Interdroplet interaction

The holdup changes are the result of interdroplet interactions, which may also have their own dynamics. Assume that this can be represented by a first order lag equation, and show how this effect may be implemented into the simulation. 

The above analysis only applies to very dilute dispersions with microemulsions which are concentrated dispersions, corrections are needed to take into account the interdroplet interaction. This is reflected in plots of In gfl) (r) versus r which become nonlinear, implying that the observed correlation functions are not single exponentials. 

The alternative NMR approach that has provided information on microemuisions is relaxation. However, on the whole, relaxation has been less informative than anticipated from earlier studies of micellar solutions and has provided little unique information on microemulsion structure, although in the case of droplet structures it is probably the most reliable way of deducing any changes in droplet size and shape, particularly for concentrated systems. The reason for this is that NMR relaxation probes the rotational diffusion of droplets, which is relatively insensitive to interdroplet interactions. This is in contrast to, for example, translational collective and self-diffusion and viscosity which depend strongly on interactions. Furthermore, NMR relaxation is a useful technique for characterizing the local properties of the surfactant film. 

Finally, relaxation is a reliable technique for monitoring changes in droplet size and shape, since it is to a good approximation independent of interdroplet interactions up to high droplet volume fractions. The reason for this is that relaxation arises from droplet reorientation and intradroplet surfactant diffusion, processes only weakly dependent on interdroplet interactions. 

The third chapter, by Wasan and Nikolov, discusses fundamental processes in emulsions, i.e., ereaming/sed-imentation, flocculation, coalescence, and final phase separation. A number of novel experimental facilities for characterization of emulsions and the above-mentioned processes are presented. This chapter highlights recent techniques such as film rheometry for dynamic film properties, capillary force balance in eonjunetion with differential microinterferometry for drainage of curved emulsion films, Kossel diffraction, imaging of interdroplet interactions, and piezo imaging spectroscopy for drop-homophase coalescence rate processes. 

Stability of a macroemulsion is an important factor as this determines its extent of usability for particle preparation or various other applications. Instability is basically coalescence of the dispersed phase droplets or Ostwald ripening (growth of large droplets at the expense of much smaller ones). When this process goes on, the emulsion eventually breaks into two layers. Other processes related to stability but considered less important [3] are (a) creaming or sedimentation, the rate of which is dependent on the difference in density between the continuous and dispersed phases, droplet size, viscosity of the continuous phase and interdroplet interaction and (b) flocculation, dependent on colloidal interactions between the droplets [8, 12]. Several factors determine the stability of macroemulsions these are discussed here in brief. This discussion is largely derived from Rosen [3] and some subsequent investigations [e.g. 6, 7, 13-15]. 

A schematic diagram presenting the comparative effects of spontaneous curvature and elasticity of the interfacial film in W/O microemulsions is shown in Fig. 3.8. In a W/O microemulsion, therefore, a maximum water solubilization can be achieved when the interfacial bending stress of rigid interfaces, as also the attractive interdroplet interaction of fluid interfaces is minimized, keeping the interfacial curvature and elasticity at an optimum level. 

Two factors have been considered [245] to control the particle size in reverse microemulsions. One of them is the number of microemulsion droplets when the number is large, the average content of the reactants per droplet becomes low, causing the formation of a large number of nuclei in the system and finally, particles of small size. Another factor for small size is reduced interdroplet interaction and exchange of materials. This may take place due to steric hindrance offered by surfactant films, or their low deformability or strong attachment to droplets. A general experience, of course, is that the two-emulsion method yields smaller particles, especially in case of metals [242]. 

For controlling interdroplet interactions, co-surfactants (alcohols of different chain lengths) were added into the system. The effective particle diameter of hydrated titania was found to decrease monotonically with increase in the chain length of the alcohol (butanol to octanol) irrespective of the water/surfactant molar ratio (10 or 20). It was also shown that with a systematic increase in the ratio [octanol]/[Ti(AOT)4], i.e. 0.2-1.0, the effective diameter of hydrated titania decreased monotonically. Finally, the particle size was found to increase with the concentration of Ti(AOT)4. 

The unique density dependence of fluid properties makes supercritical fluids attractive as solvents for colloids including microemulsions, emulsions, and latexes, as discussed in recent reviews[l-4]. The first generation of research involving colloids in supercritical fluids addressed water-in-alkane microemulsions, for fluids such as ethane and propane[2, 5]. The effect of pressure on the droplet size, interdroplet interactions[2] and partitioning of the surfactant between phases was determined experimentally[5] and with a lattice fluid self-consistent field theory[6]. The theory was also used to understand how grafted chains provide steric stabilization of emulsions and latexes. 

M.J. Hou, M. Kim, and D.O. Shah 1988 A light scattering study on the droplet size and interdroplet interaction in microemulsions of AOT-oil-water system, /. Colloid Interf. Sci. 123, 398-412. 

In Figure 10.16 the average film radius vs. interdroplet distance is shown for emulsions with size a = 0.4 i.m, y = 0.1 mNm", /1h = 5 X 10 J and Po = 100 mV. Expressions (10.3), (10.9), (10.10), (10.29) and (10.62) were used to derive lF (r z). The full (upper) curve is for an electrolyte concentration equal to 0.01 M monovalent electrolyte, while the dotted one (lower) is for 0.005 m. In both cases the interaction energy is lowest in the absence of any deformation (r = 0). Still, a well defined peak is observed at small distances which is due to the reasons discussed above. It can also be seen that the film radius seems to have non-zero values at separations where the interdroplet interactions vanish. This is due to the fact that the surface of a flexible droplet will fluctuate even if there is no second droplet to interact with. If one examines expressions (10.29) and (10.31) it becomes evident that they do not depend on the droplet positions and therefore do not decay with the distance. This reflects in a simple way the fact that due to fluctuations the droplet surface could be greater than that of a sphere with the same volume (see ref. 66 for more detailed discussion). 

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