OSTWALD RIPENING - A STOCHASTIC APPROACH
OSTWALD RIPENING - A STOCHASTIC APPROACH
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DOI：
10.1063/1.470341
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发表时间：
1995-10-22
影响因子：
4.4
通讯作者：
RUCKENSTEIN, E
中科院分区：
文献类型：
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作者：
BHAKTA, A;RUCKENSTEIN, E
奥斯特瓦尔德熟化现象的理论研究在溶液中的沉淀物，在基板上的微晶，和岛屿的不溶性表面活性剂分子在液体-空气界面。由Lifshitz和Slyozhov以及独立地由瓦格纳开发的奥斯特瓦尔德熟化的经典理论采用连续方法，其中尺寸分布是颗粒尺寸的连续函数，并且守恒方程如流体动力学中那样用颗粒生长速率作为尺寸空间中的速度来制定。它推导的情况下，其中个别粒子的扩散场不重叠，并提供了渐近表达式在大的时间为两个极端的情况下，扩散控制和动力学控制的增长。在本文中，这种连续（流体动力学）的方法的有效性进行了检查，使用更严格的随机微观方法（MCE）。详细比较了使用Lifshitz，Slyozhov，瓦格纳理论和随机微观连续性方程（MCE）的数值和渐近结果。结果表明，与MCE，“扩散控制奥斯特瓦尔德熟化”的限制情况下不再有意义，因为在界面处的动力学发挥作用，即使当从散装到颗粒的分子的运输是扩散控制。对于界面动力学控制的沉淀物生长的情况下，渐近趋势，这是独立的初始条件，在这两种情况下，被认为是更早与MCE。此外，对于这种情况（沉淀物），MCE预测的平均半径在任何给定时间都要大25%左右。虽然从两种方法获得的缩放（相对于最大值）渐近分布是相似的，但使用MCE获得的绝对（未缩放）粒度分布要宽得多，最大值几乎是使用Lifshitz，Slyozhov，瓦格纳方法获得的粒度分布的三分之一。在结果中获得的二维奥斯特瓦尔德熟化的微晶上的基板和岛屿的不溶性表面活性剂的类似的差异。(C)1995年美国物理学会。
The phenomenon of Ostwald ripening is examined theoretically for precipitates in solution, crystallites on a substrate, and islands of insoluble surfactant molecules at the liquid-air interface. The classical theory of Ostwald ripening, developed by Lifshitz and Slyozhov and independently by Wagner, employs a continuum approach in which the size distribution is a continuous function of particle size and the conservation equation is formulated as in hydrodynamics with the particle growth rate serving as a velocity in size space. It was derived for the case in which the diffusion fields of the individual particles do not overlap and provides asymptotic expressions at large times for the two extreme cases of diffusion controlled and kinetic controlled growth. In this paper, the validity of this continuum (hydrodynamic) approach is examined using a more rigorous stochastic microscopic approach (MCE). A detailed comparison is made between the numerical and asymptotic results obtained using the Lifshitz, Slyozhov, Wagner theory and the stochastic microscopic continuity equation (MCE). It is shown that with the MCE, the limiting case of ''diffusion controlled Ostwald ripening'' ceases to have significance, since the kinetics at the interface play a role even when the transport of molecules from the bulk to the particle is diffusion controlled. For the case of interface kinetic controlled growth in precipitates, the asymptotic trends, which are independent of the initial conditions in both cases, are seen much earlier with the MCE. Besides, for this case (precipitates), the MCE predicts a mean radius which is about 25% larger at any given time. While the scaled (with respect to the maximum) asymptotic distributions obtained from the two approaches are similar, the absolute (not scaled) particle size distributions obtained using the MCE are much broader and the maxima are almost a third of those obtained using the Lifshitz, Slyozhov, Wagner approach. Similar differences in the results are obtained for the two dimensional Ostwald ripening of crystallites on a substrate and islands of insoluble surfactant. (C) 1995 American Institute of Physics.