Dispersion diffusion between droplets

The LSW theory assumes that there are no interactions between droplets and, therefore, is limited to low disperse phase volume fractions. At higher volume fractions the rate of ripening is dependent on the interaction between diffusion spheres of neighboring particles. In general it is expected that emulsions with higher volume fractions of disperse phase will have broader particle size distributions and faster absolute growth rates than those predicted by LSW theory. This has in fact been verified experimentally for cobalt grains. The volume fraction... 

The computational fluid dynamics investigations listed here are all based on the so-called volume-of-fluid method (VOF) used to follow the dynamics of the disperse/ continuous phase interface. The VOF method is a technique that represents the interface between two fluids defining an F function. This function is chosen with a value of unity at any cell occupied by disperse phase and zero elsewhere. A unit value of F corresponds to a cell full of disperse phase, whereas a zero value indicates that the cell contains only continuous phase. Cells with F values between zero and one contain the liquid/liquid interface. In addition to the above continuity and Navier-Stokes equation solved by the finite-volume method, an equation governing the time dependence of the F function therefore has to be solved. A constant value of the interfacial tension is implemented in the summarized algorithm, however, the diffusion of emulsifier from continuous phase toward the droplet interface and its adsorption remains still an important issue and challenge in the computational fluid-dynamic framework. 

This diffusion occurs because the pressure is greater in the smaller droplets. The pressure difference is proportional to the interfacial tension and to the difference between the inverse radii (A P/y I/R2 1/Ri)- Diffusion is thought to be a relatively slow process, but it increases when pressure increases or other changes increase the solubility of the components of the dispersed phase in the dispersing fluid. 

Ultrasound-assisted emulsification in aqueous samples is the basis for the so-called liquid membrane process (LMP). This has been used mostly for the concentration and separation of metallic elements or other species such as weak acids and bases, hydrocarbons, gas mixtures and biologically important compounds such as amino acids [61-64]. LMP has aroused much interest as an alternative to conventional LLE. An LMP involves the previous preparation of the emulsion and its addition to the aqueous liquid sample. In this way, the continuous phase acts as a membrane between both the aqueous phases viz. those constituting the droplets and the sample). The separation principle is the diffusion of the target analytes from the sample to the droplets of the dispersed phase through the continuous phase. In comparison to conventional LLE, the emulsion-based method always affords easier, faster extraction and separation of the extract — which is sometimes mandatory in order to remove interferences from the organic solvents prior to detection. The formation and destruction of o/w or w/o emulsions by sonication have proved an effective method for extracting target species. 

In [556] an attempt was made to describe the increase of k a values with increasing disperse phase fraction (here octene the droplets being stabilized by adding the anionic tenside sodium-dodecyl-sulfate) by a film variable hold-up model , that takes into consideration the change in oil/water fraction in the G/L film and diffusion in the droplets. It succeeded in approximating the test data much better than the two-film model or Higby s penetration model. The measurements by authors and other publications consulted, showed, however, that the linear relationship between the enhancement factor m for physical absorption and the fraction ... 

The microsealed delivery device is a variation of the matrix-type transdermal system in which the drug is dispersed in a reservoir phase which is then immobilized as discrete droplets in a cross-linked polymeric matrix. Release can be further controlled by inclusion of a polymeric microporous membrane. This system therefore combines the principles of both the liquid reservoir and matrix-type devices. Rate of release of a drug from a microsealed delivery system is dependent on the partition coefficient between the reservoir droplets and the polymeric matrix the diffusivity of the drug in the reservoir, the matrix and the controlling membrane and on the solubility of the drug in the various phases. There are, obviously, many ways to achieve the desired zero-order release rate, but only nitroglycerin has been commercially formulated into this type of delivery device (Karim 1983). 

Many forms or extraction involve transfer between two liquid phases, oue of which is dispersed as droplets in the other. Various attempts at theoretical analysis have assumed that the droplets may be regarded as spherea, in which mass transfer occurs by unsteady-state molecular diffusion. The following assumptions are made ... 

An individual ccnfficiont of mass transfer for the disperse phase during free rise (or fall), k, may now be formulated. A balance na component A diffusing into a eisgnant, spherical droplet rising between points l and 2 during time dt is... 

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