Kim Min Ju, Yoon Byung Jun
Department of Chemical Engineering and Division of Mechanical and Industrial Engineering, Pohang University of Science and Technology, Pohang, 790-784, Korea
J Colloid Interface Sci. 2001 Apr 1;236(1):173-179. doi: 10.1006/jcis.2000.7382.
An iterative solution scheme is proposed for solving the electrical double-layer interactions governed by the linearized Poisson-Boltzmann equation. The method is based on the indirect integral equation formulation with the double-layer potential kernel of the linearized Poisson-Boltzmann equation. In contrast to the conventional direct integral equation approach that yields Fredholm integral equations of the first kind, the indirect integral equation approach yields well-posed Fredholm integral equations of the second kind. The eigenvalue analysis reveals that the spectral radius of the double-layer integral operator is always less than one. Thus, iterative solution schemes can be successfully implemented for solving the electrical double-layer interactions for very large and complex systems. The utility of the iterative indirect method is demonstrated for several examples which include spherical and spheroidal particles. Copyright 2001 Academic Press.
提出了一种迭代求解方案，用于求解由线性化泊松-玻尔兹曼方程控制的电双层相互作用。该方法基于线性化泊松-玻尔兹曼方程的双层势核的间接积分方程公式。与产生第一类弗雷德霍姆积分方程的传统直接积分方程方法不同，间接积分方程方法产生适定的第二类弗雷德霍姆积分方程。特征值分析表明，双层积分算子的谱半径总是小于1。因此，对于非常大且复杂的系统，可以成功地实施迭代求解方案来求解电双层相互作用。通过包括球形和椭球形颗粒在内的几个例子证明了迭代间接方法的实用性。版权所有2001年学术出版社。
