Keh HJ, Ding JM
Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan, 106-17, Republic of China
J Colloid Interface Sci. 2000 Jul 15;227(2):540-552. doi: 10.1006/jcis.2000.6918.
The sedimentation in a homogeneous suspension of charged spherical particles with an arbitrary thickness of the electric double layers is analytically studied. The effects of particle interactions are taken into account by employing a unit cell model. Overlap of the double layers of adjacent particles is allowed, and the polarization effect in the double layer surrounding each particle is considered. The electrokinetic equations that govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. An analytical expression for the settling velocity of the charged sphere in closed form is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. A closed-form formula for the sedimentation potential in a suspension of identical charged spheres is also derived by using the requirement of zero net electric current. Our results demonstrate that the effects of overlapping double layers are quite significant, even for the case of thin double layers. Copyright 2000 Academic Press.
对具有任意厚度双电层的带电球形颗粒均匀悬浮液中的沉降进行了分析研究。通过采用单胞模型考虑了颗粒间相互作用。允许相邻颗粒的双电层重叠，并考虑了围绕每个颗粒的双电层中的极化效应。假设系统仅偏离平衡状态很小，对控制单胞中电解质溶液中离子浓度分布、电势分布和流体流场的电动方程进行线性化。使用微扰方法，以颗粒的表面电荷密度（或zeta电位）作为小扰动参数，求解这些线性化方程以得到对称带电电解质的解。通过带电球体的重力、静电力和流体动力之间的平衡，得到了沉降速度的封闭形式解析表达式。利用净电流为零的条件，还推导了相同带电球体悬浮液中沉降电势的封闭形式公式。我们的结果表明，即使对于薄双电层的情况，双电层重叠的影响也相当显著。版权所有2000年学术出版社。
