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Drop deformation dynamics and gel kinetics in a co-flowing water-in-oil system
Journal of Colloid and Interface Science 286 (2005) 378–386 www.elsevier.com/locate/jcis
Drop deformation dynamics and gel kinetics in a co-flowing water-in-oil system Bernhard Walther a , Carsten Cramer b , Armin Tiemeyer b , Lars Hamberg a , Peter Fischer b , Erich J. Windhab b , Anne-Marie Hermansson a,∗ a SIK, The Swedish Institute for Food and Biotechnology, P.O. Box 5401, SE-402 29 Göteborg, Sweden b Swiss Federal Institute of Technology (ETH Zurich), Institute of Food Science and Nutrition, Laboratory of Food Process Engineering,
Schmelzbergstrasse 9, CH-8092 Zurich, Switzerland Received 27 August 2004; accepted 19 January 2005 Available online 21 February 2005
Abstract Drop deformation and superimposed gel kinetics were studied in a fast continuous-flow process for a water-in-oil system. Highly monodisperse drops were generated in a double capillary and then deformed passing through a narrowing rectangular channel geometry. Nongelling deformation experiments were used to establish the process and compare it with existing theories. Thereafter, temperature induced drop gelation was included to study its effect on deformation and gel kinetics on short timescales and at high temperature gradients. The disperse phase was a κ-carrageenan solution with additional sodium and potassium ions for gelation experiments. Sunflower oil was used for the continuous phases. Nongelling experiments showed that shear forces are able to deform drops into ellipsoids. A comparison with the small deformation theory by Taylor was surprisingly good even when drop deformation and flow conditions were not in steady state. Superimposed gelation on the deformation process showed clearly the impact of the altered rheological properties of the dispersed and continuous phase. Deformation first increased on cooling the continuous phase until the onset of gel formation, where a pronounced decrease in deformation due to increasing droplet viscosity/viscoelasticity was observed. Drop deformation analyses were then used to detect differences in gelation kinetics at high cooling rate within process times as short as 1.8 s. 2005 Elsevier Inc. All rights reserved. Keywords: Drop deformation; Shear flow; Gelation; Viscoelasticity; Viscosity; Carrageenan
1. Introduction Simultaneous drop deformation and gel formation are relevant to the formation of special emulsion and suspension properties. Flow processes and techniques are available to deform liquid emulsion droplets on their way to suspended gelled particles and thus imprint liquid–liquid deformation onto solid particles. This modifies the rheological properties of the emulsion or suspension [1,2]. To further develop such processes, drop deformation and gel kinetics have to be investigated under relevant flow conditions. * Corresponding author. Fax: +46-31-83-37-82.
E-mail address: [email protected] (A.-M. Hermansson). 0021-9797/$ – see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2005.01.054
In this investigation, drop generation, drop deformation, and gel kinetics are combined to study drop deformation in a fast continuous flow process with and without simultaneous gel formation under high temperature gradients. Particular attention is paid to the impact of gel formation, i.e., gel kinetics and the viscoelastic parameters of the disperse phase. Drops are generated in a double capillary. Deformation and gel formation occur downstream along a narrowing rectangular deformation channel, which deforms drops into ellipsoids. The process demands two continuous liquid phases, one for drop generation, the continuous generation phase, and one for drop deformation, the continuous deformation phase. In contrast to previous studies of drop deformation and simultaneous gel formation in a 4 roll-mill apparatus with silicon oil as the continuous phase [3–5], it is now pos-
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sible to study drop deformation and gel kinetics in situ in a fast continuous process with food grade sunflower oil as the continuous phase. The use of food grade sunflower oil is important regarding future applications of the process in the field of food emulsions. The Reynolds number for the channel flow was between 30 and 60 and on the drop streamline between 10 and 60 depending on the position along the channel. Drop generation with a highly monodisperse size distribution is vital for the process reproducibility. This is achieved by generating droplet from a needle’s tip in a double capillary setup. The technique uses the material properties (viscosity, interfacial tension, etc.) and the dynamics of the flow field [6]. Two main mechanisms for drop generation in the double capillary can be distinguished: the dripping mode, where drops are produced directly or very close to the needle tip, and the jetting mode, where a fluid filament of the disperse phase is stretched from the needle tip by the outer flow field and growing interfacial waves leading to a break up of the filament [7]. Since no perturbations of the flow field of the outer phase can affect the dripping mechanism, it produces nearly monodispersed emulsions and was therefore chosen as the droplet generation mechanism in this study. Process and material parameters such as the flow rate of the dispersed and continuous generation phase, viscosity ratio between the disperse phase and continuous drop generation phase, λ = ηdisp /ηcont , density and interfacial tension were optimized according to results from several investigations of drop generation [6–9]. Drop deformation has been studied for Newtonian liquids since the pioneering studies of Taylor [10,11] and is reviewed in the literature [12–14]. Several parameters are important to describe the deformation process [10–18] such as the viscosity ratio, λ, and the capillary number, Ca = (ηc Gr)/σ , which expresses the ratio between external forces and the Laplace pressure, and surfactant effects. In the given definition of the capillary number G is the deformation rate, r the drop radius, and σ the interfacial tension. Incorporating a gelling disperse phase introduces viscoelasticity to the system. Some experimental studies and computations have been done with viscoelastic drops suspended in Newtonian liquid [19–23]. For extensional flow, Tretheway and Leal [19] found experimentally that increasing the viscosity ratio increased deformation, while viscoelastic drops experience a lower deformation at a given capillary number when compared to Newtonian drops with an equivalent viscosity ratio. Their results were qualitatively consistent with the computational work of Ramaswamy and Leal, where the fluid motion and shape of a non-Newtonian drop, modelled as a Chilcott–Rallison fluid, in a steady, uniaxial extensional flow of unbounded Newtonian liquid was investigated [20]. For shear flow experiments, de Bruijn [22] found that drop elasticity reduces deformation for a given capillary number at any viscosity ratio, while Ultracki and Shi [23] reported reduced drop deformation only for viscosity ratios below 0.5, but increased deformation for viscosity ratios above 0.5.
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Wolf et al. compared the deformation of gelled gellan drops with a model by Maffetone and Minale for Newtonian drops and discovered that the measured deformation values for the gelled drops are significantly smaller than the predicted values for Newtonian drops [24–26]. Additionally, the experimental deformation values show little correlation with an increasing capillary number, whereas the model predicts a continuous increase. Wolf et al. concluded that these results are correlated to an increased interfacial tension, viscosity ratio, or viscoelasticity near gelation. To enable gel formation of the κ-carrageenan solution drops by a temperature quench below the gelation temperature, Tgel , Na+ - and K+ -ions were added. The gelation process is complex and involves a coil-helix transition followed by aggregation and network formation [27]. Studies of gel kinetics of biopolymers are usually performed in rheometers with concentric cylinders, where temperature gradients of about 10 ◦ C/min represent the limit for measuring a fast gel formation process. The aim of this work was to study the drop deformation dynamics of monodisperse drops along a narrowing channel for nongelling and gelling κ-carrageenan systems. The nonsteady-state flow process was also used to obtain information on the gel kinetics at high temperature gradients and in short time windows. The impact of flow type, flow strength, drop size, radial migration, and gel formation was investigated.
2. Description of droplet deformation Several equations are essential for studying drop deformation in combination with temperature-induced gel formation in a fast continuous flow process. Main parameters influencing the deformation are the flow rate of the continuous deformation phase, Qcont,def , the viscosity of the continuous deformation phase, ηcont,def , the viscosity of the disperse phase, ηdisp , the storage modulus of the disperse phase, G , the interfacial tension, σ , the half channel width, R, the distance from the channel centreline to the centre of the drop, rtrack , the drop diameter, d, or drop radius, r, and the position along the channel, x (Eq. (1)). D = f Qcont,def , ηcont,def , ηdisp , G , σ, R, rtrack , d, x . (1) Taylor [11] developed a theory for small deformations of Newtonian drops in Newtonian media where the deformation, D, depends on the capillary number, Ca, and the viscosity ratio, λ: 19λ + 16 . (2) 16λ + 16 The actual deformation is measured by L the major and B the minor axis of an ellipsoid and expressed as follows:
D = Ca
D=
L−B . L+B
(3)
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Assuming fully developed flow, the shear rates on the particle track can be calculated by γ˙ =
∂vcont,def (rtrack , x) Qcont,def rtrack (x) = −3 , ∂rtrack 2R(x)h R(x)2
(4)
where vcont,def is the velocity of the continuous deformation phase and h the channel depth. The above equations are used to compare deformations under different flow conditions. Knowing the particle track in the channel, we can calculate the residence time of the drops according to the equation x=x 2
tresidence = x=x1
1 dx. vcont,def (rtrack , x)
(5)
3. Materials and methods 3.1. Materials
(a)
3.1.1. κ-Carrageenan The disperse phase is an aqueous solution of κ-carrageenan. The carrageenan was delivered in powder form by CP Kelco (Wilmington, USA). It consists of 97% κ- and 3% ι-carrageenan. The powder contains 4.94 w/w% Na+ , 0.77 w/w% K+ , 0.016 w/w% Ca2+ , and 0.068 w/w% Mg+ . A κ-carrageenan concentration between 0 and 1.75 w/w% was used. For gelation experiments, sodium chloride pro analysis and extra pure food grade potassium chloride (Merck, Darmstadt, Germany) are added to a 1.5 w/w% carrageenan solution to trigger temperature-induced gel formation. The total ion concentration for the gelation experiments is 200 mM Na+ and 20 mM K+ . All ingredients were dissolved in deionized water under stirring at 90 ◦ C for 15 min. 3.1.2. Oil Refined sunflower oil (bleached and deodorized, van den Bergh and Jurgens, Rotterdam, Holland) was used for the continuous drop generation phase in the double capillary and the continuous drop deformation phase in the flow channel. The viscosity of the sunflower oil is 0.051 Pa s at 25 ◦ C, 0.034 Pa s at 35 ◦ C, 0.024 Pa s at 45 ◦ C, and 0.017 Pa s at 55 ◦ C. The density is 916 kg/m3 at 25 ◦ C.
(b) Fig. 1. Schematic drawing of (a) the double capillary injection tool and (b) the entire flow channel with all side-equipment.
3.2. Experimental setup and methods The equipment consists of one unit for drop generation, one unit for drop deformation/gelation and several temperature control units. A detailed sketch of the double capillary used for drop generation combined with an injection tool (double capillary injection tool) is given in Fig. 1a, and a schematic drawing of the rectangular flow channel used for drop deformation/gelation with all side-equipment is shown in Fig. 1b.
3.2.1. The double capillary injection tool Drop generation and injection into the flow channel are accomplished with the double capillary injection tool (Fig. 1a). Drop generation with a double capillary is done by pumping the disperse phase through a thin inner needle onto the centreline of an outer capillary where a fully developed laminar flow field of a continuous generation phase is present and detaches drops from the needle (dripping mode) [6]. The drop size is decreased by decreasing
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the flow rate of the disperse phase, Qdisp , or increasing the flow rate of the continuous generation phase, Qcont,gen . The double capillary is mounted via the injection tool on the top of the flow channel for drop deformation/gelation. The injection tool can be moved over the channel width and can consequently be placed at any position centrically or eccentrically in the deformation channel. As soon the drops leave the outer capillary of the injection tool and enter the deformation channel, they are dragged along the flow channel by the continuous deformation phase and are subjected to the flow forces acting along the streamlines prechosen by the position of the injection tool. The inner needle of the double capillary has an inner diameter of di,i = 0.1 mm and an outer diameter of di,out = 0.3 mm. Flow rates of the disperse phase, Qdisp , between 6.25 and 250 µl/min are realized using a syringe pump (Hamilton Microlab 500 series or KDS200PCE (Labinett, Göteborg, Sweden)). The inner diameter of the outer capillary is dout,i = 1 mm and the outer diameter is dout,out = 2 mm. The continuous generation phase is pumped using a gear pump (Ismatec MCP-Z Standard) covering a flow rate range Qcont,gen from 1 to 100 ml/min. 3.2.2. The flow channel Drops are deformed in a narrowing rectangular channel, which is supplied with the continuous deformation phase through the injection tool via an Ismatec MCP-Z Standard gear pump or a Liquiflo gear pump (Hydronova, Spånga, Sweden). Narrowing channel geometries are used to develop a well-defined parabolic laminar flow field with a Newtonian fluid (Poiseuille flow) where velocity gradients both in the axial and radial direction are generated. As a consequence, the impact of shear and elongation stresses on the drop shape can be investigated by varying the position of the injection tool. The channel dimensions for both the nongelling and gelling experiments are illustrated in Figs. 2a and 2b. For both setups the channel is 10.5 mm high and 20 mm deep from the injection point of the drops (x = x0 ) until the chan-
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nel starts narrowing after 30 mm (x = x1 ). Thereafter there are slight differences in the channel geometry. In the nongelling setup (Fig. 2a), the channel height decreases along 120 mm to 1.5 mm at x = x3 , and thereafter a parallel channel with a gap of 1.5 mm continues. In the gelling setup (Fig. 2b), the channel height decreases along 140 mm to 1.5 mm at x = x3 , and thereafter a parallel channel with a gap of 1.2 mm continues. Therefore the flow accelerates even after the narrowing channel in between x = x3 and x = x4 due to the step from 1.5 to 1.2 mm from the narrowing channel to the parallel channel. Positions x = x2 and x = x2 are introduced to facilitate later discussions. 3.2.3. Temperature control units Experiments with gelling systems demand temperature control of the three liquid phases. To measure and control the temperatures of the continuous oil phases, two PT 100 were placed as close to the injection tool as possible (Fig. 1a). The temperature of the disperse phase was regulated by a PID regulator, a heating wire, and a thermocouple. The heating of the disperse phase ends where the injection needle enters the injection tool (Fig. 1a). The injection tool for the continuous generation phase and for the continuous deformation phase are separated by a PVC insulation plate (Fig. 1a). The aqueous disperse phase was maintained at 100 ◦ C, the continuous generation phase at 54 ◦ C, and the continuous deformation phase was stepwise adjusted from Tcont,def = 35 to 26 ◦ C. The continuous deformation phase was used to cool the carrageenan drops below Tgel and thereby trigger temperature-induced gelation. Nongelling experiments were run at room temperature. 3.2.4. Image analysis The experiments were evaluated by image analysis. Drop deformation was observed along the channel with a moveable CCD-camera (Sony DFW-V500) with an ultrazoom lens (Navitar, UltraZoom) coupled with a microscope lens (Mitutoyo, 10×/0.28) or a macroobjective (Mörk, Mini Macro, Germany) with a 2 cm distance tube. Movies were
Fig. 2. The flow channel with its dimensions for (a) nongelling and (b) gelling experiments. All dimensions in millimeters.
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captured using BTVPro software (Version 5.4.1) and the image analysis was performed using ImageJ software (ImageJ 1.28v, National Institute of Health, USA). 3.2.5. Rheological properties The rheological properties of the disperse phase as a function of the temperature were measured by a small amplitude oscillatory shear experiment with a StressTech rheometer using a concentric cylinder geometry with a cup diameter of 22 mm and a bob diameter of 20 mm at an angular frequency of 1 Hz, and a cooling rate of 1 ◦ C/min. The storage modulus, G , and the loss modulus, G , were determined. The increase in storage modulus, G , above the noise level was taken as the rheometer gelation temperature, Tgel,rheo .
4. Results and discussion 4.1. Transient deformation of nongelling drops Deformation of nongelling drops was studied along a streamline eccentrically close to the narrowing wall and along a streamline on the centreline of the flow channel. If drops were injected from the double capillary close to the narrowing wall (Fig. 1b) drops were subjected to shear flow of the parabolic flow profile and deformations up to around D = 0.45 were achieved. Due to the low velocities of the continuous deformation phase close to the wall long residence times are realized. If the drops were injected on the centreline into the flow channel, negligible deformation was observed for two different drop diameters of 0.22 and 0.37 mm and two different flow rates of the continuous deformation phase (Qcont,def = 200, 1500 ml/min). The stresses acting on the centreline in the smooth contraction of the flow channel are not sufficient to deform the drops. In previous work, drop deformation into ellipsoids could be achieved on the centreline in contraction flow. A step decrease in the channel width from 10 to 1 or 2 mm enabled this deformation [1]. In the following, the interaction of the particle movement along the eccentric particle track and the consequences on droplet deformation and residence time needed for gelation will be discussed. 4.1.1. Particle track and residence time To maintain high shear stresses acting on the drop over a long period of time, a smooth narrowing channel geometry was chosen (Fig. 2a). The relative radial drop position, rtrack (x)/R(x), was measured at different channel positions and is illustrated in Fig. 3. Approximately 20 mm behind the injection point the velocities, vcont,gen and vcont,def , have equilibrated, and the relative particle track now decreases slightly from rtrack (x)/R(x) = 0.85 at x = 20 mm to rtrack (x)/R(x) = 0.7 at x = 120 mm. In this region the velocity of the continuous deformation phase on the centreline increases moderately. From x = 120 mm the veloc-
Fig. 3. Experimentally determined drop track and calculated velocity on the centreline as a function of the x-position along the channel for a flow rate of the continuous deformation phase, Qcont,def = 1400 ml/min (ddrop = 0.27 mm, water/sunflower oil, λ = 0.02).
ity, vcont,def , increases sharply and rtrack (x)/R(x) decreases drastically. As soon as the drops enter the straight channel at x = 150 mm, the velocity reaches its maximum value and the drops flow close to the centreline. At sufficient shear stress gradients along the drop interface, which are generated by the flow rate of the continuous deformation phase, Qcont,def , radial migration is enhanced. The phenomena is extensively reviewed and investigated by Leal [28] and Chang and Leal [29]. In dispersions, shearinduced migration of the suspended rigid particles is initiated by particle interaction and wall effects. Recent work by Li and Pozrikidis [30] pointed out that in case of liquid droplets as dispersed phase radial motion due to curvature of the velocity profile can be observed. In such cases the droplet “feels” not only a single shear stress but a shear stress gradient that is dependent on the absolute position of the droplet with respect to the centreline. The drops try to balance this stress gradient given by the Poiseuille flow profile by internal flow and consequently move towards the centreline where the shear stress gradient is zero. As pointed out by Li and Pozrikidis [30], drops near the centreline of the channel experience a reduced deformation compared to drops near the channel walls, as a result of the reduced shear rate near the centreline. This effect was generally also observed in our experiments. However, due to the choice of the narrowing channel geometry, radial migration to the centreline is less pronounced than in a straight channel geometry since the superimposed contraction counterbalances the migration. Furthermore, the migration can be suppressed when smaller droplets are used since large drops are affected by a broader stress distribution and consequently they have a strong tendency to move towards the centreline. Having analyzed the particle track we can calculate the residence time according to Eq. (5). As an approximation, it is assumed that the distance from the centreline decreases linearly along the channel for x x3 and remains constant
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Table 1 Residence time, Tresidence , of a drop within the different areas of the flow channel for Qcont,def = 800 and 1400 ml/min Qcont,def (ml/min)
Tresidence,1 (s)
Tresidence,2 (s)
Tresidence,3 (s)
800 1400
1.280 0.732
1.281 0.825
0.062 0.036
Tresidence,total (s) = 2.623 = 1.593
Fig. 5. Images of drops of different sizes at the channel position x3 = 150 mm at different flow rates of the continuous deformation phase, Qcont,def (1.75% κ-carrageenan solution/sunflower oil, λ = 4.94).
Fig. 4. Drop deformation as a function of the x-position along the channel for two different flow rates of the continuous deformation phase, Qcont,def (ddrop = 0.31 mm, water/sunflower oil, λ = 0.02).
when a drop enters the straight channel for x > x3 (Fig. 3). 0.028x + 4.557, if x x3 , rtrack (x) = (6) 0.225, if x > x3 . The particle track approximations are based on the following process parameters: Qcont,def = 800 ml/min and a drop diameter of d = 0.27 mm. For the calculation of the residence time, Eq. (5) was solved numerically for two different flow rates of the continuous deformation phase. The total residence time and residence time in areas 1, 2, and 3 (Fig. 2a) are displayed in Table 1. The residence time in area 3 is an order of magnitude smaller than in area 1 and 2. 4.1.2. Deformation along the channel The drop deformation, D, caused by the acting flow stresses, is shown in Fig. 4 as a function of the x-position along the channel for two different flow rates of the continuous deformation phase, Qcont,def = 800 and 1400 ml/min and a drop diameter of d = 0.31 mm. As shown with Eq. (4), the shear rate acting on the drop increases with the x-position in the channel due to the acceleration of the continuous deformation phase. Up to x = 100 mm the drops stay almost spherical because of weak stresses in the flow field. Thereafter deformation starts and a marked increase in drop deformation is then achieved between x2 and x3 (Fig. 2) even though the residence time is very short in this area. The largest drop deformations are obtained at around x3 where the narrowing channel turns into a straight channel. How-
ever, as soon as the deformed drops enter the straight channel (x > x3 ) the drops experience a strong migration force acting towards the centreline and start to relax back due to reduced stress (zero stress gradient regime of Poiseuille flow profile). As expected, larger deformations are obtained for higher flow rates, Qcont,def , due to the higher shear rates (Eq. (4)). 4.1.3. Drop deformation at a fixed position The impact of shear stress and drop size on the maximum drop deformation was investigated at position x3 , as shown by the images in Fig. 5. The stresses were varied by changing the flow rate of the continuous deformation phase, Qcont,def . The largest deformation is obtained at the highest flow rate of the continuous deformation phase, Qcont,def , and for the largest drops. The drops adopt ellipsoidal shapes with bulbous ends directed towards the centreline. This nonsymmetrical distortion may be attributed to internal flow and radial migration of the drops where the fluid volume tends to move towards the centreline. As can be seen in Fig. 5, this phenomenon is more pronounced for larger drops. The drop deformation is plotted as a function of the capillary number at x = x3 in Fig. 6 for a viscosity ratio of λ = 4.94. The variations in the radial position, rtrack (x) (Fig. 3), are taken into account to calculate the capillary number. The data points for different drop sizes are superimposed within the accuracy of measurement. In the flow channel, the drop deformation does not take place under steady conditions, since the drop’s residence time in each x-position is too short to reach a steady-state shape. Nor is the assumption of a fully developed flow field within the narrowing channel fulfilled. Even so, in Fig. 6 the experimental data are compared with Taylor’s small deformation theory (Eq. (2)) and the agreement between our experimental data and the theoretical curve is surprisingly good. Hence, Taylor’s theory can be used to roughly predict drop shapes in such a flow channel under nongelling conditions.
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Fig. 6. Drop deformation for different drop diameters as a function of the capillary number at the channel position x3 = 150 mm (1.75% κ-carrageenan solution/sunflower oil, λ = 4.94) and calculated deformation values according to Taylor’s theory.
Fig. 7. G (storage modulus) and G (loss modulus) of a 1.5% κ-carrageenan solution with 200 mM Na+ and 20 mM K+ as a function of temperature.
4.2. Transient deformation of gelling drops With gelation as an additional parameter the process becomes more complex. There will be not only a transient drop deformation but also a transient temperature gradient between the continuous deformation phase, the continuous generation phase, and the disperse phase. This gradient will ultimately trigger gelation of the disperse phase. The gelation behavior of the disperse phase in the rheometer is shown in Fig. 7. Gelation started at around 30 ◦ C (Tgel,rheo ≈ 30 ◦ C) and was followed by a strong increase in the storage modulus, G , and loss modulus, G . 4.2.1. Drop deformation under gelling conditions In Fig. 8 drop deformation is shown as a function of the x-position along the channel for stepwise cooling of the continuous deformation phase from Tcont,def = 35–26 ◦ C. The flow rate of the continuous deformation phase is Qcont,def = 1400 ml/min, and the drop diameter d = 0.32 mm. For the starting temperature of the continuous deformation phase,
Fig. 8. Impact of temperature-induced gelation on drop deformation as a function of the x-position along the channel (ddrop = 0.32 mm, 1.75% κ-carrageenan solution with 200 mM Na+ and 20 mM K+ /sunflower oil).
Fig. 9. Summary of maximum drop deformation at the channel position x = x4 = 180 mm and viscosity of the sunflower oil as a function of the temperature of the continuous deformation phase, Tcont,def . The rheologically determined gelation temperature, Tgel,rheo , is inserted for comparison (ddrop = 0.32 mm, 1.75% κ-carrageenan solution with 200 mM Na+ and 20 mM K+ /sunflower oil).
Tcont,def = 35 ◦ C, the deformation, D, along the channel, x, shows similar behavior to that in the nongelling experiments. The D-value stays rather low in the beginning of the narrowing channel geometry up to x2 . Thereafter a strong increase can be detected until x4 up to D = 0.47, and from then on the deformation vanishes again after the drops have migrated towards the centreline of the parallel channel. As the temperature of the continuous deformation phase is decreased, interesting changes in drop deformation can be detected after position x2 : Upon cooling down to Tcont,def = 30 ◦ C droplet deformation increases, but if cooling continues deformation decreases severely. The effect of cooling the continuous deformation phase from 35 to 26 ◦ C can be clearly seen in Fig. 9. In the figure the maximum deformation at x4 , the viscosity of the continuous deformation phase as a function of the temper-
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ature, and Tgel,rheo are shown. Decreasing the temperature of the continuous deformation phase from 35 to 30 ◦ C causes the deformation values to increase up to a maximum deformation of D = 0.63. The larger deformation is caused by the increased viscosity of the continuous deformation phase at lower temperatures since an increase in viscosity of the continuous deformation phase causes an increase in capillary number (Eq. (2)). The simultaneous increase in G and G of the disperse phase is slight and plays a minor role in the same temperature range (35–30 ◦ C) (Eq. (2) and Fig. 7). If the temperature of continuous deformation phase is below 30 ◦ C, smaller maximum deformations will be found. The onset of decreasing deformation corresponds well to the gelation temperature measured in the rheometer (Tgel,rheo ≈ 30 ◦ C) (Fig. 9). Obviously, at Tcont,def = 29 ◦ C, the temperature gradient between the continuous deformation phase and the disperse phase is sufficient to cool the disperse phase below the gelation temperature and trigger gel formation within the process time of about 1.5 s (Table 1). The additional increase in the viscosity of the continuous deformation phase by cooling it from 30 to 29 ◦ C is obviously less important than the strong increase in G and G of the disperse phase within the same temperature range. Upon further cooling, deformation continues to diminish because the higher temperature gradient promotes gelation. The match of the onset of disappearing deformation in the channel and the gelation temperature in the rheometer shows that the heat transfer from the drops to the oil is much faster than the process time. It cannot be distinguished directly from the experiments whether it is the viscous or elastic part of the gelling disperse phase that is the cause of the lower deformation of the disperse phase, since the two phenomena cannot not be separated in this system. However, it is assumed here, according to the literature discussed in the introduction [19–23], that the increasing viscoelasticity of the disperse phase provokes disappearing deformation more strongly than its increasing viscosity. The interfacial tension, σ , is assumed to be constant (σ = 0.026 N/m) over the whole process. In Fig. 8 it can further be seen that down to Tcont,def = 28 ◦ C, deformation values differ only from a channel position x = 160. But at Tcont,def = 27 and 26 ◦ C, the impact of viscoelasticity can be already detected at x = 140, 80 mm, respectively. At Tcont,def = 26 ◦ C, very little deformation is achieved and it seems that the drop forms a gel network early in the channel (around x = 80 mm or after about 1.3 s) and keeps an almost constant deformation up to x = 160 mm. A part of the deformation remains even after x4 due to the early gel formation. Obviously, the buildup of a gel network is delayed under flow until Tcont,def reaches 26 ◦ C. This delay could be ascribed to flow inside the liquid drops caused by the shear stress gradient of the Poiseuille flow [30]. Previous studies of gel formation of gelatin under high shear have shown that the gelation is delayed until the shear is decreased [31,32]. At a temperature of the continuous deformation phase, Tcont,def = 26 ◦ C, the system is strongly
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Fig. 10. Drop deformation as a function of the capillary number for different temperatures of the continuous deformation phase, Tcont,def (ddrop = 0.32 mm, 1.75% κ-carrageenan solution with 200 mM Na+ and 20 mM K+ /sunflower oil) and calculated deformation values according to Taylor’s theory (differences between calculated deformations for 35–30 ◦ C are very small and cannot be detected in the graph).
quenched and network formation can already occur in the beginning of the flow channel where shear stresses are rather low. If gel formation had not been delayed due to internal flow drops would not have been able to retract at temperatures well below the gelation temperatures but remained deformed as gelled particles. In Fig. 10 the drop deformation is plotted against the capillary number along the channel, which in this case expresses the channel length. The increasing viscosity of the continuous deformation phase with decreasing temperature was accounted for when calculating the capillary number and it was assumed that the continuous deformation phase keeps the set temperature over the whole process. Above 30 ◦ C the curves coincide quite well, and the deformation shows a linear relationship with the capillary number and fits rather well with the deformation values calculated with Taylor’s theory (dotted line in Fig. 10). Even the curve at 29 ◦ C still lies in this bulk of curves because gel formation starts only in the very end of the geometry. Hence, the gelling system above Tgel shows comparable results to the nongelling system. The curves start to deviate from the linear behavior and theoretical value at a temperature of the continuous deformation phase, Tcont,def = 28 ◦ C at a capillary number of about 0.25. With further decreasing of Tcont,def the linear relationship disappears at even lower capillary numbers, i.e., earlier in the channel. This can be attributed to a faster or earlier strong increase in the viscoelasticity of the disperse phase. These results about the impact of gelation on drop deformation can also explain the decreased drop deformation for gelled drops compared to Newtonian drops found by Wolf et al. [24]. Scaling relationships of flow kinetics and gelation kinetics were established in previous work [1,5,6] and a transformation of the presented knowledge to other flow geometries is therefore possible.
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The results in Figs. 8–10 showed the impact of gel formation on drop deformation and thereby it was possible to detect small differences in fast gel kinetics at high temperature gradients via drop deformation analysis.
5. Conclusions The present study has shown the possibility of deforming κ-carrageenan solution drops into ellipsoids under shear flow in a smooth narrowing deformation channel of a fast continuous flow process. Additionally, it was possible to study in situ the impact of temperature-induced gel formation on drop deformation along the deformation channel at time frames below 2 s. This provided an opportunity to learn about gel kinetics on such short timescales under high temperature gradients. Experimental deformation values of nongelling drops under shear flow could be recalculated surprisingly well with Taylor’s small deformation theory even though deformation occurred under nonsteady-state conditions. Gelling drops above the gelation temperature show behavior comparable to that shown by nongelling drops. Upon cooling the continuous deformation phase towards the gelation temperature of the disperse phase, its increased viscosity causes greater drop deformation. But as soon as gelation is induced, the strongly increasing storage modulus, G , and loss modulus, G , of the drops reverses the trend. Upon further cooling of the continuous deformation phase, deformation continues to decrease measurably in the fast process due to the higher temperature gradient between the phases causing faster gel kinetics. However, the formation of a gel network is delayed until the continuous deformation phase has a temperature of Tcont,def = 26 ◦ C. Under this condition the system is sufficiently quenched to induce gelation early in the deformation channel, where shear stresses, provoking internal flow and disruption of developing networks, are low. Therefore, the low deformation experienced by the droplets in the beginning of the deformation geometry is frozen in, and remains along the whole channel. The results from the described process give additional insight into gel kinetics under high temperature gradients and short timescales, thereby augmenting the knowledge obtained from established rheological measurements.
Acknowledgments The authors thank Jan Corsano, Daniel Kiechl, and Bruno Pfister for the construction of the flow cell as well as the data acquisition system. This work has been carried out with financial support from the Commission of the European Communities, specific RTD programme “Quality of
Life and Management of Living Resources,” Key Action 1-Health Food and Environment, QLK1-2000-1543 Structure Processing: “Structure engineering of emulsions by micromachined elongational flow processing.” Part of the work has been carried out with the financial support from the Swiss Federal Office for Education and Science (Project BBW 00.0072). It does not necessarily reflect the views of the Commission of the European Communities and the Swiss Federal Office for Education and Science and in no way anticipates the funding body’s future policy in the area.
References [1] B. Walther, L. Hamberg, P. Walkenström, A.-M. Hermansson, J. Colloid Interface Sci. 270 (2004) 195–204. [2] B. Wolf, W.J. Frith, S. Singleton, M. Tassieri, I.T. Norton, Rheol. Acta 40 (2001) 238–247. [3] L. Hamberg, P. Walkenström, A.-M. Hermansson, J. Colloid Interface Sci. 252 (2002) 297–308. [4] L. Hamberg, M. Wohlwend, P. Walkenström, A.-M. Hermansson, Food Hydrocolloids 17 (2003) 641–652. [5] B. Walther, P. Walkenström, A.-M. Hermansson, P. Fischer, E.J. Windhab, Food Hydrocolloids 16 (2002) 633–643. [6] C. Cramer, P. Fischer, E.J. Windhab, Chem. Eng. Sci. 59 (2004) 3045– 3058. [7] P. Fischer, K. Maruyama, E.J. Windhab, Chem. Eng. Techn. 27 (2004) 1161–1171. [8] P.B. Umbanhowar, V. Prasad, D.A. Weitz, Langmuir 16 (2000) 347– 351. [9] D.F. Zhang, H.A. Stone, Phys. Fluids 9 (8) (1997) 2234–2242. [10] G.I. Taylor, Proc. R. Soc. London A 138 (1932) 41–48. [11] G.I. Taylor, Proc. R. Soc. London A 146 (1934) 501–523. [12] H. Stone, Annu. Rev. Fluid Mech. 26 (1994) 65–102. [13] J.M. Rallison, Annu. Rev. Fluid Mech. 16 (1984) 54–66. [14] B. Walther, SIK-Report No. 682, SIK, Göteborg, 2001. [15] F.D. Rumscheidt, S.G. Mason, J. Colloid Sci. 16 (1961) 238–261. [16] F.D. Rumscheidt, S.G. Mason, J. Colloid Sci. 17 (1962) 260–269. [17] D. Megias-Alguacil, P. Fischer, E.J. Windhab, J. Colloid Interface Sci. 274 (2004) 631–636. [18] H.P. Grace, Chem. Eng. Commun. 14 (1982) 225–277. [19] D.C. Tretheway, L.G. Leal, AIChE J. 45 (5) (1999) 929–937. [20] S. Ramaswamy, L.G. Leal, J. Non-Newton. Fluid Mech. 85 (1999) 127–163. [21] W.J. Milliken, L.G. Leal, J. Non-Newton. Fluid Mech. 40 (1991) 355– 379. [22] R.A. de Bruijn, Ph.D. thesis, Technische Univ., Eindhoven, 1989. [23] L.A. Ultracki, Z.H. Shi, Poly. Eng. Sci. 32 (1992) 1824. [24] B. Wolf, W.J. Frith, I.T. Norton, J. Rheol. 45 (5) (2001) 1141–1157. [25] P.L. Maffetone, M. Minale, J. Non-Newton. Fluid Mech. 78 (1998) 227–241. [26] P.L. Maffetone, M. Minale, J. Non-Newton. Fluid Mech. 84 (1999) 105–106. [27] A.-M. Hermansson, E. Eriksson, E. Jordansson, Carbohydr. Polym. 16 (1991) 297–320. [28] L.G. Leal, Ann. Rev. Fluid Mech. 12 (1980) 435–476. [29] P.C.-H. Chang, L.G. Leal, Int. J. Multiphase Flow 7 (1981) 83–99. [30] X. Li, C. Pozrikidis, Int. J. Multiphase Flow 26 (2000) 1247–1279. [31] M. Djabourov, J. Leblond, P. Papon, J. Phys. France 49 (1988) 333– 343. [32] W. de Carvalho, M. Djabourov, Rheol. Acta 36 (6) (1997) 591–609.
Drop deformation dynamics and gel kinetics in a co-flowing water-in-oil system Bernhard Walther a , Carsten Cramer b , Armin Tiemeyer b , Lars Hamberg a , Peter Fischer b , Erich J. Windhab b , Anne-Marie Hermansson a,∗ a SIK, The Swedish Institute for Food and Biotechnology, P.O. Box 5401, SE-402 29 Göteborg, Sweden b Swiss Federal Institute of Technology (ETH Zurich), Institute of Food Science and Nutrition, Laboratory of Food Process Engineering,
Schmelzbergstrasse 9, CH-8092 Zurich, Switzerland Received 27 August 2004; accepted 19 January 2005 Available online 21 February 2005
Abstract Drop deformation and superimposed gel kinetics were studied in a fast continuous-flow process for a water-in-oil system. Highly monodisperse drops were generated in a double capillary and then deformed passing through a narrowing rectangular channel geometry. Nongelling deformation experiments were used to establish the process and compare it with existing theories. Thereafter, temperature induced drop gelation was included to study its effect on deformation and gel kinetics on short timescales and at high temperature gradients. The disperse phase was a κ-carrageenan solution with additional sodium and potassium ions for gelation experiments. Sunflower oil was used for the continuous phases. Nongelling experiments showed that shear forces are able to deform drops into ellipsoids. A comparison with the small deformation theory by Taylor was surprisingly good even when drop deformation and flow conditions were not in steady state. Superimposed gelation on the deformation process showed clearly the impact of the altered rheological properties of the dispersed and continuous phase. Deformation first increased on cooling the continuous phase until the onset of gel formation, where a pronounced decrease in deformation due to increasing droplet viscosity/viscoelasticity was observed. Drop deformation analyses were then used to detect differences in gelation kinetics at high cooling rate within process times as short as 1.8 s. 2005 Elsevier Inc. All rights reserved. Keywords: Drop deformation; Shear flow; Gelation; Viscoelasticity; Viscosity; Carrageenan
1. Introduction Simultaneous drop deformation and gel formation are relevant to the formation of special emulsion and suspension properties. Flow processes and techniques are available to deform liquid emulsion droplets on their way to suspended gelled particles and thus imprint liquid–liquid deformation onto solid particles. This modifies the rheological properties of the emulsion or suspension [1,2]. To further develop such processes, drop deformation and gel kinetics have to be investigated under relevant flow conditions. * Corresponding author. Fax: +46-31-83-37-82.
E-mail address: [email protected] (A.-M. Hermansson). 0021-9797/$ – see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2005.01.054
In this investigation, drop generation, drop deformation, and gel kinetics are combined to study drop deformation in a fast continuous flow process with and without simultaneous gel formation under high temperature gradients. Particular attention is paid to the impact of gel formation, i.e., gel kinetics and the viscoelastic parameters of the disperse phase. Drops are generated in a double capillary. Deformation and gel formation occur downstream along a narrowing rectangular deformation channel, which deforms drops into ellipsoids. The process demands two continuous liquid phases, one for drop generation, the continuous generation phase, and one for drop deformation, the continuous deformation phase. In contrast to previous studies of drop deformation and simultaneous gel formation in a 4 roll-mill apparatus with silicon oil as the continuous phase [3–5], it is now pos-
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sible to study drop deformation and gel kinetics in situ in a fast continuous process with food grade sunflower oil as the continuous phase. The use of food grade sunflower oil is important regarding future applications of the process in the field of food emulsions. The Reynolds number for the channel flow was between 30 and 60 and on the drop streamline between 10 and 60 depending on the position along the channel. Drop generation with a highly monodisperse size distribution is vital for the process reproducibility. This is achieved by generating droplet from a needle’s tip in a double capillary setup. The technique uses the material properties (viscosity, interfacial tension, etc.) and the dynamics of the flow field [6]. Two main mechanisms for drop generation in the double capillary can be distinguished: the dripping mode, where drops are produced directly or very close to the needle tip, and the jetting mode, where a fluid filament of the disperse phase is stretched from the needle tip by the outer flow field and growing interfacial waves leading to a break up of the filament [7]. Since no perturbations of the flow field of the outer phase can affect the dripping mechanism, it produces nearly monodispersed emulsions and was therefore chosen as the droplet generation mechanism in this study. Process and material parameters such as the flow rate of the dispersed and continuous generation phase, viscosity ratio between the disperse phase and continuous drop generation phase, λ = ηdisp /ηcont , density and interfacial tension were optimized according to results from several investigations of drop generation [6–9]. Drop deformation has been studied for Newtonian liquids since the pioneering studies of Taylor [10,11] and is reviewed in the literature [12–14]. Several parameters are important to describe the deformation process [10–18] such as the viscosity ratio, λ, and the capillary number, Ca = (ηc Gr)/σ , which expresses the ratio between external forces and the Laplace pressure, and surfactant effects. In the given definition of the capillary number G is the deformation rate, r the drop radius, and σ the interfacial tension. Incorporating a gelling disperse phase introduces viscoelasticity to the system. Some experimental studies and computations have been done with viscoelastic drops suspended in Newtonian liquid [19–23]. For extensional flow, Tretheway and Leal [19] found experimentally that increasing the viscosity ratio increased deformation, while viscoelastic drops experience a lower deformation at a given capillary number when compared to Newtonian drops with an equivalent viscosity ratio. Their results were qualitatively consistent with the computational work of Ramaswamy and Leal, where the fluid motion and shape of a non-Newtonian drop, modelled as a Chilcott–Rallison fluid, in a steady, uniaxial extensional flow of unbounded Newtonian liquid was investigated [20]. For shear flow experiments, de Bruijn [22] found that drop elasticity reduces deformation for a given capillary number at any viscosity ratio, while Ultracki and Shi [23] reported reduced drop deformation only for viscosity ratios below 0.5, but increased deformation for viscosity ratios above 0.5.
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Wolf et al. compared the deformation of gelled gellan drops with a model by Maffetone and Minale for Newtonian drops and discovered that the measured deformation values for the gelled drops are significantly smaller than the predicted values for Newtonian drops [24–26]. Additionally, the experimental deformation values show little correlation with an increasing capillary number, whereas the model predicts a continuous increase. Wolf et al. concluded that these results are correlated to an increased interfacial tension, viscosity ratio, or viscoelasticity near gelation. To enable gel formation of the κ-carrageenan solution drops by a temperature quench below the gelation temperature, Tgel , Na+ - and K+ -ions were added. The gelation process is complex and involves a coil-helix transition followed by aggregation and network formation [27]. Studies of gel kinetics of biopolymers are usually performed in rheometers with concentric cylinders, where temperature gradients of about 10 ◦ C/min represent the limit for measuring a fast gel formation process. The aim of this work was to study the drop deformation dynamics of monodisperse drops along a narrowing channel for nongelling and gelling κ-carrageenan systems. The nonsteady-state flow process was also used to obtain information on the gel kinetics at high temperature gradients and in short time windows. The impact of flow type, flow strength, drop size, radial migration, and gel formation was investigated.
2. Description of droplet deformation Several equations are essential for studying drop deformation in combination with temperature-induced gel formation in a fast continuous flow process. Main parameters influencing the deformation are the flow rate of the continuous deformation phase, Qcont,def , the viscosity of the continuous deformation phase, ηcont,def , the viscosity of the disperse phase, ηdisp , the storage modulus of the disperse phase, G , the interfacial tension, σ , the half channel width, R, the distance from the channel centreline to the centre of the drop, rtrack , the drop diameter, d, or drop radius, r, and the position along the channel, x (Eq. (1)). D = f Qcont,def , ηcont,def , ηdisp , G , σ, R, rtrack , d, x . (1) Taylor [11] developed a theory for small deformations of Newtonian drops in Newtonian media where the deformation, D, depends on the capillary number, Ca, and the viscosity ratio, λ: 19λ + 16 . (2) 16λ + 16 The actual deformation is measured by L the major and B the minor axis of an ellipsoid and expressed as follows:
D = Ca
D=
L−B . L+B
(3)
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Assuming fully developed flow, the shear rates on the particle track can be calculated by γ˙ =
∂vcont,def (rtrack , x) Qcont,def rtrack (x) = −3 , ∂rtrack 2R(x)h R(x)2
(4)
where vcont,def is the velocity of the continuous deformation phase and h the channel depth. The above equations are used to compare deformations under different flow conditions. Knowing the particle track in the channel, we can calculate the residence time of the drops according to the equation x=x 2
tresidence = x=x1
1 dx. vcont,def (rtrack , x)
(5)
3. Materials and methods 3.1. Materials
(a)
3.1.1. κ-Carrageenan The disperse phase is an aqueous solution of κ-carrageenan. The carrageenan was delivered in powder form by CP Kelco (Wilmington, USA). It consists of 97% κ- and 3% ι-carrageenan. The powder contains 4.94 w/w% Na+ , 0.77 w/w% K+ , 0.016 w/w% Ca2+ , and 0.068 w/w% Mg+ . A κ-carrageenan concentration between 0 and 1.75 w/w% was used. For gelation experiments, sodium chloride pro analysis and extra pure food grade potassium chloride (Merck, Darmstadt, Germany) are added to a 1.5 w/w% carrageenan solution to trigger temperature-induced gel formation. The total ion concentration for the gelation experiments is 200 mM Na+ and 20 mM K+ . All ingredients were dissolved in deionized water under stirring at 90 ◦ C for 15 min. 3.1.2. Oil Refined sunflower oil (bleached and deodorized, van den Bergh and Jurgens, Rotterdam, Holland) was used for the continuous drop generation phase in the double capillary and the continuous drop deformation phase in the flow channel. The viscosity of the sunflower oil is 0.051 Pa s at 25 ◦ C, 0.034 Pa s at 35 ◦ C, 0.024 Pa s at 45 ◦ C, and 0.017 Pa s at 55 ◦ C. The density is 916 kg/m3 at 25 ◦ C.
(b) Fig. 1. Schematic drawing of (a) the double capillary injection tool and (b) the entire flow channel with all side-equipment.
3.2. Experimental setup and methods The equipment consists of one unit for drop generation, one unit for drop deformation/gelation and several temperature control units. A detailed sketch of the double capillary used for drop generation combined with an injection tool (double capillary injection tool) is given in Fig. 1a, and a schematic drawing of the rectangular flow channel used for drop deformation/gelation with all side-equipment is shown in Fig. 1b.
3.2.1. The double capillary injection tool Drop generation and injection into the flow channel are accomplished with the double capillary injection tool (Fig. 1a). Drop generation with a double capillary is done by pumping the disperse phase through a thin inner needle onto the centreline of an outer capillary where a fully developed laminar flow field of a continuous generation phase is present and detaches drops from the needle (dripping mode) [6]. The drop size is decreased by decreasing
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the flow rate of the disperse phase, Qdisp , or increasing the flow rate of the continuous generation phase, Qcont,gen . The double capillary is mounted via the injection tool on the top of the flow channel for drop deformation/gelation. The injection tool can be moved over the channel width and can consequently be placed at any position centrically or eccentrically in the deformation channel. As soon the drops leave the outer capillary of the injection tool and enter the deformation channel, they are dragged along the flow channel by the continuous deformation phase and are subjected to the flow forces acting along the streamlines prechosen by the position of the injection tool. The inner needle of the double capillary has an inner diameter of di,i = 0.1 mm and an outer diameter of di,out = 0.3 mm. Flow rates of the disperse phase, Qdisp , between 6.25 and 250 µl/min are realized using a syringe pump (Hamilton Microlab 500 series or KDS200PCE (Labinett, Göteborg, Sweden)). The inner diameter of the outer capillary is dout,i = 1 mm and the outer diameter is dout,out = 2 mm. The continuous generation phase is pumped using a gear pump (Ismatec MCP-Z Standard) covering a flow rate range Qcont,gen from 1 to 100 ml/min. 3.2.2. The flow channel Drops are deformed in a narrowing rectangular channel, which is supplied with the continuous deformation phase through the injection tool via an Ismatec MCP-Z Standard gear pump or a Liquiflo gear pump (Hydronova, Spånga, Sweden). Narrowing channel geometries are used to develop a well-defined parabolic laminar flow field with a Newtonian fluid (Poiseuille flow) where velocity gradients both in the axial and radial direction are generated. As a consequence, the impact of shear and elongation stresses on the drop shape can be investigated by varying the position of the injection tool. The channel dimensions for both the nongelling and gelling experiments are illustrated in Figs. 2a and 2b. For both setups the channel is 10.5 mm high and 20 mm deep from the injection point of the drops (x = x0 ) until the chan-
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nel starts narrowing after 30 mm (x = x1 ). Thereafter there are slight differences in the channel geometry. In the nongelling setup (Fig. 2a), the channel height decreases along 120 mm to 1.5 mm at x = x3 , and thereafter a parallel channel with a gap of 1.5 mm continues. In the gelling setup (Fig. 2b), the channel height decreases along 140 mm to 1.5 mm at x = x3 , and thereafter a parallel channel with a gap of 1.2 mm continues. Therefore the flow accelerates even after the narrowing channel in between x = x3 and x = x4 due to the step from 1.5 to 1.2 mm from the narrowing channel to the parallel channel. Positions x = x2 and x = x2 are introduced to facilitate later discussions. 3.2.3. Temperature control units Experiments with gelling systems demand temperature control of the three liquid phases. To measure and control the temperatures of the continuous oil phases, two PT 100 were placed as close to the injection tool as possible (Fig. 1a). The temperature of the disperse phase was regulated by a PID regulator, a heating wire, and a thermocouple. The heating of the disperse phase ends where the injection needle enters the injection tool (Fig. 1a). The injection tool for the continuous generation phase and for the continuous deformation phase are separated by a PVC insulation plate (Fig. 1a). The aqueous disperse phase was maintained at 100 ◦ C, the continuous generation phase at 54 ◦ C, and the continuous deformation phase was stepwise adjusted from Tcont,def = 35 to 26 ◦ C. The continuous deformation phase was used to cool the carrageenan drops below Tgel and thereby trigger temperature-induced gelation. Nongelling experiments were run at room temperature. 3.2.4. Image analysis The experiments were evaluated by image analysis. Drop deformation was observed along the channel with a moveable CCD-camera (Sony DFW-V500) with an ultrazoom lens (Navitar, UltraZoom) coupled with a microscope lens (Mitutoyo, 10×/0.28) or a macroobjective (Mörk, Mini Macro, Germany) with a 2 cm distance tube. Movies were
Fig. 2. The flow channel with its dimensions for (a) nongelling and (b) gelling experiments. All dimensions in millimeters.
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captured using BTVPro software (Version 5.4.1) and the image analysis was performed using ImageJ software (ImageJ 1.28v, National Institute of Health, USA). 3.2.5. Rheological properties The rheological properties of the disperse phase as a function of the temperature were measured by a small amplitude oscillatory shear experiment with a StressTech rheometer using a concentric cylinder geometry with a cup diameter of 22 mm and a bob diameter of 20 mm at an angular frequency of 1 Hz, and a cooling rate of 1 ◦ C/min. The storage modulus, G , and the loss modulus, G , were determined. The increase in storage modulus, G , above the noise level was taken as the rheometer gelation temperature, Tgel,rheo .
4. Results and discussion 4.1. Transient deformation of nongelling drops Deformation of nongelling drops was studied along a streamline eccentrically close to the narrowing wall and along a streamline on the centreline of the flow channel. If drops were injected from the double capillary close to the narrowing wall (Fig. 1b) drops were subjected to shear flow of the parabolic flow profile and deformations up to around D = 0.45 were achieved. Due to the low velocities of the continuous deformation phase close to the wall long residence times are realized. If the drops were injected on the centreline into the flow channel, negligible deformation was observed for two different drop diameters of 0.22 and 0.37 mm and two different flow rates of the continuous deformation phase (Qcont,def = 200, 1500 ml/min). The stresses acting on the centreline in the smooth contraction of the flow channel are not sufficient to deform the drops. In previous work, drop deformation into ellipsoids could be achieved on the centreline in contraction flow. A step decrease in the channel width from 10 to 1 or 2 mm enabled this deformation [1]. In the following, the interaction of the particle movement along the eccentric particle track and the consequences on droplet deformation and residence time needed for gelation will be discussed. 4.1.1. Particle track and residence time To maintain high shear stresses acting on the drop over a long period of time, a smooth narrowing channel geometry was chosen (Fig. 2a). The relative radial drop position, rtrack (x)/R(x), was measured at different channel positions and is illustrated in Fig. 3. Approximately 20 mm behind the injection point the velocities, vcont,gen and vcont,def , have equilibrated, and the relative particle track now decreases slightly from rtrack (x)/R(x) = 0.85 at x = 20 mm to rtrack (x)/R(x) = 0.7 at x = 120 mm. In this region the velocity of the continuous deformation phase on the centreline increases moderately. From x = 120 mm the veloc-
Fig. 3. Experimentally determined drop track and calculated velocity on the centreline as a function of the x-position along the channel for a flow rate of the continuous deformation phase, Qcont,def = 1400 ml/min (ddrop = 0.27 mm, water/sunflower oil, λ = 0.02).
ity, vcont,def , increases sharply and rtrack (x)/R(x) decreases drastically. As soon as the drops enter the straight channel at x = 150 mm, the velocity reaches its maximum value and the drops flow close to the centreline. At sufficient shear stress gradients along the drop interface, which are generated by the flow rate of the continuous deformation phase, Qcont,def , radial migration is enhanced. The phenomena is extensively reviewed and investigated by Leal [28] and Chang and Leal [29]. In dispersions, shearinduced migration of the suspended rigid particles is initiated by particle interaction and wall effects. Recent work by Li and Pozrikidis [30] pointed out that in case of liquid droplets as dispersed phase radial motion due to curvature of the velocity profile can be observed. In such cases the droplet “feels” not only a single shear stress but a shear stress gradient that is dependent on the absolute position of the droplet with respect to the centreline. The drops try to balance this stress gradient given by the Poiseuille flow profile by internal flow and consequently move towards the centreline where the shear stress gradient is zero. As pointed out by Li and Pozrikidis [30], drops near the centreline of the channel experience a reduced deformation compared to drops near the channel walls, as a result of the reduced shear rate near the centreline. This effect was generally also observed in our experiments. However, due to the choice of the narrowing channel geometry, radial migration to the centreline is less pronounced than in a straight channel geometry since the superimposed contraction counterbalances the migration. Furthermore, the migration can be suppressed when smaller droplets are used since large drops are affected by a broader stress distribution and consequently they have a strong tendency to move towards the centreline. Having analyzed the particle track we can calculate the residence time according to Eq. (5). As an approximation, it is assumed that the distance from the centreline decreases linearly along the channel for x x3 and remains constant
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383
Table 1 Residence time, Tresidence , of a drop within the different areas of the flow channel for Qcont,def = 800 and 1400 ml/min Qcont,def (ml/min)
Tresidence,1 (s)
Tresidence,2 (s)
Tresidence,3 (s)
800 1400
1.280 0.732
1.281 0.825
0.062 0.036
Tresidence,total (s) = 2.623 = 1.593
Fig. 5. Images of drops of different sizes at the channel position x3 = 150 mm at different flow rates of the continuous deformation phase, Qcont,def (1.75% κ-carrageenan solution/sunflower oil, λ = 4.94).
Fig. 4. Drop deformation as a function of the x-position along the channel for two different flow rates of the continuous deformation phase, Qcont,def (ddrop = 0.31 mm, water/sunflower oil, λ = 0.02).
when a drop enters the straight channel for x > x3 (Fig. 3). 0.028x + 4.557, if x x3 , rtrack (x) = (6) 0.225, if x > x3 . The particle track approximations are based on the following process parameters: Qcont,def = 800 ml/min and a drop diameter of d = 0.27 mm. For the calculation of the residence time, Eq. (5) was solved numerically for two different flow rates of the continuous deformation phase. The total residence time and residence time in areas 1, 2, and 3 (Fig. 2a) are displayed in Table 1. The residence time in area 3 is an order of magnitude smaller than in area 1 and 2. 4.1.2. Deformation along the channel The drop deformation, D, caused by the acting flow stresses, is shown in Fig. 4 as a function of the x-position along the channel for two different flow rates of the continuous deformation phase, Qcont,def = 800 and 1400 ml/min and a drop diameter of d = 0.31 mm. As shown with Eq. (4), the shear rate acting on the drop increases with the x-position in the channel due to the acceleration of the continuous deformation phase. Up to x = 100 mm the drops stay almost spherical because of weak stresses in the flow field. Thereafter deformation starts and a marked increase in drop deformation is then achieved between x2 and x3 (Fig. 2) even though the residence time is very short in this area. The largest drop deformations are obtained at around x3 where the narrowing channel turns into a straight channel. How-
ever, as soon as the deformed drops enter the straight channel (x > x3 ) the drops experience a strong migration force acting towards the centreline and start to relax back due to reduced stress (zero stress gradient regime of Poiseuille flow profile). As expected, larger deformations are obtained for higher flow rates, Qcont,def , due to the higher shear rates (Eq. (4)). 4.1.3. Drop deformation at a fixed position The impact of shear stress and drop size on the maximum drop deformation was investigated at position x3 , as shown by the images in Fig. 5. The stresses were varied by changing the flow rate of the continuous deformation phase, Qcont,def . The largest deformation is obtained at the highest flow rate of the continuous deformation phase, Qcont,def , and for the largest drops. The drops adopt ellipsoidal shapes with bulbous ends directed towards the centreline. This nonsymmetrical distortion may be attributed to internal flow and radial migration of the drops where the fluid volume tends to move towards the centreline. As can be seen in Fig. 5, this phenomenon is more pronounced for larger drops. The drop deformation is plotted as a function of the capillary number at x = x3 in Fig. 6 for a viscosity ratio of λ = 4.94. The variations in the radial position, rtrack (x) (Fig. 3), are taken into account to calculate the capillary number. The data points for different drop sizes are superimposed within the accuracy of measurement. In the flow channel, the drop deformation does not take place under steady conditions, since the drop’s residence time in each x-position is too short to reach a steady-state shape. Nor is the assumption of a fully developed flow field within the narrowing channel fulfilled. Even so, in Fig. 6 the experimental data are compared with Taylor’s small deformation theory (Eq. (2)) and the agreement between our experimental data and the theoretical curve is surprisingly good. Hence, Taylor’s theory can be used to roughly predict drop shapes in such a flow channel under nongelling conditions.
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Fig. 6. Drop deformation for different drop diameters as a function of the capillary number at the channel position x3 = 150 mm (1.75% κ-carrageenan solution/sunflower oil, λ = 4.94) and calculated deformation values according to Taylor’s theory.
Fig. 7. G (storage modulus) and G (loss modulus) of a 1.5% κ-carrageenan solution with 200 mM Na+ and 20 mM K+ as a function of temperature.
4.2. Transient deformation of gelling drops With gelation as an additional parameter the process becomes more complex. There will be not only a transient drop deformation but also a transient temperature gradient between the continuous deformation phase, the continuous generation phase, and the disperse phase. This gradient will ultimately trigger gelation of the disperse phase. The gelation behavior of the disperse phase in the rheometer is shown in Fig. 7. Gelation started at around 30 ◦ C (Tgel,rheo ≈ 30 ◦ C) and was followed by a strong increase in the storage modulus, G , and loss modulus, G . 4.2.1. Drop deformation under gelling conditions In Fig. 8 drop deformation is shown as a function of the x-position along the channel for stepwise cooling of the continuous deformation phase from Tcont,def = 35–26 ◦ C. The flow rate of the continuous deformation phase is Qcont,def = 1400 ml/min, and the drop diameter d = 0.32 mm. For the starting temperature of the continuous deformation phase,
Fig. 8. Impact of temperature-induced gelation on drop deformation as a function of the x-position along the channel (ddrop = 0.32 mm, 1.75% κ-carrageenan solution with 200 mM Na+ and 20 mM K+ /sunflower oil).
Fig. 9. Summary of maximum drop deformation at the channel position x = x4 = 180 mm and viscosity of the sunflower oil as a function of the temperature of the continuous deformation phase, Tcont,def . The rheologically determined gelation temperature, Tgel,rheo , is inserted for comparison (ddrop = 0.32 mm, 1.75% κ-carrageenan solution with 200 mM Na+ and 20 mM K+ /sunflower oil).
Tcont,def = 35 ◦ C, the deformation, D, along the channel, x, shows similar behavior to that in the nongelling experiments. The D-value stays rather low in the beginning of the narrowing channel geometry up to x2 . Thereafter a strong increase can be detected until x4 up to D = 0.47, and from then on the deformation vanishes again after the drops have migrated towards the centreline of the parallel channel. As the temperature of the continuous deformation phase is decreased, interesting changes in drop deformation can be detected after position x2 : Upon cooling down to Tcont,def = 30 ◦ C droplet deformation increases, but if cooling continues deformation decreases severely. The effect of cooling the continuous deformation phase from 35 to 26 ◦ C can be clearly seen in Fig. 9. In the figure the maximum deformation at x4 , the viscosity of the continuous deformation phase as a function of the temper-
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ature, and Tgel,rheo are shown. Decreasing the temperature of the continuous deformation phase from 35 to 30 ◦ C causes the deformation values to increase up to a maximum deformation of D = 0.63. The larger deformation is caused by the increased viscosity of the continuous deformation phase at lower temperatures since an increase in viscosity of the continuous deformation phase causes an increase in capillary number (Eq. (2)). The simultaneous increase in G and G of the disperse phase is slight and plays a minor role in the same temperature range (35–30 ◦ C) (Eq. (2) and Fig. 7). If the temperature of continuous deformation phase is below 30 ◦ C, smaller maximum deformations will be found. The onset of decreasing deformation corresponds well to the gelation temperature measured in the rheometer (Tgel,rheo ≈ 30 ◦ C) (Fig. 9). Obviously, at Tcont,def = 29 ◦ C, the temperature gradient between the continuous deformation phase and the disperse phase is sufficient to cool the disperse phase below the gelation temperature and trigger gel formation within the process time of about 1.5 s (Table 1). The additional increase in the viscosity of the continuous deformation phase by cooling it from 30 to 29 ◦ C is obviously less important than the strong increase in G and G of the disperse phase within the same temperature range. Upon further cooling, deformation continues to diminish because the higher temperature gradient promotes gelation. The match of the onset of disappearing deformation in the channel and the gelation temperature in the rheometer shows that the heat transfer from the drops to the oil is much faster than the process time. It cannot be distinguished directly from the experiments whether it is the viscous or elastic part of the gelling disperse phase that is the cause of the lower deformation of the disperse phase, since the two phenomena cannot not be separated in this system. However, it is assumed here, according to the literature discussed in the introduction [19–23], that the increasing viscoelasticity of the disperse phase provokes disappearing deformation more strongly than its increasing viscosity. The interfacial tension, σ , is assumed to be constant (σ = 0.026 N/m) over the whole process. In Fig. 8 it can further be seen that down to Tcont,def = 28 ◦ C, deformation values differ only from a channel position x = 160. But at Tcont,def = 27 and 26 ◦ C, the impact of viscoelasticity can be already detected at x = 140, 80 mm, respectively. At Tcont,def = 26 ◦ C, very little deformation is achieved and it seems that the drop forms a gel network early in the channel (around x = 80 mm or after about 1.3 s) and keeps an almost constant deformation up to x = 160 mm. A part of the deformation remains even after x4 due to the early gel formation. Obviously, the buildup of a gel network is delayed under flow until Tcont,def reaches 26 ◦ C. This delay could be ascribed to flow inside the liquid drops caused by the shear stress gradient of the Poiseuille flow [30]. Previous studies of gel formation of gelatin under high shear have shown that the gelation is delayed until the shear is decreased [31,32]. At a temperature of the continuous deformation phase, Tcont,def = 26 ◦ C, the system is strongly
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Fig. 10. Drop deformation as a function of the capillary number for different temperatures of the continuous deformation phase, Tcont,def (ddrop = 0.32 mm, 1.75% κ-carrageenan solution with 200 mM Na+ and 20 mM K+ /sunflower oil) and calculated deformation values according to Taylor’s theory (differences between calculated deformations for 35–30 ◦ C are very small and cannot be detected in the graph).
quenched and network formation can already occur in the beginning of the flow channel where shear stresses are rather low. If gel formation had not been delayed due to internal flow drops would not have been able to retract at temperatures well below the gelation temperatures but remained deformed as gelled particles. In Fig. 10 the drop deformation is plotted against the capillary number along the channel, which in this case expresses the channel length. The increasing viscosity of the continuous deformation phase with decreasing temperature was accounted for when calculating the capillary number and it was assumed that the continuous deformation phase keeps the set temperature over the whole process. Above 30 ◦ C the curves coincide quite well, and the deformation shows a linear relationship with the capillary number and fits rather well with the deformation values calculated with Taylor’s theory (dotted line in Fig. 10). Even the curve at 29 ◦ C still lies in this bulk of curves because gel formation starts only in the very end of the geometry. Hence, the gelling system above Tgel shows comparable results to the nongelling system. The curves start to deviate from the linear behavior and theoretical value at a temperature of the continuous deformation phase, Tcont,def = 28 ◦ C at a capillary number of about 0.25. With further decreasing of Tcont,def the linear relationship disappears at even lower capillary numbers, i.e., earlier in the channel. This can be attributed to a faster or earlier strong increase in the viscoelasticity of the disperse phase. These results about the impact of gelation on drop deformation can also explain the decreased drop deformation for gelled drops compared to Newtonian drops found by Wolf et al. [24]. Scaling relationships of flow kinetics and gelation kinetics were established in previous work [1,5,6] and a transformation of the presented knowledge to other flow geometries is therefore possible.
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The results in Figs. 8–10 showed the impact of gel formation on drop deformation and thereby it was possible to detect small differences in fast gel kinetics at high temperature gradients via drop deformation analysis.
5. Conclusions The present study has shown the possibility of deforming κ-carrageenan solution drops into ellipsoids under shear flow in a smooth narrowing deformation channel of a fast continuous flow process. Additionally, it was possible to study in situ the impact of temperature-induced gel formation on drop deformation along the deformation channel at time frames below 2 s. This provided an opportunity to learn about gel kinetics on such short timescales under high temperature gradients. Experimental deformation values of nongelling drops under shear flow could be recalculated surprisingly well with Taylor’s small deformation theory even though deformation occurred under nonsteady-state conditions. Gelling drops above the gelation temperature show behavior comparable to that shown by nongelling drops. Upon cooling the continuous deformation phase towards the gelation temperature of the disperse phase, its increased viscosity causes greater drop deformation. But as soon as gelation is induced, the strongly increasing storage modulus, G , and loss modulus, G , of the drops reverses the trend. Upon further cooling of the continuous deformation phase, deformation continues to decrease measurably in the fast process due to the higher temperature gradient between the phases causing faster gel kinetics. However, the formation of a gel network is delayed until the continuous deformation phase has a temperature of Tcont,def = 26 ◦ C. Under this condition the system is sufficiently quenched to induce gelation early in the deformation channel, where shear stresses, provoking internal flow and disruption of developing networks, are low. Therefore, the low deformation experienced by the droplets in the beginning of the deformation geometry is frozen in, and remains along the whole channel. The results from the described process give additional insight into gel kinetics under high temperature gradients and short timescales, thereby augmenting the knowledge obtained from established rheological measurements.
Acknowledgments The authors thank Jan Corsano, Daniel Kiechl, and Bruno Pfister for the construction of the flow cell as well as the data acquisition system. This work has been carried out with financial support from the Commission of the European Communities, specific RTD programme “Quality of
Life and Management of Living Resources,” Key Action 1-Health Food and Environment, QLK1-2000-1543 Structure Processing: “Structure engineering of emulsions by micromachined elongational flow processing.” Part of the work has been carried out with the financial support from the Swiss Federal Office for Education and Science (Project BBW 00.0072). It does not necessarily reflect the views of the Commission of the European Communities and the Swiss Federal Office for Education and Science and in no way anticipates the funding body’s future policy in the area.
References [1] B. Walther, L. Hamberg, P. Walkenström, A.-M. Hermansson, J. Colloid Interface Sci. 270 (2004) 195–204. [2] B. Wolf, W.J. Frith, S. Singleton, M. Tassieri, I.T. Norton, Rheol. Acta 40 (2001) 238–247. [3] L. Hamberg, P. Walkenström, A.-M. Hermansson, J. Colloid Interface Sci. 252 (2002) 297–308. [4] L. Hamberg, M. Wohlwend, P. Walkenström, A.-M. Hermansson, Food Hydrocolloids 17 (2003) 641–652. [5] B. Walther, P. Walkenström, A.-M. Hermansson, P. Fischer, E.J. Windhab, Food Hydrocolloids 16 (2002) 633–643. [6] C. Cramer, P. Fischer, E.J. Windhab, Chem. Eng. Sci. 59 (2004) 3045– 3058. [7] P. Fischer, K. Maruyama, E.J. Windhab, Chem. Eng. Techn. 27 (2004) 1161–1171. [8] P.B. Umbanhowar, V. Prasad, D.A. Weitz, Langmuir 16 (2000) 347– 351. [9] D.F. Zhang, H.A. Stone, Phys. Fluids 9 (8) (1997) 2234–2242. [10] G.I. Taylor, Proc. R. Soc. London A 138 (1932) 41–48. [11] G.I. Taylor, Proc. R. Soc. London A 146 (1934) 501–523. [12] H. Stone, Annu. Rev. Fluid Mech. 26 (1994) 65–102. [13] J.M. Rallison, Annu. Rev. Fluid Mech. 16 (1984) 54–66. [14] B. Walther, SIK-Report No. 682, SIK, Göteborg, 2001. [15] F.D. Rumscheidt, S.G. Mason, J. Colloid Sci. 16 (1961) 238–261. [16] F.D. Rumscheidt, S.G. Mason, J. Colloid Sci. 17 (1962) 260–269. [17] D. Megias-Alguacil, P. Fischer, E.J. Windhab, J. Colloid Interface Sci. 274 (2004) 631–636. [18] H.P. Grace, Chem. Eng. Commun. 14 (1982) 225–277. [19] D.C. Tretheway, L.G. Leal, AIChE J. 45 (5) (1999) 929–937. [20] S. Ramaswamy, L.G. Leal, J. Non-Newton. Fluid Mech. 85 (1999) 127–163. [21] W.J. Milliken, L.G. Leal, J. Non-Newton. Fluid Mech. 40 (1991) 355– 379. [22] R.A. de Bruijn, Ph.D. thesis, Technische Univ., Eindhoven, 1989. [23] L.A. Ultracki, Z.H. Shi, Poly. Eng. Sci. 32 (1992) 1824. [24] B. Wolf, W.J. Frith, I.T. Norton, J. Rheol. 45 (5) (2001) 1141–1157. [25] P.L. Maffetone, M. Minale, J. Non-Newton. Fluid Mech. 78 (1998) 227–241. [26] P.L. Maffetone, M. Minale, J. Non-Newton. Fluid Mech. 84 (1999) 105–106. [27] A.-M. Hermansson, E. Eriksson, E. Jordansson, Carbohydr. Polym. 16 (1991) 297–320. [28] L.G. Leal, Ann. Rev. Fluid Mech. 12 (1980) 435–476. [29] P.C.-H. Chang, L.G. Leal, Int. J. Multiphase Flow 7 (1981) 83–99. [30] X. Li, C. Pozrikidis, Int. J. Multiphase Flow 26 (2000) 1247–1279. [31] M. Djabourov, J. Leblond, P. Papon, J. Phys. France 49 (1988) 333– 343. [32] W. de Carvalho, M. Djabourov, Rheol. Acta 36 (6) (1997) 591–609.