Emulsions drop deformation

A. Z. Zinchenko, R. H. Davis 2002, (Shear flow of highly concentrated emulsions of deformable drops by numerical simulations),/. Fluid Mech. 455, 21. 

To summarize, if the polydisperse emulsion is mainly composed of big drops, even after few seconds of shear, one obtains a well calibrated emulsion (with a mean diameter close to 6 pm) all the drops deform into threads of different... 

It should be emphasised that polymeric surfactants prevent the coalescence of water droplets in the multiple emulsion drops, as well as coalescence of the latter drops themselves. This is due to the interfacial rheology of the polymeric surfactant films. As a result of the strong lateral repulsion between the stabilising chains at the interface (PHS chains at the W/O interface and PEO chains at the O/W interface), these films resist deformation under shear and hence produce a viscoelastic film. On approach of the two droplets, this film prevents deformation of the interface so as to prevent coalescence. 

Large-scale simulations of concentrated emulsion flows, Philos. Trans. R. Soc. London Ser. A 361, 813—45 (2003) C. D. Eggleton, T. M. Tsai, and K. J. Stebe, Tip streaming from a drop in the presence of surfactants, Phy. Rev. Lett. 87, 048302/1-4 (2001) X. Li and C. Pozrikidis, Effect of surfactants on drop deformation and on the rheology of dilute emulsions in Stokes flow, J. Fluid Mech. 341, 165-94 (1997). 

Since, for = 0 to the quantity in the square bracket ranges from 1.00 to 1.18, the drop deformability D = 0.55k. Thus, a small deformation of Newtonian drops in Newtonian matrix varies linearly with the capillarity number. This proportionality was indeed demonstrated in Couette-type rheometer for a series of com symp/silicon oil emulsions [Elemans, 1989]. 

In the case of low interfacial coverage with surfactant, the collision of two emulsion drops (step A—in Fig. 2) usually terminates with their coalescence (step B—>C in Fig. 2). The merging of the two drops occurs when a small critical distance between their surfaces, hj. is reached. Sometimes, depending on the specific conditions (larger drop size, attractive surface forces, smaller surface tension, etc., — see, e.g.. Ref. 2), the approach of the two drops could be accompanied with a deformation in the zone of their contact (step B—>D in Fig. 2) in this way a liquidfilm of almost uniform thickness h is formed in the contact zone. This film could also have a critical thickness h, of rupture in fact, the film rupture is equivalent to drop coalescence (see step D—>C in Fig. 2). The mechanisms of coalescence... 

Figure 2 Possible consequences from a collision between two emulsion drops. Step A B the two drops approach each other imder the action of a driving force F the viscous friction, accom-pan3nng the expulsion of liquid from the gap between the two drops, decelerates their approach. Step B —> C after reaching a given critical distance between the two drop surfaces coalescence takes place. Step B —> D after reaching a given threshold distance, hjjjy, between the two drop surfaces, called the inversion thickness, the spherical drops deform and a film is formed in the zone of their contact. Step D —> C the film, intervening between the two drops, thins and evenmally breaks after reaching a certain critical thickness, then the two drops coalesce.

Let US consider two spherical emulsion drops approaching each other, which interact through the van der Waals attractive surface force. Sooner or later interfacial deformation will occur in the zone of drop-drop contact. The calculations (138) show that, if the drop radius a is greater than 80 jm, the drop interfaces bend inwards (under the action of the hydrodynamic pressure) and a dimple is formed in the contact zone soon the dimple transforms into an almost plane-parallel film (Fig. 2D). In contrast, if the drop radius... 

To illustrate the effeets of various factors on the velocity of approach of two deforming emulsion drops (Fig. 15a) we used the general expression from Ref 137 (the infinite series expansion) to calculate the mobility factor the results are shown in Figs 16 and 17. First of all, in Fig. 16 we illustrate the effects of bulk and surface diffusion. For that reason Qy = V-ylV- Q is plotted versus the parameter b, related to the bulk diffusivity, for various values of hjk, is related to the siuface diffusivity, see Eq. (54). If the hydrodynamic interaction were operative only in the film, then one would obtain V- IV- q > 1. However, all calculated values of are less than 0.51 (Fig. 16) this fact is ev-... 

Equation (61) determines the transitional distance between two spherical emulsion drops. An analog of this equation for the case of two deformed drops (Fig. 15a) has been obtained in the form of a transcendental equation (2, 136) ... 

Equation (89) was obtained for deforming emulsion drops, i.e., for drops which can approach each other at a surface-to-siuface distance less than the inversion thickness see Eq. (72). Another possibility is the drops to remain spherical dining their collision, up to their eventual coalescence at A = h in such a case the expressions for Kj and Kjj, which are to be substituted in Eq. (88), differ from Eqs (76) and (77). 

Experimental and theoretical results show evidence that the capillary-wave mechanism is the most fi equent reason for the coalescence of both deformed and spherical emulsion drops. For a certain critieal thiekness (widdi), of the film (gap) between two emulsion drops the amplitude of the thermally excited fluctuation capillary waves begins to grow, promoted by the surface forces, and causes film rupture. The capillary waves can bring about coalescence of two spherical emulsion drops, when flic distance between fliem becomes smaller than a certain critical value, which is estimated to be about 10—50 nm (see Sec. 

FIGURE 6.2. Important functions of capillary forces in practical situations, (a) As two emulsion drops approach, the pressure at the nearest surfaces increases, deforming the drops and enlarging the radius of curvature in the immediate area. That deformation causes the capillary pressure in the regions outside that area to decrease in a relative sense, suctioning continuous phase from between the drops and increasing the likelihood of contact and flhn rupture or coalescence, b) In capillary displacement, the liquid that preferentially wets the solid will displace the less wetting liquid. 

Starting with cell model of creeping flow, Choi and Schowalter [113] derived a constitutive equation for an emulsion of deformable Newtonian drops in a Newtonian matrix. The authors characterized the interphase with an ill-defined interfacial tension coefficient, Vu, affecting the capillarity number, k = (Judfvu. The analysis indicated that depending on magnitude of /cy the emulsion may be elastic, characterized by two relaxation times. For the steady-state shearing, the authors expressed the relative viscosity of emulsions and the first normal stress difference as ... 

Drop deformability in dilute emulsion was treated by Taylor [117, 118], who introduced three dimensionless, microrheological parameters the viscosity ratio, the capillarity number, and the reduced time, namely... 

The effects of wall slip, interfacial properties, drop size distribution, and drop deformability in emulsions have been discussed in References [134,140-143]. The performance of bio-emulsions was considered by Stokes et al. [144] and Danker et al. [145]. 

Li Xiaofan, and Pozrikidis Constantine. The effect of surfactants on drop deformation and on the rheology of dilute emulsions in stokes flow. J. Fluid. Mech. 341 no. 25 (1997) 165-194. 

Biswas and Haydon [20] found some correlation between the viscoelastic properties of protein (albumin or arabinic acid) films at the 0/W interface and the stability of emulsion drops against coalescence. Viscoelastic measurements were carried out using creep and stress relaxation measurements (using a specially designed interfacial rheometer). A constant torque or stress a (mN m ) was applied and the deformation y was measured as a function of time for 30 minutes. After this period the torque was removed and y (which changes sign) was measured as a function of time to obtain the recovery curve. The results are illustrated in Fig. 5.18. From the creep curves one... 

The high shear viscosities are not significantly differing for different drop sizes. At elevated shear rates, higher secondary drop deformation for larger drop diameter equilibrates the degree of viscous friction between the emulsion drops of different size [54]. In all cases, the Bird-Carreau model ((23.1) dashed line) was an excellent fit to the experimental results (symbols). 

Windhab EJ et al. Emulsion processing - From single-drop deformation to design of complex processes and products. Chem Eng Sci 2005 60(8-9) 2101-2113. 

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