly good reproducibility even for complex shapes. Re-cently, work with small drops, for shear flow in combination withgel formation of biopolymer mixtures, has been presented (18).The drops obtained were ellipsoidal and varied widely in length.
The aim of this study was to investigate the shaping of smallbiopolymer drops under the combination of cold-set gelling anddeformation by extensional flow. Specific parameters of interestin this study were the kinetics in terms of fast/slow gel forma-tion (κ-carrageenan/gelatine); small drop sizes (down to 22 µm);deformation forces on the drop (viscosity of the oil in the contin-uous phase and rate of elongation); and cooling of the biopoly-mer (temperature of the continuous phase). The shaping hasbeen evaluated in terms of deformation and been presented with
a chosen shape factor with the aim of making it possible to tailorthe shape of a biopolymer drop.¨ M, AND HERMANSSON
MATERIALS AND METHODS
Biopolymers
Gelatine, with Bloom strength 250 and a molecular weight of118 kDa, was obtained from Extraco, Klippan, Sweden.
κ-Carrageenan from Eucheuma cottonii type III was pur-chased from Sigma Chemicals (St. Louis, MO). To obtain thepotassium form, the κ-carrageenan was prepared by ion ex-change with a commercial ion-exchange resin at 85◦C, AG50W-X8, Bio–Rad, according to the procedure described byHermansson et al. (16).
Oil
The oil used as the continuous phase in the experiments aswell as the continuous phase in the emulsion was silicone oil,polydimethylsiloxane, PDMS, named Wacker Silicone FluidAK5 000 and Wacker Silocone Fluid AK10 000, from Wacker-Chemie GmbH, Burghausen, Germany. For the experiments,both low- and high-viscosity oils were prepared. The low-viscosity oil, consisting exclusively of AK5 000, had a viscosityof 7.5 Pa s at 5◦C and 6.7 Pa s at 10◦C. The high-viscosity oilwas prepared from equal amounts of AK5 000 and AK10 000and had a viscosity of 10.6 Pa s at 5◦C and 9.4 Pa s at 10◦C.The viscosities were measured on a Bohlin VOR Rheometer(Bohlin Instruments, Chichester, UK) equipped with the Mil-lennium software (Redogen i Lund, Oved, Sweden).
Additives
As an emulsifier in the emulsion, a cetyldimethicone copolyolwith the trade name Abil EM 90 from Goldschmidt AG (Essen,Germany) was used. To increase the quality of the micrographsand in order to reduce the image measurement error, aniline bluewas used as a contrast agent. Aniline blue was obtained fromRiedel De Haen AG (Seelze-Hannover, Germany).
Four-Roll Mill
A four-roll mill (4-RM), Fig. 1 (5), was built and adapted toa microscope by the workshop of the Institute of Food Science/Food Process Engineering at ETH (Zurich, Switzerland). Thiswas described in more detail earlier (19). By letting one pair ofthe rolls rotate in one direction and the other pair in the oppositedirection, a hyperbolic flow field is generated in the center ofthe chamber (20). By placing a drop at the center line, close tothe stagnation point in the center, the drop will be exposed toan extensional flow. First the drop will be accelerated from thestagnation point to the narrowest gap between the rollers andthen, after passing the narrowest gap, the drop will be exposed
to retardation in the outflow from the rollers (17). In the investi-gations, the speeds of the rolls were 10 and 30 rpm.
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GELLING BIOPOLYMERFIG. 1. A schematic picture of the 4-roll mill: (a–d) rollers, (e) injectionpoint, (f) sample chamber. Distances are in millimeters.
Preparation
Gelatine or κ-carrageenan was mixed with 0.5% aniline blueand water to a concentration of 15% for gelatine and 1% forκ-carrageenan. The water was pure deionized for gelatine, andfor κ-carrageenan the deionized water was adjusted with NaCl toa concentration of 100 mM. The water solution was then heatedto 90◦C and held at 90◦C for 15 min. The viscosity of the watersolutions was 40 mPas and 8 mPas at 30◦C for gelatine andκ-carrageenan, respectively. A volume of 400 µl of the watersolution was mixed into 30 g of silicone oil and stirred into anemulsion with drops with a maximum diameter of 1 mm. Theemulsion was degassed and again tempered to 90◦C. Emulsifierwas added and the emulsion was gently stirred by hand until thesize of most of the drops was estimated to be less than 500 µm.The emulsion was again degassed and tempered to 90◦C.
Drop Deformation Process
End shape experiments. To deform the drops in the emulsionin the end shape experiments, the following process was used:The continuous oil phase in the 4-RM was tempered to 5 or10◦C. The rollers were started and run in advance to ensurethat a steady-state flow field had been developed. A volume of50 µl of the tempered emulsion was injected with a pipette,with a tip less than 1 mm, into the flow field at a point on thecenter line 3.5 mm downstream from the center of the 4-RM.The emulsion followed the center streamline from the center,between the rollers, and out to the outer part of the 4-RM. Whenmost of the drops had run through between the rollers, the flowwas stopped. The emulsion was kept in the continuous fluid for60 s to ensure that the drops had gelled and become fixated.Finally, the drops were gently taken out of the 4-RM and placedon a slide for further microscopy studies. To validate the impact
of the prehistory before the process, emulsion was also injectedN ELONGATION FLOW 299
into an immovable flow, following the same procedure. Dropsfrom these experiments are called unprocessed in the results.
Shaping progress experiments. For the shaping progress ex-periments, the same setup was used as for the end shape experi-ments, with fixed conditions in the 4-RM of 10◦C, 10 rpm, andAK5000. A macroscope was placed at selected positions alongthe center line, in order to record the process details. The dropdeformation kinetics was investigated both in the flow and withstop-flow monitoring. With stop-flow, the relaxation of the dropwas monitored when the flow was stopped when the drops wereat different selected positions along the flow line.
Microscopy
Light microscopy was used to study the drop form in theend shape experiments. The processed emulsion from the4-RM on the slides was put, without further preparation, undera digitalized light microscope (Microphoto-FXA, Nikon Corp.,Tokyo, Japan) and color micrographs were taken of the drops ata 10× magnification.
Macroscopy
A macroscopic technique was used for the shaping progressexperiments. The macrographs were taken with a HamamatsuC6157, 3 CCD Color Video Camera (Hamamatsu PhotonicsK.K., Hamamatsu City, Japan) connected to a frame grabberin a workstation equipped with the image analysis programMicroGOP 2000/S (Contextvision AB, Linkoping, Sweden).The camera was equipped with a Zork MiniMakro 1 : 2, 8(Rodenstock, Germany), and the camera was tilted at an 15◦ an-gle from the normal of the oil surface in the 4-RM to obtain goodpicture quality. To avoid motion-induced blurring, the electronicshutter of the camera was set to 1/10,000 s. The macrographswere taken in gray scale.
Image Analysis
The analysis was done with the program MicroGOP 2000/Sfrom Contextvision AB (Linkoping, Sweden).
End shape experiments. The color micrographs, 768 ×576 pixels, were extracted into three gray scale images repre-senting blue, red, and green. The gray images had a pixel valuebetween 0 and 255. The blue and the red gray images werethresholded and converted into black and white images. Theblack and white images were manually compared with the grayimages and the images that best described the shape and size ofthe drop were chosen. In the chosen image all noise and objectsthat did not belong to the drop were removed. The program mea-sured the following parameters for each drop: area, perimeter,a, and b; a is defined as the maximum distance between any twopoints on the object’s circumference and b is defined as the max-imum distance in the object perpendicular to a. The Eq Diameterand Ratio were calculated from the measured parameters. TheEq diameter is the equivalent diameter defined as the diameter if
the object had been a perfect circle with the same area, and the
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300 HAMBERG, WALKENSTRratio is the ratio between a and b (see Shape Parameter belowfor more details).
Shaping progress experiments. The gray macrographs,768 × 288 pixels, for flow monitoring were adjusted for bettercontrast, thresholded, and converted to black and white images.The program then measured and calculated the same parame-ters as for the end shape measurements except for ratio. Ratiowas replaced with equivalent ratio, defined as a/Eq diameter(see Shape Parameter below for more details). To determine themagnification and position, reference points were marked andmeasured at the bottom of the 4-RM.
Investigated Parameters
The shape was tested against four parameters: the tempera-ture in the cell, the viscosity of the continuous phase in the cell,the speed of the rollers in the 4-RM, and the size of single dropsin the emulsions. For the first three parameters, an experimentaldesign with only a high and a low value was chosen. The sepa-rate values were chosen to be the minimum and the maximumfor the parameters that were functioning in the process for bothgelatine and κ-carrageenan. These values were experimentallydetermined by a separate prestudy. The values for cell tempera-ture were set to 5 and 10◦C. The oil viscosities were set to 5 and7.5 Pa s. Here the viscosity refers to the viscosity at a standardtemperature, 25◦C. Finally, the speeds of the rollers were set toa minimum of 10 rpm and a maximum of 30 rpm. The fourthparameter, size, was taken as equal to Eq Diameter. Size was notpossible to set in advance and therefore it was measured in themicrographs along with the response. Only drops with a size ofmore than 22 µm and less than 230 µm were measured and usedin the analysis. In total, 1073 drops were analyzed for gelatineand 991 drops for κ-carrageenan.
Statistics
In the end shape investigation, the statistical evaluation wasdone with multiple regression analysis. Temperature, oil, andspeed were coded with −1 and 1 for minimum and maximumvalues, respectively. Size and shape were transformed accord-ing to log transformation. All the transformations were done toensure a normal distribution for the parameters. The model fit-ted against was a linear model between the parameters and theresponse, without any cross or quadratic terms. The fitting wasdone according to the least squares method. The significancefor the coefficients in the model was tested separately with theT value against the t distribution. The significance for the modelwas tested with the F value compared to the F distribution.
Shape Parameter
The description of shape with only one parameter is not un-ambiguous for an ellipsoid-like drop. In the literature three mainparameters exist: the Taylor parameter, D, Ratio, A, and Equiv-
alent Ratio, AEq. The different parameters have different advan-tages and originate from separate areas. The Taylor parameter¨ M, AND HERMANSSON
(4, 5) is one of the most common parameters for characterizingdrop deformation and is defined as
D = a − b
a + b. [4]
The advantage of D is that it efficiently describes small defor-mations of drops with an ellipsoidal shape. The value of D goesfrom 0 for a perfect sphere to 1 for an infinitely long fiber. Al-though good for small deformations, D poorly describes the dif-ferences in shape when the difference between a and b becomeslarge. For large deformed drops, the parameter Aspect Ratio,here only called Ratio, A, is more frequently used instead (21):
A = l
d= a
b. [5]
Here l is the length of the drop and d is the diameter. For adrop l and d will correspond to a and b and the value of Awill vary from 1, for a sphere, to ∞, for an infinitely long drop,e.g., a fiber. The advantage of this parameter is that it describeslarge deformed particles and is easily apprehensible. The dis-advantage of the Aspect Ratio parameter is that it is sensitive tothe measurements of the often small parameter b. A small inac-curacy in the measurement could lead to large deviations, andunless the drop is fixated before measurement, the parameteris not favorable for drops. For large deformation and breakupof nonfixated drops, the parameter AEq (21) could be usedinstead:
AEq = L
DEq= a
DEq. [6]
L is here the length of the drop while the drop is deformed, thesame as a, and DEq is the diameter of the sphere with the equiv-alent area as the deformed drop. The advantage is that it is morerobust than the Aspect Ratio, but it is not easily apprehensible.The value of AEq starts with 1 for the sphere and goes to ∞, foran infinitely long fiber.
RESULTS
Shape
Typically shaped drops from the end shape experiment areshown in Fig. 2. All of them are approximately ellipsoidal andcould therefore obviously be well described with the two mea-surements of a and b. The Shape parameter is not unambiguous,and the parameter used will have an impact on the interpretationof the results, as pointed out in the previous section. To illus-trate the differences in value and how well they correspond toeasily visible differences in Fig. 2, three numbers are presentedin the upper corner of each micrograph. The three parametersare the Taylor parameter, the Ratio, and the Equivalent Ratio,
respectively. The differences between all micrographs are ap-proximately 0.5 units of the Ratio. The differences between
GELLING BIOPOLYMER IN ELONGATION FLOW 301
FIG. 2. The micrographs show the differences in value of the shape factor. The three numbers on the lefthand side of each drop are the Taylor parameter, Ratio,
and Equivalent Ratio.micrographs a, b, c, and d are clearly visible, but for e to hthe differences seem to be much less. Regardless of the shapeparameter chosen, the representation will always suppress andstrengthen different parts of the deformation that are possible todetect in the micrographs into a ellipsoidal shape. Conclusionsbased on the parameters will therefore also suppress some shapesand strengthen others. This is important to have in mind whendrawing conclusions from one Shape parameter. In this study,the Ratio = a/b is the first choice for the end shape results be-cause of its apprehensibility and good description of changesin large deformations. Hence, small deformations will be sup-pressed. Due to a relatively large measurement uncertainty inthe shaping progress experiments the Equivalent Ratio is usedthere also at the expense of the small deformations.
End Shape Experiment
Gelatine. In Fig. 3 the measured shape factor, the Ratio,is plotted as a function of size for all 1220 drops of gelatineand marked with different indications according to process, e.g.,speed. All the points from the unprocessed group, injected into
FIG. 3. Shape, i.e., Ratio, plotted against Size, i.e., Eq Diameter [µm], for
gelatine. The black cross indicates a roller speed of 30 rpm, black boxes referto 10 rpm, and the gray circles correspond to 0 rpm, e.g., unprocessed.an immovable flow, are along the x axis regardless of size. For thetwo processed groups of drops, an evident cone shape is presentin the figure. The group processed at high speed, 30 rpm, has acone with the narrow end for small sizes with shape factor valuesaround 1 and for the large end, values between 1 and 4 for sizesaround 200 µm. For the group with low speed, 10 rpm, the coneis narrower, with a large part of the values between 1 and 3at 200 µm. For almost all different sizes, the maximum valueswithin the 10-rpm group are lower than the maximum valuesin the 30-rpm group. For the points in Fig. 3, no differencesare made between different values of Temperature and for theViscosity of the continuous phase.
κ-Carrageenan. The corresponding presentation of mea-sured shape factor vs size for 1150 drops of κ-carrageenan isshown in Fig. 4. The unprocessed group differs from the othertwo; it has all its points lined up along the x axis at a shape factorvalue close to 1. The 10-rpm group has its points between shapefactors of 1 and 4.5 for all sizes. Finally, the 30-rpm group hasits points distributed between shape factor values of 1 and 6 forthe whole range of size investigated, 22 to 229 µm. Although
FIG. 4. Shape, i.e., Ratio, plotted against Size, i.e., Eq Diameter [µm], for
κ-carrageenan. The black cross indicates a roller speed of 30 rpm, black boxesrefer to 10 rpm, and the gray circles correspond to 0 rpm, e.g., unprocessed.
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302 HAMBERG, WALKENSTRTABLE 1Statistics for Gelatine
βi SE Ti F Significancea
Temperature −0.00819 1073 0.63 NoOil 0.047551 1073 3.67 YesSpeed 0.091554 1073 6.97 YesSize 1.300679 53.5 26.9 YesShape −0.67376 769 51.5 YesModel 597 739 YesResidual 172
a Critical values are taken from t1068 (2.1) and F1068,5 (0.98) at the 5% sig-nificance level.
the points in the processed groups are well spread in their inter-vals, sufficiently more points are located in the lower regions ofthe shape factor interval. For the points in Fig. 4, no differenceswere made between different values of temperature and for theviscosity of the continuous phase.
Statistics
Model and significance. The simple modeling of a leastsquare fit to a liner relation between drop size, roller speed,temperature in the cell, and viscosity of the continuous phase,and to the response shape, was carried out with a multiple regres-sion analysis. The model is presented in Eq. [7] and the valuesfor the different parameters are presented in Table 1 for gelatineand in Table 2 for κ-carrageenan:
Y = XTβ. [7]
Here Y is Shape, X is Temperature, Viscosity, Speed, or Size,and β corresponds to β0, β1, β2, β3, β4. The parameters are re-calculated according to the transformations and coding detailedunder materials and Methods. For gelatine the tests resulted inpositive significance for the model and for all parameters exceptTemperature, and for κ-carrageenan the tests resulted in positivesignificance for the model and for all parameters including theTemperature in the investigated area.
TABLE 2Statistics for κ-Carrageenan
βi SE Ti F Significancea
Temperature 0.051617 991 4.20 YesOil 0.10434 991 8.51 YesSpeed 0.079597 991 6.41 YesSize 0.546638 70.7 12.0 YesShape −0.20581 212 16.6 YesModel 69.8 96.8 YesResidual 142
a Critical values are taken from t986 (2.1) and F986,5 (0.98) at the 5% signifi-cance level.
¨ M, AND HERMANSSON
FIG. 5. The β coefficients for the parameters are shown.
Comparison between the biopolymers. Figure 5 presentsthe β coefficients for gelatine and κ-carrageenan as barsgrouped according to the different parameters. The bars de-scribing Size effect show a large difference between gelatineand κ-carrageenan. The gelatine bar is more than twice as largeas the bar for κ-carrageenan. The opposite is found for the Oilparameter bars, with the κ-carrageenan bar more than double thesize of the gelatine bar. For the parameter Speed, both the barsare at approximately the same height. Finally, for the bars show-ing the Temperature effect, the κ-carrageenan value is higherthan the one for gelatine. The gelatine β coefficient representedby the bar is not significant. In Fig. 5, the value for β0 is ex-cluded; β0 represents the mean value of the transformed Shapefactor and corresponds to the retransformed values of 1.21 forgelatine and 1.62 for κ-carrageenan. The arithmetic means are1.35 and 1.89 for gelatine and κ-carrageenan, respectively.
Shaping Progress Experiments
The shaping progress results are presented in terms of thefixation zones, Fig. 6, similar to the results of Walther et al. (17).
FIG. 6. Enlarged area around the center line with fixation zones 1, 2, and 3.Letters c and i indicate the center and the injection point, respectively.
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FIG. 7. The macrographs show gelatine drops in a flow approximately 15 mm from the starting point. The left one was taken before the stop, and the right one
was taken 9 s after the stop.All three zones are located along the center line, and zone 1 startsafter the injection point and finishes approximately 20 mm fromthe center point, before the narrowest gap between the rollers.Zone 2 covers the area in the narrowest gap at a distance between20 and 35 mm from the center. Finally, zone 3 is located in theouter area after the gap, at a distance of 35 mm and onward awayfrom the center point.
In zone 1, at the center line, the flow velocity of the con-tinuous phase is constantly increasing through the area, withan estimated elongation rate of around 1 s−1 for the low rollerspeed and around 3 s−1 for the high speed. The flow speed of thecontinuous phase reaches its maximum in zone 2, with valuesaround 20 and 60 mm/s for low and high speeds, respectively.At the same time the elongation rate drops from positive to neg-ative with the same magnitude as that in zone 1. The flow alongthe center line is slowing and approaching immobility in zone 3.However, the drops are tending to leave the center line and de-tach to the left or right, instead of stopping. The elongation ratein the x axis direction is diminishing from the peak values in thebeginning of zone 3 of around − 1and − 3 s−1.
Stop-flow monitoring. The stop-flow results of the shaping
progress experiments are shown in Figs. 7 and 8 for gelatine and For κ-carrageenan the situation is different. In Figs. 9a and Figs. 9 and 10 for κ-carrageenan, respectively. In the figures, 9b, the marked drop in the middle in the macrograph showsFIG. 8. The macrographs show gelatine drops in a flow approximately 46 mmwas taken 10 s after the stop.
drops of biopolymer are shown in the middle of the shapingprocess, inside the 4-RM. The drops move from the left to theright in the macrographs, and the figures marked a were takenjust before stopping the rollers and figures marked b were takenaround 10 s later. The macrographs in Figs. 7 to 10 are nottaken exactly perpendicular to the surface, but slightly fromthe side. This means that the distance between the drops in themacrographs is a mixture of the distance both sideways and inheight in the real process.
In Figs. 7a and 7b, the gelatine emulsion is shown inside theaccelerating flow field in the later stages of zone 1. The twodrops, marked by the arrow in the middle of Fig. 7a, are thesame two drops that are marked in Fig. 7b. Before the stop oneof the drops is clearly deformed, but after the flow field is stoppedin Fig. 7b the drop has relaxed and the resulting deformation isvery small. Figures 8a and 8b show a position after the narrowestgap, in the retardation flow field in zone 3. Two marked dropsare coming in from the left in Fig. 8a. In Fig. 8b, taken 10 slater, after stopping the flow, the first drop has the same, verydeformed, shape as in Fig. 8a. The second drop, clearly visiblein Fig. 8a, but more diffuse in 8b, is less ellipsoidal shaped afterthe stop.
from the starting point. The left one was taken before the stop, and the right one
304 HAMBERG, WALKENSTROM, AND HERMANSSON
FIG. 9. The macrographs show κ-carrageenan drops in a flow approximately 8 mm from the starting point. The left one was taken before the stop, and the
right one was taken 12 s after the stop.hardly any difference in shape compared with the macrograph,Fig. 9b, taken at the same place 12 s later. The drop in the mid-dle of Fig. 9a is just before the stop in the center of zone 1.Figures 10a and 10b show the area between two rollers inthe narrowest gap in zone 2. Right after Fig. 10a was takenthe rollers were stopped and after 10 s the macrograph inFig. 10b was captured. The macrograph shows that the elon-gated drop from Fig. 10a has not changed shape after the flow hadstopped.
Flow monitoring. The gelatine and κ-carrageenan resultsfrom the flow monitoring measurements are shown in Figs. 11and 12. The graphs show the shaping progress, in terms of Equiv-alent Ratio against position along the center line. Here an alter-native definition of Equivalent Ratio is used where a, in thedefinition of Eq. [6], is restricted to having the same directionas the flow. The connected dots originate from the same dropin different macrographs taken in one sequence. Different areashave been monitored, and the result is shown by the separategroups in the horizontal direction, four groups for gelatine andthree for κ-carrageenan.
For both biopolymers, group I covers the injection point and
zone 1. The lines show an increase corresponding to an initial it is first strongly negative and ends with a minor negative value deformation. For group II, covering the area of zone 2, there but with a large confidence interval.FIG. 10. The macrographs show κ-carrageenan drops in a flow approximatelyright one was taken 10 s after the stop.
is a small increase for both biopolymers that, for group III forκ-carrageenan, levels out to a stable value in the beginning ofzone 3. Gelatine, in Fig. 11, continues with a steep decreasewithin group III, with an end value below 1. The last groupfor gelatine, group IV, shows the last part of zone 3 and hasone line that levels out around 1 and others that levels out atvalues below 0.5. The first behavior corresponds to a drop thatis fixated in a spherical shape, and the second behavior is froma drop that elongates and fixates in another direction than alongthe x axis. The number of measurements was reduced in groupIV due to problems with the contrast but the large differencesare reasonable and are believed to reflect behavior.
The average size, e.g., Eq Diameter, of the drops is 460 µmfor gelatine and 290 µm for κ-carrageenan. In Figs. 11 and12 values from drops larger than average are colored gray anddrops smaller than average are colored black. The grays have atendency to have higher values than the blacks in groups I, II, andIII and lower within group IV. The regression coefficients froma linear least square fit of the groups are presented in Table 3.The values are large and positive in zone 1 and still positivebut smaller from zone 2 for both gelatine and κ-carrageenan. Inzone 3, the value forκ-carrageenan is around 0, while for gelatine
21 mm from the starting point. The left one was taken before the stop, and the
305
chosen fo(10 and 3
GELLING BIOPOLYMER IN ELONGATION FLOW
p
FIG. 11. Evolution of the Equivalent Ratio for gelatine droDISCUSSION
Shape
κ-Carrageenan is on average more ellipsoidal shaped thangelatine. The higher mean values for the shape factor for κ-carrageenan, 1.62, compared to 1.21 for gelatine, show that it iseasier to shape κ-carrageenan than gelatine within the interval
r the parameters Temperature (5 and 10◦C), Speed0
of the gelatine drops is slower than that for κ-carrageenan andard the end
rpm), Oil (Ak 5000 and Ak7500), and Size (22 therefore relaxation of the gelatine drops occurs towFIG. 12. Evolution of the Equivalent Ratio for κ-carrageenan d
s. The measurements are grouped I to IV, from left to right.
and 230 µm). Also, the most shaped drops, with a shape fac-tor value above 5, are made of κ-carrageenan. One reason forthis is that the viscosity of κ-carrageenan is around five timessmaller than the viscosity for gelatine, 8 mPa s compared with40 mPa s at 30◦C. This is in good accordance with the investi-gations and theories of deformation of nongelling liquid dropsin Eqs. [1] to [3]. Another reason could be that the fixation
rops. The measurements are grouped I to III, from left to right.
O
306 HAMBERG, WALKENSTRTABLE 3Slopes for the Groups
Group
I II III IV
GelatineSlope 0.55 0.28 −0.74 −0.1695% confidence interval (±) 0.34 0.11 0.12 0.19
CarrageenanSlope 0.42 0.19 −0.04 —95% confidence interval (±) 0.16 0.14 0.04 —
of the process. This phenomenon is discussed in more detaillater.
The large spread in the shape factor between equal sized drops,visible in Figs. 3 and 4, and as large residuals after modelingcould in part be explained by the fact that single drops have beenstudied within an injected emulsion. Although the pipette usedfor the injection of the emulsion has a tip of less than 1 mm,it is considerable compared with the diameter of the drop. Thisresults in a position distribution in radii direction of the emulsion.Drops in the outer part of the emulsion, close to the continuousphase, will be exposed to a slightly different process than thedrops that are more in the center of the emulsion.
All the significant process parameters, for both biopolymers,show a positive correlation with the shape factor, see Fig. 5.Hence an increase in any parameter will correspond to increasedshape factor. Figure 5 also shows that κ-carrageenan is moreaffected by changes in Oil and Temperature, while a change inSize more clearly affects the explanation of the shape factor forgelatine than for κ-carrageenan within the measured interval.
Kinetics
The shaping progress investigations show that the differentgel formation kinetics of gelatine and κ-carrageenan create largedifferences in the shaping process for the biopolymers. As forlarge drops (17), the fixation zones provide the clue to the in-terpretation of the other parameters. The area before the inletbetween the rollers has been denoted fixation zone 1. The areabetween the rollers, around the point of nearest gap between therollers, as fixation zone 2, and the area in the outlet as fixationzone 3 (Fig. 6).
Gelatine. The slow gel formation of gelatine results in thevaried behavior for the drops shown in Figs. 7 and 8. The fixationapparently takes place in all three zones and from the stop-flowmacrographs from zone 1, Fig. 7, it is clear that the larger dropis not fixed and the slightly smaller drop is fixed. The same ap-pearance could be seen for the large drops early in zone 3, Fig. 8.One drop in Fig. 8a is already shaped and fixed, and the otheris not. Compared with the drops in the end shape experiments,
all the above-mentioned drops are among the largest found, andit is impossible to conclude anything for the smaller ones from¨ M, AND HERMANSSON
the macrographs. Nevertheless, the fact that one of the dropsin Fig. 7 is not fixed leads to the conclusion that relaxation ofthe gelatine drop is possible in zone 3. Most of the “relaxation”should be forced by the retardation flow and should not, strictlyspeaking, be named relaxation. “True” relaxation could also bepresent, as the forces acting in the center line direction on thedrop surface become smaller and smaller. From the flow moni-toring result in Fig. 11, it is concluded that slow gel formationmakes it possible to have not only one elongation of the largedrops, but two. The first elongation is located in zones 1 and 2and is orientated along the center line. The second elongation isperpendicular to the center line and occurs late in zone 3. Thisis the reason for Equivalent Ratio values below 1 in zone 3. Thisalso explains the drop orientation in Fig. 8. The second elonga-tion is due to the flow line divergence in the outflow and shouldonly exist for large drops that have on average a late fixation;see the discussion below about size.
κ-Carrageenan. For κ-carrageenan, with faster gel forma-tion than gelatine, the procedure of fixation takes place almostexclusively in zone 1 in the inlet. The reason for concluding thatthe shaping of κ-carrageenan occurs in zone 1 comes from shap-ing progress monitoring. The fact that the drops ofκ-carrageenando not substantially change shape when the flow is stopped, ei-ther in zone 2, Fig. 10, or late in zone 1, Fig. 9, indicates that theshaping and most of the fixation must be done before zone 2.This is also in good accordance with the flow monitoring resultsin Fig. 12, where the slope is almost 0 in zone 3 for all drops.The smaller drops already show the same behavior in zone 2.The reason for concluding that the shaping is located in zone 1and not earlier is that the drops have been found to be spheri-cal when they leave the injection point and enter zone 1. Thishas been found both in the shaping progress experiments andin the end shape experiments. In the end shape experiments theunprocessed drops have a spherical shape. These drops wereexposed to all the process treatments before the start of zone 1.It is also reasonable to believe from a theoretical point of view,since the flow is slow close to the stagnation point so that thesurface forces should be able to dominate and minimize the sur-face of the drop. The drops in shaping progress monitoring arelarger than those in the end shape experiment, but the conclu-sion should also apply to smaller sizes; see the discussion belowabout size.
Size
The end shape effect of drop size is different for gelatineand κ-carrageenan (see Figs. 3–5), but for both biopolymersthe shaping increases with size. The size effect for gelatinecontrols both the values of the shape factor and its spread, result-ing in the previously presented cone shape of the response. Forκ-carrageenan, size is less important for the spread, but still im-portant for the value. The explanation for the effect of size isthat size has a large effect on the temperature inside the drop.
Larger drops take longer to cool down and therefore couldbe fixed later in the process. This phenomenon is visible in
I
GELLING BIOPOLYMERFigs. 11 and 12, where the larger drops have both higher val-ues and steeper slopes. The difference in size effect between thebiopolymers is not due to differences in size distribution betweengelatine and κ-carrageenan, since the differences are minor. In-stead, different kinetics could be the reason. The differencesmake κ-carrageenan less sensitive to temperature differenceswith size, since the supposed time scale for κ-carrageenan gelformation could be short compared to the heat transfer timescale in the drop. The gel formation speed of the gel transfor-mation for gelatine is slower and could be on a time scale com-parable with the heat transfer time scale. This requires furtherstudy.
Size exerts an effect not only in combination with gel forma-tion speed but also in combination with the flow. Larger dropsare not exposed only to pure elongation flow, as they will exceedthe center flow line to a higher extent than small drops and beexposed to a mixture between elongation, shear, and elongationin other directions than along the center line. This is pronouncedin the outflow and causes the second elongation perpendicularto the center line late in zone 3 for gelatine found in Fig. 11. Thiswill not only affect the shape and the drop direction in the flowbut will also introduce a size effect, since deformation by shearis not size independent like elongation (9). In the end shape mea-surements, the result of this has been seen in very large drops,bigger than 230 µm, which are not shaped as perfect ellipsoidsbut have tilted ends.
Speed
The results of different roller speeds are visible in Figs. 3and 4. Higher speed creates more deformed drops for both gela-tine and κ-carrageenan. This is due to the larger forces actingon the drop surface at the higher roller speed, and it is in accor-dance with all previous studies and theories of drop deformationof fluids (see Eqs. [1] to [3]). For the drop deformation of gellingbiopolymers, the speed of the rollers also affects the residencetime and therefore the viscosity inside the drop at a specific pointin the process. More exactly, the time for a drop to reach a spe-cial point in the 4-RM becomes shorter with increasing speed,and a shorter time results in higher temperature inside the dropand therefore a lower viscosity if the cooling rate is not affectedby the speed. Lower viscosity of the drop should also contributeto a larger deformation. Still, assuming that the speed of therollers does not affect the cooling rate, the zone of fixation forthe drops could differ. This difference will have a minor impacton κ-carrageenan, since it is fast enough to fixate in zone 1 forall the different roller speeds, but for gelatine it could shift thefixation to a later zone. It is not possible to compare or ana-lyze the differing importance of these effects further from theinvestigations of this study.
Oil
The effect of oil in the continuous phase on end shape is
closely related to the viscous properties of the oil and the sur-face tension at the interface between oil and biopolymer. TheN ELONGATION FLOW 307
viscosity alters the flow and the viscosity ratio between the dropand the continuous fluid. The effect on shape is due to the fact thathigh-viscosity oil deforms the drops to a greater extent than low-viscosity oil. The differences in the effects of oil that are foundin values of the β coefficient for gelatine and κ-carrageenanpresented in Fig. 5 might be explained by differences in sur-face tension, but this has to be further investigated. The oil willalso affect the degree of relaxation in the outlet by introducinga larger resistance for the “true” relaxation in a higher viscos-ity fluid than in a lower viscosity fluid. This would result in apositive contribution to the β coefficient for gelatine.
Temperature in the Continuous Phase
The effect on temperature is significant, but small, forκ-carrageenan and not significant for gelatine. The reason forthis is not easy to find as temperature influences many of the pa-rameters that could affect the deformation of the drop. First ofall, an increase in temperature of the continuous phase reducesthe initial temperature difference between the drop and the con-tinuous phase. This slows down the cooling rate and thereby in-creases the temperature of a drop at certain place in the process,leading to lower viscosity. The slower cooling rate also leads toa shift of fixation to a later zone. Both these mechanisms causelarger deformation of the drop.
The increase in temperature also results in a decrease in theviscosity ratio, which could reduce deformation. The viscosityratio is decreased by the decrease in the viscosity of the oil. Inthe experiments the shift in the viscosity of the oil due to temper-ature is less than that due to type. Finally, temperature facilitatesa relaxation inside the outlet for gelatine drops both by the pre-viously mentioned viscosity decrease and by a supposed slowerfixation of the drop. To find out more about the temperature ef-fect and separate the positive and negative contributions so asto be able to use temperature as a shape controlling parameter,more investigations have to be carried out.
SUMMARY
In the experimental range of our setup, it is possible to tailorthe shape of the drops in an emulsion and create ellipsoid drops,even at small drop sizes. κ-Carrageenan is more easily shapedthan gelatine and is less size dependent. The fast kinetics ofκ-carrageenan result in early fixation in zone 1, while for gela-tine the slow kinetics spread fixation out in later areas, zones 2and 3. For large drops of gelatine, even a second drop elonga-tion, perpendicular to the center line, is possible. Speed and oilviscosity both have a clear positive correlation with shape, buttemperature has a more complex impact.
Based on the results from the shaping of gelatine andκ-carrageenan in an elongation flow, it is concluded that thefinal fixated end shape of the drops is closely connected withthe kinetics of gel formation. The impact of process parameters
is in accordance with well-known deformation theories. Hence,the kinetics of both gel formation and deformation have to be
308 HAMBERG, WALKENSTR
considered if one is to be able to tailor the shape of a biopolymerdrop and use its functionality.
ACKNOWLEDGMENTS
This work was carried out with financial support from the Swedish LiFTprogram (Future Technologies for Food Production) and the EU project Struc-ture Engineering of Emulsions by Micromachined Elongation Flow Process-ing (QLK-CT-2000-01543) within the RTD programme Quality of Life andManagement of Living Resources. The participates of the EU project, especiallyDr. Peter Fischer (ETH, Zurich, Switzerland), are gratefully acknowledged forvaluable discussions during the preparation of the manuscript. Ola Engwall(CTH, Goteborg, Sweden) is thanked for help with statistics.
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