Lifshitz-Slyozov theory

The interaction among the clusters via the common diffusion held leads in general to a coarsening of the clusters with time t. One denotes this by Ostwald ripening [58,96] (see Sec. HID). According to the Lifshitz-Slyozov theory [58] on this process, the typical cluster radius R increases as... 

A first attempt at this was accomplished in [16] where the Lifshitz-Slyozov theory was adopted to allow for spatial variations including the concept of the local particle size distribution. In that work, however, undue emphasis was placed on the diffusion of the particles and the concept of forming macroscopic length scale patterns via the svegliabile mechanism was not realized (see a discussion in the other paper of the author in these proceedings). 

If the ripening is controlled by diffusion across the continuous phase, then the cube of the diameter increases linearly with time (a = 3) and the ripening rate S23 can be derived using the Lifshitz and Slyozov theory [2,3] ... 

Using the conventional Lifshitz-Slyozov arguments [74,75] based on the Kelvin equation, one might expect [73,76] that the 3D crystallite growth, occurring via 2D diffusion, should follow Eq. (18) with n = 4. This value, however, is much lower than observed in experiments. The appreciable difference between the theory and experiment is actually not surprising, because the applicability of the Lifshitz-Slyozov model to nm crystallites is far from obvious (e.g., the curvature of such crystallites is an ill-defined quantity). 

Landau theory 188, 268, 275 Leibler theory 183, 263-286 Leonard-Jones fluids 242 Lifshitz-Slyozov type growth 258... 

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. 

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

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. ... 

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. 

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 ... 

What factors make survival unlikely Clearly, the most serious is Ostwald ripening (see, e.g., Ref. 42). Gases have enough solubility in most liquids to make Ostwald ripening a significant mechanism for bubble size redistribution to occur on reasonable time scales. For the case of gas bubbles in water, this mechanism will be quite rapid. The original theory for crystalline solids was outlined by Lifshitz and Slyozov [43], and applies equally to gas bubbles. In an... 

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