Time-Dependent Ostwald Ripening

Before the scaling regime mentioned above is reached, the distribution function varies with time. The precipitates could have a modified Gaussian distribution of sizes, which is given by [19]  

By using the distributions with varying and a, the variation in the properties of the distribution with time can be analyzed. For the distributions with a broad width, the standard deviation of the distribution decreases to the characteristic steady-state value, whereas for the distributions with a narrow width, the standard deviation increases to the steady-state value. We may interpret this behavior during the transient regime to mean that the scaling regime acts as a strong attractor for the evolution of the precipitate size distribution. 

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Schroeder A, Fleig J, Giyaznov D, Maier J, Sitte W. 2006. Quantitative model of electrochemical Ostwald ripening and its application to the time-dependent electrode potential of nanocrystalline metals. J Phys Chem B 110 12274-12280. 

Figure 9.5 Schematic illustration of the phase-separation process after a temperature quench into the spinodal region of the phase diagram. The time dependence of the temperature quench from the spinodal temperature to some final temperature Tfinai is shown in the top diagram. This quench time can be made arbitrarily fast, in which case it has no effect on the time period over which the linear or other regimes persist. The bottom diagram shows the maximum-scattering wavevector qm of the spinodal pattern as a function of time t, with qm oc r . At first, in the linear regime, qm is constant, so that a = 0 but as the pattern coarsens, qm decreases, initially as qm oc due to diffusive Ostwald ripening. Later, when the interfaces are well defined, if the morphology is bicontinuous, there is a crossover to a fast hydrodynamic regime with q , oct. (From Tanaka 1995, reprinted with permission from the American Physical Society.)...

This equation describes the time rate of change of the distribution function. It cannot be solved analytically, except for special cases. However, depending on the assumptions made it simplifies to the models of crystallite migration or Ostwald ripening, both in continuous or discrete form, as is shown in a forthcoming paper. 

Enomoto Y, Kawasaki K, Tokuyama M (1987) The time-dependent behavior of the Ostwald ripening for the finite volume fraction. Acta Metall 35 915-922... 

Macro- and miniemulsions are thermodynamically unstable. If not stabilized, the droplets tend to fiocculate, coalesce, sediment or cream [2-4]. Other instabilities, such as Ostwald ripening and phase inversion, are also known. At worst, an emulsion will break, i.e. the two phases will separate completely. A product becoming unstable will lose its quality within a short period of time and thus cannot be commercialized. Therefore, even in natural emulsion-based products, amphiphilic molecules are found (e.g. lecithin and proteins in egg yolk and milk and artificial surfactants and emulsifiers in cosmetics and chemical products. They adsorb at the droplets interfaces and stabilize them against flocculation and coalescence. Adsorption and stabilization mechanisms depend on the molecular structure of a surfactant or an emulsifier as depicted in Figure 20.1. Stabilization mechanisms are summarized in... 

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