Theory of diffusion-limited precipitation
Theory of diffusion-limited precipitation
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DOI：
10.1016/0022-3697(58)90053-2
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发表时间：
1958-09
影响因子：
4
通讯作者：
F. Ham
中科院分区：
文献类型：
--
作者：
F. Ham
本文提出了一个简单的理论，描述了从过饱和溶液到颗粒阵列的扩散限制一般沉淀。我们计算的时间依赖性的小球形，球状和圆柱形颗粒的过量溶质的未沉淀部分。对于小的t，该分数具有exp（-bt n）的形式。如果粒子从最初可以忽略不计的尺寸与恒定的偏心率增长，和增长是完全扩散限制，我们发现n= 3 - 2的所有球体，包括杆和磁盘以及球体。这与早期的评价形成对比，早期的评价给出了圆盘n= 5 2，棒n= 2，这是不正确的。对于圆柱形粒子，我们发现n= 1。此外，对于初始尺寸有限的小圆盘和小棒，n为1，这些圆盘和小棒在生长过程中保持高度偏心并且不明显改变它们的较长尺寸。无论颗粒形状如何，当分数小于1 2时，未沉淀分数近似由[G exp（-at）]给出。我们还给出了一个精确的解的时间依赖的扩散方程的增长的球形粒子在无限介质中，我们表明，在严格的扩散限制条件下的粒子增长与恒定的偏心率和它的尺寸是成比例的。
A simple theory for diffusion-limited general precipitation from a supersaturated solution upon an array of particles is described. We calculate the time-dependence of the unprecipitated fraction of the excess solute for small spherical, spheroidal, and cylindrical particles. This fraction has the form exp (—bt n) for small t. If the particles grow from initially negligible dimensions with constant eccentricity, and the growth is entirely diffusion-limited, we find n= 3 2 for all spheroids, including rods and disks as well as spheres. This contrasts with earlier evaluations, which gave n= 5 2 for disks and n= 2 for rods and which are incorrect. We find n= 1 for cylindrical particles. Also, n is 1 for small disks and rods, of finite initial dimensions, that remain highly eccentric and do not alter their longer dimensions appreciably during growth. Regardless of particle shape, the unprecipitated fraction is given approximately by [G exp (—at)] when the fraction is less than 1 2. We also give an exact solution of the time-dependent diffusion equation for the growth of a spheroidal particle in an infinite medium, and we show that under strictly diffusion-limited conditions the particle grows with constant eccentricity and that its dimensions are proportional to√ t.