Lifshitz-Slyozov-Wagner theory

Rinaldo, S. G., Lee, W., Stumper, J., and Eikerling, M. 2012. Nonmonotonic dynamics in Lifshitz-Slyozov-Wagner theory Ostwald ripening in nanopartiele catalysts. 

Ostwald ripening is observed when the substance of the emulsion droplets (we will call it component 1) exhibits at least minimal solubility in the continuous phase, p. As discussed above, the chemical potential of this substance in the larger droplets is lower than in the smaller droplets see Equation 5.115. Then a diffusion transport of component 1 from the smaller toward the larger droplets will take place. Consequently, the size distribution of the droplets in the emulsion will change with time. The kinetic theory of Ostwald ripening was developed by Lifshitz and Slyozov, Wagner, and further extended and applied by other authors. " The basic equations of this theory are the following. 

In 1961, Lifshitz, Slyozov, and Wagner [31] (LSW) performed a mathematical investigation of Ostwald ripening in the case where diffusion of solute particles is the slowest rate-determining process (famously known as the LSW theory). The derivation first states how a cluster grows in a supersaturated solution. This theory assumes the coarsening phase as noninteracting, spherical, and fixed in space. 

In 1961, the classical theory of particle coarsening was developed at about the same time, but independently, by Lifshitz and Slyozov [1] and Wagner [2], Most of the... 

This process was first recognized by Ostwald and is known as Ostwald ripening. The mathematical details were worked out independently by Lifshitz and Slyozov and by Wagner ° and is known as the LSW theory. However, this theory is based on a mean field approximation and is restricted to low volume fraction systems. Voorhees and coworkers extended the LSW theory to finite volume fraction systems and conducted a series of flight experiments designed to test this and similar theories. ... 

The basic theory of Ostwald ripening was developed independently by Greenwood (4), Wagner (5), and Lifshitz and Slyozov (6). It is often referred to as the LSW theory. The idealized system considered in the LSW theory is required to satisfy three conditions during the coarsening process ... 

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