Lifshitz-Slezov-Wagner

According to the Lifshitz-Slezov-Wagner (LSW) theory [15-18], the rate of Ostwald ripening (Ro) can be expressed as... 

Exact solution to the problem of change of the average particle size and of particle size distribution with time was given by E.M. Lifshitz, V.P. Slezov and C. Wagner [58-61]. We will present their treatment with some simplifications. 

Closely similar expressions for particle (grain) growth in dispersed systems of widely-separated particles by solution of the smaller particles in the matrix and precipitation on the larger particles have been derived by Greenwood ( °), Wagner ( ), Lifshitz and Slezov ( ), and Li and Oriani ( ). All these authors assumed the particles to be spherical, so that the variation of solubility with particle size was given by the Thomson-Freundlich equation,... 

Therefore, the only process that may produce coarsening of nano-emulsions is Ostwald ripening. It is described by the LSW theory, formulated by Lifshitz and Slezov [68] and independently by Wagner [69], Several authors have indicated that this theory can be applied to macroemulsions with reasonable accuracy [79,80], It has also been reported that the presence of microemulsion droplets in the continuous phase accelerates the Ostwald ripening rate by increasing the diffusion coefficient [80,81], However, this effect is relatively small because microemulsion droplets have much smaller diffusion coefficients than molecules. 

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