Simple analytic solution of the rate equations for the early-stage aggregation kinetics of colloidal particles
Simple analytic solution of the rate equations for the early-stage aggregation kinetics of colloidal particles
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DOI：
10.1007/s00396-013-3085-8
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发表时间：
2013-10
影响因子：
2.4
通讯作者：
H. Ohshima
中科院分区：
文献类型：
--
作者：
H. Ohshima
由DLVO理论得到的两个接近的胶体粒子相互作用势能在粒子间相互作用能的势曲线上可以表现为最大值、初级最小值和次级最小值。Behrens和Borkovec （J胶体界面学报225:460,2000）考虑了次级极小值的影响，考虑了一组耦合的非线性微分速率方程，并推导了速率方程的近似解及其精确数值解。本文给出了这些速率方程的一种改进的简单解析解。所得到的解涉及两个不同的（快和慢）指数衰减常数，发现与速率方程的数值解非常吻合，误差可以忽略不计。
The potential energy of the interaction between two approaching colloidal particles obtained by the DLVO theory can exhibit a maximum, a primary minimum, and a secondary minimum on the potential curve of the interparticle interaction energy. Behrens and Borkovec (J Colloid Interface Sci 225: 460, 2000) considered a set of coupled nonlinear differential rate equations for the early-stage aggregation kinetics of colloidal particles by taking into account the influence of the secondary minimum and derived an approximate solution to the rate equations as well as their exact numerical solutions. In the present article, an improved simple analytic solution is derived for these rate equations. The obtained solution, which involves two distinct (fast and slow) exponentially decay constants, is found to be in excellent agreement with numerical solutions to the rate equations with negligible errors.