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aqueous dispersions
Chemical Engineering Science 56 (2001) 3247–3255
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The e!ect of volume fraction and impeller speed on the structure and drop size in aqueous=aqueous dispersions A. W. Pacek ∗ , P. Ding, A. W. Nienow School of Chemical Engineering, The University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Received 1 June 2000; received in revised form 2 January 2001; accepted 16 January 2001
Abstract The mean drop size and the structure of two-phase aqueous=aqueous dispersions, one-phase sodium alginate-rich of viscosity
∼0:25 Pa s and the other sodium caseinate-rich of viscosity ∼0:022 Pa s, have been measured in an unba5ed vessel 6tted with a
helical screw impeller. The measurements were carried out over a range of volume fractions and at Reynolds numbers in the range from laminar to low transitional. In addition, the interfacial tension between the two phases has been measured in situ using a recently developed drop retraction technique, which, for the 6rst time, has been successfully applied at a high volume fraction of the dispersed phase. At low volume fractions of the viscous phase (viscosity ratio, = d =c ≈ 10), drops of that phase are seen much as in equivalent aqueous=oil dispersions but the functionality between the drop size and impeller speed is di!erent. As the volume fraction of the viscous phase increases, the structure 6rst changes to a striated one, something never seen in “pure” oil=aqueous dispersions. The striated structure also evolves into complex (droplets-in-drops) in samples withdrawn from the vessel and within the vessel when stirring is stopped. This implies that the system is in a phase inversion region, but contrary to oil=water dispersions, there is not a rapid switch from one phase being continuous to the other, i.e. the phase inversion region appears to be very stable in time. On a further increase of the volume fraction of the viscous phase, phase inversion occurs when stirring but a striated structure continues to exist, i.e. there is no dramatic change of structure as found with aqueous=oil dispersions undergoing phase inversion. However, when a sample is withdrawn or the impeller is stopped, the complex droplets-in-drops formation no longer appears and only a simple dispersed structure develops. Only at very low speeds and volume fractions of the low viscosity dispersed phase, i.e., ∼0:1, do drops re-appear in the vessel when stirring. Overall, it can be concluded that there is a very signi6cant di!erence in the behavior of oil=aqueous and aqueous=aqueous dispersions. ? 2001 Elsevier Science Ltd. All rights reserved. Keywords: Aqueous=aqueous dispersion; Drop size; Striations; Viscosity ratio; Agitation
1. Introduction Aqueous–aqueous two-phase systems (ATPS) are used in the food industry (Tolstoguzov, 1996), in the separation of biological materials (Huddleston & Lyddiatt, 1990) and such systems can also be used in extraction of metal ions and other inorganic components (Graber, Andrews, & Asenjo, 1999). However, the literature on ATPS is limited to equilibrium data, e.g., phase diagrams are available for many phase separating systems (Zaslavsky, 1995) but even the accuracy of that data is questionable (Pacek, Ding, Nienow, & Wedd, 2000). ∗ Corresponding author. Tel.: +44-121-414-5308; fax: 44-121414-5324. E-mail address: [email protected] (A. W. Pacek).
Whatever the application of ATPS, an understanding of the inIuence of hydrodynamic conditions on the structure and the stable drop size is essential. In the food industry, the structure has a strong inIuence on the sense of taste and in bioseparation or extraction, the interfacial area is important in determining the rate of mass transfer. ATPS are often processed in stirred vessels, but there is practically no information in the open literature on the inIuence of hydrodynamic conditions on the structure of the dispersion, drop sizes, the dynamics of breakage or coalescence, etc. It is often assumed that ATPS are essentially similar to oil=aqueous dispersions (Mitchell & Ledward, 1986). Accepting this general assumption, certain consequences, which are not often spelt out, have also to be recognized.
0009-2509/01/$ - see front matter ? 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 1 ) 0 0 0 1 5 - X
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Firstly, the structure of pure (no surface active agents) oil=aqueous systems exposed to suNciently intensive hydrodynamic conditions is such that up to 30% volume fraction of one phase, that phase is always present in the form of simple drops. Secondly, the structure of the aqueous=oil dispersion at phase inversion is inherently unstable and within a relatively short time (¡ 1 min) a dispersion becomes either oil or aqueous continuous (Nienow, Pacek, & Homer, 1994) even though the dispersed phase structure might be complex. Additionally, this assumption implies that the theory which is used to calculate the maximum stable drop size (the concept of critical Capillary or Weber number), breakage (Janssen & Meijer, 1993) and coalescence rates (Chesters, 1991) in oil=aqueous dispersions can be directly applied to aqueous=aqueous dispersion if the physical properties of both phases and the interfacial tension are known. In this paper, a preliminary investigation of the inIuence of hydrodynamic conditions on the structure of ATPS in a mixture of phase separating biopolymers: sodium alginate (NaA), sodium caseinate (NaC) are reported. Those biopolymers were selected because they phase separate without gelling so that, in this respect, they are similar to oil=water dispersions. The results clearly show that there are, however, a number of major di!erences between aqueous=aqueous and aqueous=oil dispersions. 2. Experimental 2.1. Approach As phase separation occurs when the aqueous solutions of two incompatible polymers are mixed together, in principle, it is possible to obtain the dispersion by directly mixing pure NaA solution with pure NaC solution. After mixing, phase separation occurs but the volumetric ratio of separated phases is not known a priori (unless an accurate phase diagram is already available) and also the physical properties of each phase (which are usually very di!erent from the properties of the original solutions) are not known. Therefore, in the experiments reported below, a di!erent procedure was adopted. First, aqueous solutions of both biopolymers were made (stock solutions). Next those solutions were mixed, equilibrated and separated, and 6nally the separated solutions, Na alginate rich (NaA-rich) and Na caseinate rich (NaC-rich), were used to prepare a range of dispersions with both the composition (volume fraction of dispersed phase) and physical properties of each phase being well de6ned. 2.2. Materials The stock solutions of NaA and NaC were prepared following the procedure outlined by Blonk, Endenburg,
Koning, Weisenborn, and Winkel, (1995). Na-caseinate (molecular weight ∼25; 000 Da, supplied by Sigma, lot 36H0408) gives solutions of relatively low viscosity so the powder was gradually added to deionized, distilled water at room temperature and mixed by a magnetic stirrer. The pH of the solution was continuously monitored and adjusted to pH = 7 using 0:1 N NaOH. The 6nal solution was centrifuged at 170=s for 2:5 h to separate undissolved particles. NaA (Manucol DM, molecular weight ∼500; 000 Da, supplied by Kelco lot No 590961) gives much more viscous solutions and therefore it had to be dissolved in a jacketed stirred vessel connected to a water bath and 6tted with helical screw impeller. NaA powder was gradually added to deionized, distilled water at ◦ 50 C whilst continuously stirring at N = 5=s. pH was continuously monitored and adjusted with 0:1 N NaOH to ◦ pH = 7. The 6nal solution was heated to 70 C and “conditioned” at this temperature for 30 min and after that ◦ time cooled to 22 C. Sodium azide at concentration of 0:03% w=w was added to both solutions to avoid biological degradation. The stock solutions were mixed and equilibrated for two hours and separated into NaA-rich and NaC-rich phases by centrifugation for 8 h at 300=s. The equilibrated NaA-rich (1.7% NaA, 1.3% NaC) was initially used as the dispersed phase and the equilibrated NaC-rich (8.2% NaC, 0.5% NaA) as the continuous one. 2.2.1. Physical properties of both phases The density of NaA-rich and NaC-rich were measured by density bottle (NaA-rich = 1015 kg=m3 , NaC-rich = 1020 kg=m3 ). The rheological properties of both phases and a 5.5% NaA-rich in NaC-rich dispersion were measured by a Carri-Med, CSL rheometer. The results are shown in Fig. 1 and the experimental data were 6tted to the power low model: = K ˙n−1
(1)
with K and n values also shown in Fig. 1. Both NaA-rich and NaC-rich phases (Fig. 1a) as well as the 5.5% dispersion on NaA-rich in NaC-rich (Fig. 1b) are very weakly non-Newtonian (n ¿ 0:95). Therefore, it is unlikely that such low degree of non-linearity alone can cause such drastic changes in the behavior of the aqueous=aqueous dispersion compared to Newtonian aqueous=oil dispersions as discussed below. As both NaA-rich and NaC-rich phases mainly contain water, the density of both phases is practically the same. In addition, the phases are suNciently viscous that interfacial tension cannot be measured by the pendant drop method as the drop will not detach from the nozzle, nor can the sessile or spinning drop methods be used. Therefore, the retracting drop method as recently developed was used and extended from considering a single drop (Sigillo, Di Santo, Guido, & Grizzutti, 1997; Guido & Villone, 1999) to multiple drops as actually
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Fig. 1. The apparent viscosity of: (a) NaA-rich phase ( ) and NaC-rich phase (•); (b) 5.5% v=v NaA-rich in NaC-rich dispersion, symbols—experimental data, lines—best 6t from the power-law model with K and n values shown in the graphs.
produced by agitation. In this method, the interfacial tension can be measured either by imposing steady state shear on the drop, thus producing an ellipsoid, and measuring the equilibrium drop shape; or by measuring the time evolution of the shape of the drop after removing the stress (Sigillo et al., 1997). There are two versions of the latter method that di!er in their de6nition of the deformation coeNcient and thus the relationships developed. Sigillo et al. (1997), de6ned the deformation parameter as a ratio of the lengths of the ellipsoid axes ( = a=b) and developed the following expression relating the interfacial tension, , viscosity ratio, , and deformation parameter : exp 1 + 2=(5( − 1) 2 ) 1 d I ( exp ) =
(((1 + 2=5)=) )0:125 (1 − )
0 1 (t − t0 ); (2) where 0 is the deformation at the moment that shearing is stopped (t = t0 ) and exp is deformation at time, t, with c R∞ ; (2a) = 0:465 where R∞ is the radius of the undeformed, spherical drop. Guido and Villone (1999) adopted a more common de6nition of the deformation parameter D = (a − b)=(a + b), and developed the following expression for deformation parameter: t 40( + 1) ; (3) D = D0 exp − (2 + 3)(19 + 16) R∞ c =
where D0 is the deformation parameter at t = t0 . Here, the gradual change of the structure of the dispersion from one containing deformed drops to spherical ones in response to the change of the shear rate from a 6nite value (corresponding to the impeller rotating) to zero (the impeller stopped) was employed to obtain these
deformation parameters and to calculate interfacial tension. Such a procedure enabled the measurements of interfacial tension to be made directly in the vessel without withdrawing samples. Making the measurements in situ is very important because the withdrawing of the sample would generally cause additional distortion of the drops and limit the accuracy of the results. The change of structure inside the vessel was continuously recorded by the video technique (Pacek, Moore, Calabrese, & Nienow, 1994a). Fig. 2 shows example of video images as the initially deformed ellipsoidal drop (Fig. 2a, t = 0) changes (Fig. 2b, t = 30 s) into a spherical one (Fig. 2c, t = 1 min) when retraction is completed. In total, 3000 images were available within 1 min of recording. However, as the retraction was slow, only 13 images (every 5 s) were digitized and the deformation parameters as a function of time were calculated from these digitized images using in-house image analyzing software. The experimental results (points) are shown in Fig. 3. According to the 6rst method, if the values of I ( exp ) are plotted as a function of time, the data should line on the straight line with the slope equal 1= and the interfacial tension can be calculated from Eqs. (2) and (2a). The regression line shown in Fig. 3a (r 2 = 0:982) clearly shows that the experimental data can be approximated by a straight line and the calculated interfacial tension is equal = 1:178 × 10−6 N=m. From Fig. 3b, the best 6t line of Eq. (3) gives = 1:102 × 10−6 N=m. Recently, Guido, Simeone, and Alfani (1999) used the same method to measure interfacial tension of a single drop of NaA in a NaC system at a similar viscosity ratio but with absolute values of the viscosity of each phase about ten times higher that in the reported case. They obtained values of 8:15 × 10−6 N=m. Considering the extremely low values of interfacial tension as well as the di!erences in viscosity (because of the di!erent molecular weight of the polymers employed), the agreement is rather good.
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Fig. 2. The images of retracting drop: (a) time 0 s, (b) time 30 s, (c) time 1 min.
Fig. 3. Deformation parameter as a function of time; (a) calculated from Eqs. (2) and (2a); (b) calculated from Eq. (3), (•) experimental data.
2.3. Experimental rig and procedure The stirred vessel (T = 0:1 m) was Iat bottomed, without ba5es and the liquid height, H , was equal to the vessel diameter. This vessel was placed in a water bath of square cross section made from optically Iat glass to avoid distortion and to control tempera◦ ture to 20 C. Agitation was by helical screw impeller (D = 0:06 m; pitch = 0:02 m), placed 0:01 m from the bottom. The structure of the dispersion was observed and when appropriate, drop sizes were measured. Mean sizes and size distributions were also obtained using the video-microscope-computer system described in detail previously (Pacek et al., 1994a). Two sets of experiments were carried out. In the 6rst set, the e!ect of the impeller speed on mean drop size of the 5.5% v=v NaA-rich phase dispersed in the NaC-rich phase was investigated (∼10). Initially, the impeller speed was increased stepwise from 0.067 to 0:33 rps, to 0.67 and to 1:0 rps. Next, the impeller speed was reduced stepwise from 1 to 0:67 rps, to 0.33 and 6nally to 0:067 rps. At each impeller speed, the dispersion was stirred for at least 60 min. The Reynolds number varied from 10 to 160 when calculated assuming a constant viscosity (see Fig. 1) of NaC-rich of 0:022 Pa s. Thus, the Iow was laminar or just into the transitional Iow regime
(Harnby, Edwards, & Nienow, 1997). Drop sizes were measured directly in the vessel, approximately 2 mm from the wall both during agitation and after stopping it. In the second set of experiments, the inIuence of the volume fraction of NaA-rich phase on the structure of the dispersion was investigated at two impeller speeds, 0.13 and 0:67 rps i.e. Re ¡ 10, laminar Iow. The volume fraction of NaA-rich was gradually increased from 5.5% v=v NaA-rich until the system inverted (assessed as discussed below) to become NaA-rich continuous and NaC-rich dispersed (∼0:1). Further increases of NaA-rich led to a steadily lower fraction of NaC-rich dispersed. At each composition of dispersion, the structure was recorded and analyzed. In certain cases, samples were removed from the vessel and the change of structure followed on a microscope slide with the video system but with a higher magni6cation. 3. Results and discussion 3.1. Steady state sizes in the diluted NaA-rich in NaC-rich dispersion Steady state Sauter mean drop diameters as a function of increasing and decreasing impeller speed are
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Fig. 4. Sauter mean diameters after impeller speed was increased (◦) and after impeller speed was decreased ( ).
summarized in Fig. 4. When the impeller speed increased, the steady state was approached via breakage and when the impeller speed decreased, the steady state was approached via coalescence. At higher impeller speeds, there is a very good agreement between the equilibrium drop mean diameters from both directions. There is, however, a di!erence between them at the lowest impeller speed. Here, the drops after the impeller speed was decreased were approximately 20% smaller than the drops developed after the initial mixture was agitated. This di!erence might be explained by the fact that at this very low speed, the time was insuNcient for equilibrium to be reached, either by breakage, or especially due to coalescence (Calabrese, Pacek, & Nienow, 1993). For aqueous-oil dispersion, it has been shown that the maximum stable drop size (critical drop size of radius, Rmax ) in laminar Iow can be calculated from the critical Capillary number Cacr c R ˙ max ; (4) Cacr = = =Rmax where Cacr depends on and on the type of Iow. In rotational shear (or Couette) Iow, Cacr , strongly depends on and if ¿ 4, dispersed drops cannot be broken (Grace, 1982; Janssen & Meijer, 1993). On the other hand, for two-dimensional elongation Iow, Cacr is less dependent on and for 10−3 6 6 10+3 , Cacr lies between 1 and 0.1. Thus, in this type of Iow, drops can be broken regardless of (Janssen & Meijer, 1993). Here, = 10, and the drops were broken, becoming smaller as the impeller speed increased. Such a result implies either: (1) that the drops were exposed to elongation Iow which is highly probable in the complex 3D Iow 6eld produced by the helical screw impeller; or (2) that APTS do not obey the same breakage rules as aqueous=oil systems if the Iow is purely rotational. To calculate Cacr , it is necessary to know the local shear rate. Such data are not readily available for the system used here and the values vary throughout the vessel. A modi6ed critical capillary number, Cacr−m may be de6ned in terms of the average shear rate ˙A with the help of the
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Fig. 5. A modi6ed critical Capillary number Caar−m (see Eq. (4)) based on drop size d32 , measured after increase of impeller speed (steady state approached via breakage).
well-established correlation with impeller speed (Harnby et al., 1997)
˙A = ks N
(5)
if it is assumed that ˙A represents the impact of both shear and elongation Iow (though the development of the concept by Metzner and Otto (Harnby et al., 1997) was for shear Iow alone). Therefore, [dmax =2]ks Nc : (6) Cacr−m = As ks is constant for a particular impeller-vessel con6guration, then Cacr−m like Cacr should depend only on the viscosity ratio. Fig. 5 shows Cacr−m assuming ks = 10 (Harnby et al., 1997) and dmax = d32 , as a function of N . Thus, Cacr−m values are in the range 0.2–1.2. However, in the range = 10–20 for pure elongational Iow for oil=aqueous dispersions, Cacr (Eq. (4)) equals 0.1. Therefore, it would appear that the drops are bigger than would be predicted from the theory developed for oil=aqueous dispersions. However, it should also be recognized that a number of major assumptions have been made in this analysis which must make these conclusions somewhat tentative. From Fig. 4, it is also clear that the functionality between drop size and impeller speed is very di!erent to one predicted by Eq. (6), i.e., dmax ≈ N −1 (Eqs. (4) and (6) if Cacr or Cacr−m are constant) and the best 6t to the experimental data is: d32 = 16:56N −0:27 :
(7)
There appears to be another major di!erence between oil=water and aqueous=aqueous dispersions. In oil=aqueous systems, before a drop is broken, it is 6rst deformed and consequently it becomes unstable (Rallison, 1984). Janssen and Meijer (1993) reported that the breakage time at = 3:6 vary between 4 and 6 s. In the present experiments, the images of drops were obtained at frequency of 50 Hz. Careful observation of hundreds of images taken after step increased of impeller speed
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did not show any drop deformation leading to breakage. This fact seems to imply that drops simply burst at breakage i.e. it happens too quickly to be observed even at 50 frames=s. 3.2. The in5uence of the volume fraction of the two phases and of the impeller speed on the structure of dispersions The volume fraction of NaA-rich was increased stepwise from 5.5 to 98.9% and at each volume fraction, the dispersion was stirred at 0.13 and 0:66 rps for 30 mins. The structure of the dispersion was monitored in three ways representing two di!erent scales. Firstly, visual observation of the macro structure in the whole vessel showed that there was no di!erence between the top and the bottom of the vessel, e.g. the system was well mixed at this scale. Secondly, the microstructure was observed directly in the vessel using the video technique (scale ranging from 0.2 to 1 mm, resolution approx. 20 m) at di!erent positions along the height of the vessel. Thirdly, samples were withdrawn from di!erent positions in the vessel and analyzed using a higher magni6cation optical microscope (scale below 0:2 mm, resolution approx. 5 m). In both the latter cases, the observed structures (qualitatively) were independent of the position along the height of the vessel. Thus, under all conditions, the vessel contents could be considered well mixed at the macroscale. On the other hand, at the microscale, quite di!erent structures were seen depending on the composition, impeller speed and whether the structure was observed in situ or in a withdrawn sample. These microstructures are summarized in Table 1, Figs. 6 and 7. Initially, up to approx. 30% v=v. NaA-rich, spherical drops of NaA-rich phase in NaC-rich phase were seen both in the vessel and in the sample and the structure was rather similar to the structure of oil=aqueous dispersions. However, the e!ect of volume fraction of dispersed phase was much smaller than in oil=aqueous dispersions, the increases of volume fraction of dispersed phase having only a marginal e!ect on drop size. The increase of drop size with volume fraction of dispersed phase in oil=aqueous dispersions is usually attributed to an increase of coalescence rate (Pacek, Nienow, & Moore, 1994b). Clearly, as already shown here, aqueous=aqueous dispersions separate and coalesce much more slowly than oil=aqueous ones. It is suggested that this much slower coalescence is the reason for the insensitivity of the drop size to volume fraction of dispersed phase. As the volume fraction of dispersed phase was increased above 30%, a gradual change of the structure of the dispersion was observed. At volume fractions between 30% and 40%, NaA-rich drops started to deform, taking on ellipsoidal shapes similar to those shown in Fig. 2 but which did not break under shear. These shapes could be
Fig. 6. Striations (tubular-like structures) of NaA-rich in NaC-rich dispersion observed in situ during stirring in “the phase inversion region” at a volume fraction of NaA-rich phase of 54%: (a) original video image, (b) part of the image after electronic magni6cation and enhancement.
seen both directly in the vessel, with some strongly deformed drops also being seen in the withdrawn samples. The increase of volume fraction of NaA-rich phase above approximately 40% led to a striated, macrostructure in the whole vessel as shown in Fig. 6. Fig. 6a shows the video image of the structure inside the vessel whilst stirring. Even in this image, the striations (lines rather than drops as in oil=water dispersions at the same volume fraction) can be seen. However, the quality of the image is not good enough to characterize the striations. Simple image processing (Paint Shop Software, Version 5.01) enabled a signi6cant enhancement of the original image (see Fig. 6b) to the extent that the dimensions of the striations can be estimated. However, for the interpretation of Figs. 6a and b, one has to remember that the structure of the dispersion in the vessel is three-dimensional
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Table 1 The structure of NaA-rich=NaC-rich dispersions Volume fraction of NaA-rich (%)
Dispersed phase
5.5 8.9 15.9 21.5 30.1 38.2 46.4 53.6 65.9 78.0 80.5 93.0 98.9
Na-alginate rich Na-alginate rich Na-alginate rich Na-alginate rich Na-alginate rich Na-alginate rich Phase inversion region Phase inversion region Phase inversion region Na-caseinate rich Na-caseinate rich Na-caseinate rich Na-caseinate rich
Structure In the vessel
In the sample
Drops Drops Drops Drops Drops Deformed drops Striationsa Striationsa Striationsa Striations Striations Striationsb Striationsc
Drops Drops Drops Drops Drops Drops Multiple dispersion Multiple dispersion Multiple dispersion Drops Drops Drops Drops
a Drops-in-drops
in the vessel after impeller was stopped, the phase inversion occurred in this region. drops at 8 rpm. c Spherical drops at 8 rpm. b Deformed
whereas the images show only two dimensions. Considering that the velocity 6eld in a stirred vessel is also inherently three dimensional, the term striated does not seem to be entirely appropriate. It is suggested that the term tubular-like structures would be better. From Fig. 6b, the diameter of these “tubes” can be estimated as between 8– 20 m with lengths exceeding 400 m. The tubular-like structures observed in the vessel during stirring evolved into drops of di!erent size, ranging from very large and complex (droplets-in-drops, multiple dispersion) to very small when the impeller was stopped (see Fig. 7a). The complex drops were also observed in the samples taken from the dispersion under stirring conditions (tubular-like structure in the vessel) and an example of such a structure is shown in Fig. 7b. As multiple dispersions in oil=aqueous systems are typically associated with phase inversion (Pacek et al., 1994b), it is assumed that these structures in ATPS also indicate an approach to phase inversion. 1 Therefore this region is called here “the phase inversion region”. The complex, multiple dispersions, indicating “the phase inversion region” were observed from approx. 40% to approx. 75% NaA-rich phase. In addition, over 40 –75% range of volume fractions of NaA-rich phase, such complex structures were always present both in the vessel and in the sample however long stirring was continued. 1 Precise determination of a phase boundary (the phase inversion region) in aqueous=aqueous dispersions is much more diNcult than in oil=aqueous dispersions. Whilst in oil=aqueous dispersions, phase inversion can be precisely detected by monitoring the conductivity of the dispersion (Nienow et al., 1994), its detection in an aqueous=aqueous dispersion requires an analysis of the structure of the dispersion. This analysis is usually done on a sample from the mixture using confocal microscopy (Foster, Underdown, Brown, Ferdinands, & Norton, 1997).
Above 75% of NaA-rich, the strati6ed structure continued to exist with the threads becoming more uniform and when the impeller was stopped, the threads slowly broke into the drops of about 10 –15 m diameter. In addition, the samples withdrawn from the vessel developed a typical simple dispersed structure, with similar sizes drops. The threads when stirring and the drops observed under static conditions were all of a size essentially independent of the impeller speed. It was concluded that this simple structure seen after ceasing agitation and in withdrawn samples, indicated that phase inversion had occurred, i.e. that the NaC-rich phase was now dispersed. Only at a volume fraction of NaC-rich dispersed phase below 10% v=v was an e!ect of impeller speed on the structure of the dispersion observed. At 0:67 rps, threads still existed whereas at 0:13 rps, a mixture of deformed and spherical drops was observed. In addition, when agitation at 0:67 rps was stopped, the threads reformed into a series of very uniform small drops, of the order of 15 m diameter equivalent to those seen at 0:13 rps. Clearly, there is a di!erence between the structure of dilute dispersions when NaA-rich is dispersed as compared to NaC-rich being dispersed. In summary, it would appear that overall three stable dispersions can be produced: NaA-rich in NaC-rich, NaC-rich in NaA-rich, each with their own characteristic behavior, and a complex phase inversion region with strati6ed structures under dynamic conditions which evolve into multiple dispersions under static conditions. 4. Conclusions To the authors’ knowledge, this is the 6rst time that the structure and dynamic behavior of agitated aqueous=aqueous dispersions has been discussed in some
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mainly water and perhaps because NaC is a rather strong surface-active agent. Notation a b Cacr Cacr−m d dmax d32 D D0 ks K n N R∞ Rmax Re t t0
longer axis of deformed drop, m shorter axis of deformed drop, m critical Capillary number [Eq. (2)], dimensionless modi6ed critical Capillary number [Eq. (4)], dimensionless drop size, m maximum drop size, m Sauter mean diameter, m deformation parameter = (a − b)=(a+b), dimensionless deformation parameter at t0 , dimensionless shear rate constant, dimensionless consistency constant, Pa sn power-law index, dimensionless impeller speed, rps unperturbed or 6nal drop radius, m maximum stable drop radius, m impeller Reynolds number, dimensionless time, s time at which drop retraction measurement starts, s
Greek letters
Fig. 7. Complex, multiple dispersed structures in the phase inversion region 54% NaA-rich in NaC-rich dispersion after ceasing stirring: (a) in the vessel after 3 min; (b) in a sample after approx. 1 min from withdrawal.
detail. The results show that the analogy between “pure” aqueous=oil and aqueous=aqueous dispersions is rather limited. The major di!erence is that the structure of ATPS depends critically on which phase is dispersed and the overall composition of the system and to lesser extent on the hydrodynamic conditions. There is also a much wider range of concentrations over which ATPS dispersions are complex and over which the system appears to be in a stable “phase inversion” state. In this complex region, striations or “tubular-like” structures are seen and such phenomena have not been reported for aqueous=oil systems, where essentially the dispersed phase is always in the form of drops. In ATPS dispersions, the breakage mechanism also appears to be di!erent and even when dilute, they do not follow the same stable drop size relationships. It should also be stressed that the interfacial tension was extremely low, probably because both phases contain
c d
deformation parameter = (a=b), dimensionless viscosity ratio (d =c ), dimensionless viscosity of continuous phase, Pa s viscosity of dispersed phase, Pa s density, kg=m3 interfacial tension, N=m
Acknowledgements This work forms part of the project Processing of Biopolymer Mixture for Zero and Low Fat Foods, FAIR CT97 3022-Biomix, sponsored by European Union. The authors would like to acknowledge very helpful discussions with many academic and industrial colleagues involved in this Biomix project; and also with Prof. Ian Norton and Dr. Tim Foster (Unilever Research Colworth Lab, Sharnbrook, UK). References Blonk, J. C. G., Endenburg, J., van Koning, M. M. G., Weisenborn, P. C. M., & Winkel, C. (1995). A new CSLM-based method for determination of the phase behavior of aqueous mixture of biopolymers. Carbohydrate Polymers, 28, 287–295.
A. W. Pacek et al. / Chemical Engineering Science 56 (2001) 3247–3255 Calabrese, R. V., Pacek, A. W., & Nienow, A. W. (1993). Coalescence of viscous drops in stirred dispersions, The 1993 Institution of Chemical Engineers Research Event, Birmingham, UK, January Rugby, UK; Institution of Chemical Engineers (pp. 642– 644). Chesters, A. K. (1991). The modeling of coalescence processes in Iuid-liquid dispersions: A review of current understanding. Transactions of the Institution of Chemical Engineers, 69A, 259–270. Foster, T. J., Underdown, J., Brown, C. R. T., Ferdinando, D. P., & Norton, I. T. (1997). Emulsion behaviour of non-gelled biopolymer mixtures. In E. Dickinson & B. Bergensthal (Eds.), Food colloids: Proteins, lipids and polysaccharides. RSC: Cambridge, (p. 346). Graber, T. A., Andrews, B. A., & Asenjo, J. A. (1999). A model for the partition of metal ions in aqueous two-phase system. 11th International Conference on Partitioning in Aqueous Two Phase Systems, Atlanta, 27 June–2 July. Grace, H. P. (1982). Dispersion phenomena in high viscosity immiscible Iuid systems and application of static mixers as dispersion devices in such systems. Chemical Engineering Communication, 14, 225–277. Guido, S., Simeone, M., & Alfani, A. (1999). Interfacial tension of aqueous biopolymer mixtures. Proceedings of the sixth conference of food engineering, A.I.Ch.E. annual meeting, Dallas, (pp. 193–198). Guido, S., & Villone, M. (1999). Measurement of interfacial tension by drop retraction analysis. Journal of Colloid and Interface Science, 209, 247–250. Harnby, N., Edwards, M. F., & Nienow, A. W. (Eds.). (1997). Mixing in the process industries. (2nd ed.). paperback Oxford: Butterworth- Heinemann. Huddleston, J. G., & Lyddiatt, A. (1990). Aqueous two-phase systems in biochemical recovery. Systematic analysis, design and implementation of practical processes for the recovery of proteins. Applied Biochemistry and Biotechnology, 26, 249–279.
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Janssen, J. M. H., & Meijer, H. E. H. (1993). Droplet break-up mechanisms: Stepwise equilibrium versus transient dispersion. Journal of Rheology, 37, 597–608. Mitchell, J. R., & Ledward, D. A. (Eds.). (1986). Functional properties of food macromolecules. Amsterdam: Elsevier Applied Sciences. Nienow, A. W., Pacek, A. W., & Homer, J. (1994). Fundamental studies of phase inversion in a stirred vessel. Eighth European Conference on Mixing, Institution of Chemical Engineers, Symposium Series, vol. 136 (pp. 171–178). Pacek, A. W., Moore, I. P. T., Calabrese, R. V., & Nienow, A. W. (1994a). Video technique for measuring dynamics of liquid–liquid dispersion during phase inversion. A.I.Ch.E. Journal, 40, 1940– 1949. Pacek, A. W., Ding, P., Nienow, A. W., & Wedd, M. (2000). Phase separation and drop size distributions in “homogeneous” Na-alginate=Na-caseinate mixture. Carbohydrate Polymers, 42, 401–409. Pacek, A. W., Nienow, A. W., & Moore, A. W. (1994b). On the structure of turbulent liquid–liquid dispersed Iow in an agitated vessel. Chemical Engineering Science, 49, 3485–3498. Rallison, J. M. (1984). The deformation of small viscous drops and bubbles in shear Iows. Annual Review of Fluid Mechanics, 16, 45–55. Sigillo, I., Di Santo, L., Guido, S., & Grizzutti, N. (1997). Comparative measurements of interfacial tension in a model polymer blend. Polymer Engineering and Science, 37, 1540– 1549. Tolstoguzov, V. B., 1996. Application of phase separated biopolymer systems. In: G. O. Phillips, P. A. Williams, & D. J. Wedlock (Eds.). Gums and Stabilizers for Food Industry. Oxford: IRL Press, (pp. 150 –160). Zaslavsky, B. Y. (1995). Aqueous two phase partitioning. New York: Marcel Dekker Inc.
www.elsevier.nl/locate/ces
The e!ect of volume fraction and impeller speed on the structure and drop size in aqueous=aqueous dispersions A. W. Pacek ∗ , P. Ding, A. W. Nienow School of Chemical Engineering, The University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Received 1 June 2000; received in revised form 2 January 2001; accepted 16 January 2001
Abstract The mean drop size and the structure of two-phase aqueous=aqueous dispersions, one-phase sodium alginate-rich of viscosity
∼0:25 Pa s and the other sodium caseinate-rich of viscosity ∼0:022 Pa s, have been measured in an unba5ed vessel 6tted with a
helical screw impeller. The measurements were carried out over a range of volume fractions and at Reynolds numbers in the range from laminar to low transitional. In addition, the interfacial tension between the two phases has been measured in situ using a recently developed drop retraction technique, which, for the 6rst time, has been successfully applied at a high volume fraction of the dispersed phase. At low volume fractions of the viscous phase (viscosity ratio, = d =c ≈ 10), drops of that phase are seen much as in equivalent aqueous=oil dispersions but the functionality between the drop size and impeller speed is di!erent. As the volume fraction of the viscous phase increases, the structure 6rst changes to a striated one, something never seen in “pure” oil=aqueous dispersions. The striated structure also evolves into complex (droplets-in-drops) in samples withdrawn from the vessel and within the vessel when stirring is stopped. This implies that the system is in a phase inversion region, but contrary to oil=water dispersions, there is not a rapid switch from one phase being continuous to the other, i.e. the phase inversion region appears to be very stable in time. On a further increase of the volume fraction of the viscous phase, phase inversion occurs when stirring but a striated structure continues to exist, i.e. there is no dramatic change of structure as found with aqueous=oil dispersions undergoing phase inversion. However, when a sample is withdrawn or the impeller is stopped, the complex droplets-in-drops formation no longer appears and only a simple dispersed structure develops. Only at very low speeds and volume fractions of the low viscosity dispersed phase, i.e., ∼0:1, do drops re-appear in the vessel when stirring. Overall, it can be concluded that there is a very signi6cant di!erence in the behavior of oil=aqueous and aqueous=aqueous dispersions. ? 2001 Elsevier Science Ltd. All rights reserved. Keywords: Aqueous=aqueous dispersion; Drop size; Striations; Viscosity ratio; Agitation
1. Introduction Aqueous–aqueous two-phase systems (ATPS) are used in the food industry (Tolstoguzov, 1996), in the separation of biological materials (Huddleston & Lyddiatt, 1990) and such systems can also be used in extraction of metal ions and other inorganic components (Graber, Andrews, & Asenjo, 1999). However, the literature on ATPS is limited to equilibrium data, e.g., phase diagrams are available for many phase separating systems (Zaslavsky, 1995) but even the accuracy of that data is questionable (Pacek, Ding, Nienow, & Wedd, 2000). ∗ Corresponding author. Tel.: +44-121-414-5308; fax: 44-121414-5324. E-mail address: [email protected] (A. W. Pacek).
Whatever the application of ATPS, an understanding of the inIuence of hydrodynamic conditions on the structure and the stable drop size is essential. In the food industry, the structure has a strong inIuence on the sense of taste and in bioseparation or extraction, the interfacial area is important in determining the rate of mass transfer. ATPS are often processed in stirred vessels, but there is practically no information in the open literature on the inIuence of hydrodynamic conditions on the structure of the dispersion, drop sizes, the dynamics of breakage or coalescence, etc. It is often assumed that ATPS are essentially similar to oil=aqueous dispersions (Mitchell & Ledward, 1986). Accepting this general assumption, certain consequences, which are not often spelt out, have also to be recognized.
0009-2509/01/$ - see front matter ? 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 1 ) 0 0 0 1 5 - X
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Firstly, the structure of pure (no surface active agents) oil=aqueous systems exposed to suNciently intensive hydrodynamic conditions is such that up to 30% volume fraction of one phase, that phase is always present in the form of simple drops. Secondly, the structure of the aqueous=oil dispersion at phase inversion is inherently unstable and within a relatively short time (¡ 1 min) a dispersion becomes either oil or aqueous continuous (Nienow, Pacek, & Homer, 1994) even though the dispersed phase structure might be complex. Additionally, this assumption implies that the theory which is used to calculate the maximum stable drop size (the concept of critical Capillary or Weber number), breakage (Janssen & Meijer, 1993) and coalescence rates (Chesters, 1991) in oil=aqueous dispersions can be directly applied to aqueous=aqueous dispersion if the physical properties of both phases and the interfacial tension are known. In this paper, a preliminary investigation of the inIuence of hydrodynamic conditions on the structure of ATPS in a mixture of phase separating biopolymers: sodium alginate (NaA), sodium caseinate (NaC) are reported. Those biopolymers were selected because they phase separate without gelling so that, in this respect, they are similar to oil=water dispersions. The results clearly show that there are, however, a number of major di!erences between aqueous=aqueous and aqueous=oil dispersions. 2. Experimental 2.1. Approach As phase separation occurs when the aqueous solutions of two incompatible polymers are mixed together, in principle, it is possible to obtain the dispersion by directly mixing pure NaA solution with pure NaC solution. After mixing, phase separation occurs but the volumetric ratio of separated phases is not known a priori (unless an accurate phase diagram is already available) and also the physical properties of each phase (which are usually very di!erent from the properties of the original solutions) are not known. Therefore, in the experiments reported below, a di!erent procedure was adopted. First, aqueous solutions of both biopolymers were made (stock solutions). Next those solutions were mixed, equilibrated and separated, and 6nally the separated solutions, Na alginate rich (NaA-rich) and Na caseinate rich (NaC-rich), were used to prepare a range of dispersions with both the composition (volume fraction of dispersed phase) and physical properties of each phase being well de6ned. 2.2. Materials The stock solutions of NaA and NaC were prepared following the procedure outlined by Blonk, Endenburg,
Koning, Weisenborn, and Winkel, (1995). Na-caseinate (molecular weight ∼25; 000 Da, supplied by Sigma, lot 36H0408) gives solutions of relatively low viscosity so the powder was gradually added to deionized, distilled water at room temperature and mixed by a magnetic stirrer. The pH of the solution was continuously monitored and adjusted to pH = 7 using 0:1 N NaOH. The 6nal solution was centrifuged at 170=s for 2:5 h to separate undissolved particles. NaA (Manucol DM, molecular weight ∼500; 000 Da, supplied by Kelco lot No 590961) gives much more viscous solutions and therefore it had to be dissolved in a jacketed stirred vessel connected to a water bath and 6tted with helical screw impeller. NaA powder was gradually added to deionized, distilled water at ◦ 50 C whilst continuously stirring at N = 5=s. pH was continuously monitored and adjusted with 0:1 N NaOH to ◦ pH = 7. The 6nal solution was heated to 70 C and “conditioned” at this temperature for 30 min and after that ◦ time cooled to 22 C. Sodium azide at concentration of 0:03% w=w was added to both solutions to avoid biological degradation. The stock solutions were mixed and equilibrated for two hours and separated into NaA-rich and NaC-rich phases by centrifugation for 8 h at 300=s. The equilibrated NaA-rich (1.7% NaA, 1.3% NaC) was initially used as the dispersed phase and the equilibrated NaC-rich (8.2% NaC, 0.5% NaA) as the continuous one. 2.2.1. Physical properties of both phases The density of NaA-rich and NaC-rich were measured by density bottle (NaA-rich = 1015 kg=m3 , NaC-rich = 1020 kg=m3 ). The rheological properties of both phases and a 5.5% NaA-rich in NaC-rich dispersion were measured by a Carri-Med, CSL rheometer. The results are shown in Fig. 1 and the experimental data were 6tted to the power low model: = K ˙n−1
(1)
with K and n values also shown in Fig. 1. Both NaA-rich and NaC-rich phases (Fig. 1a) as well as the 5.5% dispersion on NaA-rich in NaC-rich (Fig. 1b) are very weakly non-Newtonian (n ¿ 0:95). Therefore, it is unlikely that such low degree of non-linearity alone can cause such drastic changes in the behavior of the aqueous=aqueous dispersion compared to Newtonian aqueous=oil dispersions as discussed below. As both NaA-rich and NaC-rich phases mainly contain water, the density of both phases is practically the same. In addition, the phases are suNciently viscous that interfacial tension cannot be measured by the pendant drop method as the drop will not detach from the nozzle, nor can the sessile or spinning drop methods be used. Therefore, the retracting drop method as recently developed was used and extended from considering a single drop (Sigillo, Di Santo, Guido, & Grizzutti, 1997; Guido & Villone, 1999) to multiple drops as actually
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Fig. 1. The apparent viscosity of: (a) NaA-rich phase ( ) and NaC-rich phase (•); (b) 5.5% v=v NaA-rich in NaC-rich dispersion, symbols—experimental data, lines—best 6t from the power-law model with K and n values shown in the graphs.
produced by agitation. In this method, the interfacial tension can be measured either by imposing steady state shear on the drop, thus producing an ellipsoid, and measuring the equilibrium drop shape; or by measuring the time evolution of the shape of the drop after removing the stress (Sigillo et al., 1997). There are two versions of the latter method that di!er in their de6nition of the deformation coeNcient and thus the relationships developed. Sigillo et al. (1997), de6ned the deformation parameter as a ratio of the lengths of the ellipsoid axes ( = a=b) and developed the following expression relating the interfacial tension, , viscosity ratio, , and deformation parameter : exp 1 + 2=(5( − 1) 2 ) 1 d I ( exp ) =
(((1 + 2=5)=) )0:125 (1 − )
0 1 (t − t0 ); (2) where 0 is the deformation at the moment that shearing is stopped (t = t0 ) and exp is deformation at time, t, with c R∞ ; (2a) = 0:465 where R∞ is the radius of the undeformed, spherical drop. Guido and Villone (1999) adopted a more common de6nition of the deformation parameter D = (a − b)=(a + b), and developed the following expression for deformation parameter: t 40( + 1) ; (3) D = D0 exp − (2 + 3)(19 + 16) R∞ c =
where D0 is the deformation parameter at t = t0 . Here, the gradual change of the structure of the dispersion from one containing deformed drops to spherical ones in response to the change of the shear rate from a 6nite value (corresponding to the impeller rotating) to zero (the impeller stopped) was employed to obtain these
deformation parameters and to calculate interfacial tension. Such a procedure enabled the measurements of interfacial tension to be made directly in the vessel without withdrawing samples. Making the measurements in situ is very important because the withdrawing of the sample would generally cause additional distortion of the drops and limit the accuracy of the results. The change of structure inside the vessel was continuously recorded by the video technique (Pacek, Moore, Calabrese, & Nienow, 1994a). Fig. 2 shows example of video images as the initially deformed ellipsoidal drop (Fig. 2a, t = 0) changes (Fig. 2b, t = 30 s) into a spherical one (Fig. 2c, t = 1 min) when retraction is completed. In total, 3000 images were available within 1 min of recording. However, as the retraction was slow, only 13 images (every 5 s) were digitized and the deformation parameters as a function of time were calculated from these digitized images using in-house image analyzing software. The experimental results (points) are shown in Fig. 3. According to the 6rst method, if the values of I ( exp ) are plotted as a function of time, the data should line on the straight line with the slope equal 1= and the interfacial tension can be calculated from Eqs. (2) and (2a). The regression line shown in Fig. 3a (r 2 = 0:982) clearly shows that the experimental data can be approximated by a straight line and the calculated interfacial tension is equal = 1:178 × 10−6 N=m. From Fig. 3b, the best 6t line of Eq. (3) gives = 1:102 × 10−6 N=m. Recently, Guido, Simeone, and Alfani (1999) used the same method to measure interfacial tension of a single drop of NaA in a NaC system at a similar viscosity ratio but with absolute values of the viscosity of each phase about ten times higher that in the reported case. They obtained values of 8:15 × 10−6 N=m. Considering the extremely low values of interfacial tension as well as the di!erences in viscosity (because of the di!erent molecular weight of the polymers employed), the agreement is rather good.
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Fig. 2. The images of retracting drop: (a) time 0 s, (b) time 30 s, (c) time 1 min.
Fig. 3. Deformation parameter as a function of time; (a) calculated from Eqs. (2) and (2a); (b) calculated from Eq. (3), (•) experimental data.
2.3. Experimental rig and procedure The stirred vessel (T = 0:1 m) was Iat bottomed, without ba5es and the liquid height, H , was equal to the vessel diameter. This vessel was placed in a water bath of square cross section made from optically Iat glass to avoid distortion and to control tempera◦ ture to 20 C. Agitation was by helical screw impeller (D = 0:06 m; pitch = 0:02 m), placed 0:01 m from the bottom. The structure of the dispersion was observed and when appropriate, drop sizes were measured. Mean sizes and size distributions were also obtained using the video-microscope-computer system described in detail previously (Pacek et al., 1994a). Two sets of experiments were carried out. In the 6rst set, the e!ect of the impeller speed on mean drop size of the 5.5% v=v NaA-rich phase dispersed in the NaC-rich phase was investigated (∼10). Initially, the impeller speed was increased stepwise from 0.067 to 0:33 rps, to 0.67 and to 1:0 rps. Next, the impeller speed was reduced stepwise from 1 to 0:67 rps, to 0.33 and 6nally to 0:067 rps. At each impeller speed, the dispersion was stirred for at least 60 min. The Reynolds number varied from 10 to 160 when calculated assuming a constant viscosity (see Fig. 1) of NaC-rich of 0:022 Pa s. Thus, the Iow was laminar or just into the transitional Iow regime
(Harnby, Edwards, & Nienow, 1997). Drop sizes were measured directly in the vessel, approximately 2 mm from the wall both during agitation and after stopping it. In the second set of experiments, the inIuence of the volume fraction of NaA-rich phase on the structure of the dispersion was investigated at two impeller speeds, 0.13 and 0:67 rps i.e. Re ¡ 10, laminar Iow. The volume fraction of NaA-rich was gradually increased from 5.5% v=v NaA-rich until the system inverted (assessed as discussed below) to become NaA-rich continuous and NaC-rich dispersed (∼0:1). Further increases of NaA-rich led to a steadily lower fraction of NaC-rich dispersed. At each composition of dispersion, the structure was recorded and analyzed. In certain cases, samples were removed from the vessel and the change of structure followed on a microscope slide with the video system but with a higher magni6cation. 3. Results and discussion 3.1. Steady state sizes in the diluted NaA-rich in NaC-rich dispersion Steady state Sauter mean drop diameters as a function of increasing and decreasing impeller speed are
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Fig. 4. Sauter mean diameters after impeller speed was increased (◦) and after impeller speed was decreased ( ).
summarized in Fig. 4. When the impeller speed increased, the steady state was approached via breakage and when the impeller speed decreased, the steady state was approached via coalescence. At higher impeller speeds, there is a very good agreement between the equilibrium drop mean diameters from both directions. There is, however, a di!erence between them at the lowest impeller speed. Here, the drops after the impeller speed was decreased were approximately 20% smaller than the drops developed after the initial mixture was agitated. This di!erence might be explained by the fact that at this very low speed, the time was insuNcient for equilibrium to be reached, either by breakage, or especially due to coalescence (Calabrese, Pacek, & Nienow, 1993). For aqueous-oil dispersion, it has been shown that the maximum stable drop size (critical drop size of radius, Rmax ) in laminar Iow can be calculated from the critical Capillary number Cacr c R ˙ max ; (4) Cacr = = =Rmax where Cacr depends on and on the type of Iow. In rotational shear (or Couette) Iow, Cacr , strongly depends on and if ¿ 4, dispersed drops cannot be broken (Grace, 1982; Janssen & Meijer, 1993). On the other hand, for two-dimensional elongation Iow, Cacr is less dependent on and for 10−3 6 6 10+3 , Cacr lies between 1 and 0.1. Thus, in this type of Iow, drops can be broken regardless of (Janssen & Meijer, 1993). Here, = 10, and the drops were broken, becoming smaller as the impeller speed increased. Such a result implies either: (1) that the drops were exposed to elongation Iow which is highly probable in the complex 3D Iow 6eld produced by the helical screw impeller; or (2) that APTS do not obey the same breakage rules as aqueous=oil systems if the Iow is purely rotational. To calculate Cacr , it is necessary to know the local shear rate. Such data are not readily available for the system used here and the values vary throughout the vessel. A modi6ed critical capillary number, Cacr−m may be de6ned in terms of the average shear rate ˙A with the help of the
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Fig. 5. A modi6ed critical Capillary number Caar−m (see Eq. (4)) based on drop size d32 , measured after increase of impeller speed (steady state approached via breakage).
well-established correlation with impeller speed (Harnby et al., 1997)
˙A = ks N
(5)
if it is assumed that ˙A represents the impact of both shear and elongation Iow (though the development of the concept by Metzner and Otto (Harnby et al., 1997) was for shear Iow alone). Therefore, [dmax =2]ks Nc : (6) Cacr−m = As ks is constant for a particular impeller-vessel con6guration, then Cacr−m like Cacr should depend only on the viscosity ratio. Fig. 5 shows Cacr−m assuming ks = 10 (Harnby et al., 1997) and dmax = d32 , as a function of N . Thus, Cacr−m values are in the range 0.2–1.2. However, in the range = 10–20 for pure elongational Iow for oil=aqueous dispersions, Cacr (Eq. (4)) equals 0.1. Therefore, it would appear that the drops are bigger than would be predicted from the theory developed for oil=aqueous dispersions. However, it should also be recognized that a number of major assumptions have been made in this analysis which must make these conclusions somewhat tentative. From Fig. 4, it is also clear that the functionality between drop size and impeller speed is very di!erent to one predicted by Eq. (6), i.e., dmax ≈ N −1 (Eqs. (4) and (6) if Cacr or Cacr−m are constant) and the best 6t to the experimental data is: d32 = 16:56N −0:27 :
(7)
There appears to be another major di!erence between oil=water and aqueous=aqueous dispersions. In oil=aqueous systems, before a drop is broken, it is 6rst deformed and consequently it becomes unstable (Rallison, 1984). Janssen and Meijer (1993) reported that the breakage time at = 3:6 vary between 4 and 6 s. In the present experiments, the images of drops were obtained at frequency of 50 Hz. Careful observation of hundreds of images taken after step increased of impeller speed
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did not show any drop deformation leading to breakage. This fact seems to imply that drops simply burst at breakage i.e. it happens too quickly to be observed even at 50 frames=s. 3.2. The in5uence of the volume fraction of the two phases and of the impeller speed on the structure of dispersions The volume fraction of NaA-rich was increased stepwise from 5.5 to 98.9% and at each volume fraction, the dispersion was stirred at 0.13 and 0:66 rps for 30 mins. The structure of the dispersion was monitored in three ways representing two di!erent scales. Firstly, visual observation of the macro structure in the whole vessel showed that there was no di!erence between the top and the bottom of the vessel, e.g. the system was well mixed at this scale. Secondly, the microstructure was observed directly in the vessel using the video technique (scale ranging from 0.2 to 1 mm, resolution approx. 20 m) at di!erent positions along the height of the vessel. Thirdly, samples were withdrawn from di!erent positions in the vessel and analyzed using a higher magni6cation optical microscope (scale below 0:2 mm, resolution approx. 5 m). In both the latter cases, the observed structures (qualitatively) were independent of the position along the height of the vessel. Thus, under all conditions, the vessel contents could be considered well mixed at the macroscale. On the other hand, at the microscale, quite di!erent structures were seen depending on the composition, impeller speed and whether the structure was observed in situ or in a withdrawn sample. These microstructures are summarized in Table 1, Figs. 6 and 7. Initially, up to approx. 30% v=v. NaA-rich, spherical drops of NaA-rich phase in NaC-rich phase were seen both in the vessel and in the sample and the structure was rather similar to the structure of oil=aqueous dispersions. However, the e!ect of volume fraction of dispersed phase was much smaller than in oil=aqueous dispersions, the increases of volume fraction of dispersed phase having only a marginal e!ect on drop size. The increase of drop size with volume fraction of dispersed phase in oil=aqueous dispersions is usually attributed to an increase of coalescence rate (Pacek, Nienow, & Moore, 1994b). Clearly, as already shown here, aqueous=aqueous dispersions separate and coalesce much more slowly than oil=aqueous ones. It is suggested that this much slower coalescence is the reason for the insensitivity of the drop size to volume fraction of dispersed phase. As the volume fraction of dispersed phase was increased above 30%, a gradual change of the structure of the dispersion was observed. At volume fractions between 30% and 40%, NaA-rich drops started to deform, taking on ellipsoidal shapes similar to those shown in Fig. 2 but which did not break under shear. These shapes could be
Fig. 6. Striations (tubular-like structures) of NaA-rich in NaC-rich dispersion observed in situ during stirring in “the phase inversion region” at a volume fraction of NaA-rich phase of 54%: (a) original video image, (b) part of the image after electronic magni6cation and enhancement.
seen both directly in the vessel, with some strongly deformed drops also being seen in the withdrawn samples. The increase of volume fraction of NaA-rich phase above approximately 40% led to a striated, macrostructure in the whole vessel as shown in Fig. 6. Fig. 6a shows the video image of the structure inside the vessel whilst stirring. Even in this image, the striations (lines rather than drops as in oil=water dispersions at the same volume fraction) can be seen. However, the quality of the image is not good enough to characterize the striations. Simple image processing (Paint Shop Software, Version 5.01) enabled a signi6cant enhancement of the original image (see Fig. 6b) to the extent that the dimensions of the striations can be estimated. However, for the interpretation of Figs. 6a and b, one has to remember that the structure of the dispersion in the vessel is three-dimensional
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Table 1 The structure of NaA-rich=NaC-rich dispersions Volume fraction of NaA-rich (%)
Dispersed phase
5.5 8.9 15.9 21.5 30.1 38.2 46.4 53.6 65.9 78.0 80.5 93.0 98.9
Na-alginate rich Na-alginate rich Na-alginate rich Na-alginate rich Na-alginate rich Na-alginate rich Phase inversion region Phase inversion region Phase inversion region Na-caseinate rich Na-caseinate rich Na-caseinate rich Na-caseinate rich
Structure In the vessel
In the sample
Drops Drops Drops Drops Drops Deformed drops Striationsa Striationsa Striationsa Striations Striations Striationsb Striationsc
Drops Drops Drops Drops Drops Drops Multiple dispersion Multiple dispersion Multiple dispersion Drops Drops Drops Drops
a Drops-in-drops
in the vessel after impeller was stopped, the phase inversion occurred in this region. drops at 8 rpm. c Spherical drops at 8 rpm. b Deformed
whereas the images show only two dimensions. Considering that the velocity 6eld in a stirred vessel is also inherently three dimensional, the term striated does not seem to be entirely appropriate. It is suggested that the term tubular-like structures would be better. From Fig. 6b, the diameter of these “tubes” can be estimated as between 8– 20 m with lengths exceeding 400 m. The tubular-like structures observed in the vessel during stirring evolved into drops of di!erent size, ranging from very large and complex (droplets-in-drops, multiple dispersion) to very small when the impeller was stopped (see Fig. 7a). The complex drops were also observed in the samples taken from the dispersion under stirring conditions (tubular-like structure in the vessel) and an example of such a structure is shown in Fig. 7b. As multiple dispersions in oil=aqueous systems are typically associated with phase inversion (Pacek et al., 1994b), it is assumed that these structures in ATPS also indicate an approach to phase inversion. 1 Therefore this region is called here “the phase inversion region”. The complex, multiple dispersions, indicating “the phase inversion region” were observed from approx. 40% to approx. 75% NaA-rich phase. In addition, over 40 –75% range of volume fractions of NaA-rich phase, such complex structures were always present both in the vessel and in the sample however long stirring was continued. 1 Precise determination of a phase boundary (the phase inversion region) in aqueous=aqueous dispersions is much more diNcult than in oil=aqueous dispersions. Whilst in oil=aqueous dispersions, phase inversion can be precisely detected by monitoring the conductivity of the dispersion (Nienow et al., 1994), its detection in an aqueous=aqueous dispersion requires an analysis of the structure of the dispersion. This analysis is usually done on a sample from the mixture using confocal microscopy (Foster, Underdown, Brown, Ferdinands, & Norton, 1997).
Above 75% of NaA-rich, the strati6ed structure continued to exist with the threads becoming more uniform and when the impeller was stopped, the threads slowly broke into the drops of about 10 –15 m diameter. In addition, the samples withdrawn from the vessel developed a typical simple dispersed structure, with similar sizes drops. The threads when stirring and the drops observed under static conditions were all of a size essentially independent of the impeller speed. It was concluded that this simple structure seen after ceasing agitation and in withdrawn samples, indicated that phase inversion had occurred, i.e. that the NaC-rich phase was now dispersed. Only at a volume fraction of NaC-rich dispersed phase below 10% v=v was an e!ect of impeller speed on the structure of the dispersion observed. At 0:67 rps, threads still existed whereas at 0:13 rps, a mixture of deformed and spherical drops was observed. In addition, when agitation at 0:67 rps was stopped, the threads reformed into a series of very uniform small drops, of the order of 15 m diameter equivalent to those seen at 0:13 rps. Clearly, there is a di!erence between the structure of dilute dispersions when NaA-rich is dispersed as compared to NaC-rich being dispersed. In summary, it would appear that overall three stable dispersions can be produced: NaA-rich in NaC-rich, NaC-rich in NaA-rich, each with their own characteristic behavior, and a complex phase inversion region with strati6ed structures under dynamic conditions which evolve into multiple dispersions under static conditions. 4. Conclusions To the authors’ knowledge, this is the 6rst time that the structure and dynamic behavior of agitated aqueous=aqueous dispersions has been discussed in some
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mainly water and perhaps because NaC is a rather strong surface-active agent. Notation a b Cacr Cacr−m d dmax d32 D D0 ks K n N R∞ Rmax Re t t0
longer axis of deformed drop, m shorter axis of deformed drop, m critical Capillary number [Eq. (2)], dimensionless modi6ed critical Capillary number [Eq. (4)], dimensionless drop size, m maximum drop size, m Sauter mean diameter, m deformation parameter = (a − b)=(a+b), dimensionless deformation parameter at t0 , dimensionless shear rate constant, dimensionless consistency constant, Pa sn power-law index, dimensionless impeller speed, rps unperturbed or 6nal drop radius, m maximum stable drop radius, m impeller Reynolds number, dimensionless time, s time at which drop retraction measurement starts, s
Greek letters
Fig. 7. Complex, multiple dispersed structures in the phase inversion region 54% NaA-rich in NaC-rich dispersion after ceasing stirring: (a) in the vessel after 3 min; (b) in a sample after approx. 1 min from withdrawal.
detail. The results show that the analogy between “pure” aqueous=oil and aqueous=aqueous dispersions is rather limited. The major di!erence is that the structure of ATPS depends critically on which phase is dispersed and the overall composition of the system and to lesser extent on the hydrodynamic conditions. There is also a much wider range of concentrations over which ATPS dispersions are complex and over which the system appears to be in a stable “phase inversion” state. In this complex region, striations or “tubular-like” structures are seen and such phenomena have not been reported for aqueous=oil systems, where essentially the dispersed phase is always in the form of drops. In ATPS dispersions, the breakage mechanism also appears to be di!erent and even when dilute, they do not follow the same stable drop size relationships. It should also be stressed that the interfacial tension was extremely low, probably because both phases contain
c d
deformation parameter = (a=b), dimensionless viscosity ratio (d =c ), dimensionless viscosity of continuous phase, Pa s viscosity of dispersed phase, Pa s density, kg=m3 interfacial tension, N=m
Acknowledgements This work forms part of the project Processing of Biopolymer Mixture for Zero and Low Fat Foods, FAIR CT97 3022-Biomix, sponsored by European Union. The authors would like to acknowledge very helpful discussions with many academic and industrial colleagues involved in this Biomix project; and also with Prof. Ian Norton and Dr. Tim Foster (Unilever Research Colworth Lab, Sharnbrook, UK). References Blonk, J. C. G., Endenburg, J., van Koning, M. M. G., Weisenborn, P. C. M., & Winkel, C. (1995). A new CSLM-based method for determination of the phase behavior of aqueous mixture of biopolymers. Carbohydrate Polymers, 28, 287–295.
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