Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan.
Electrophoresis. 2021 Nov;42(21-22):2134-2142. doi: 10.1002/elps.202100181. Epub 2021 Aug 6.
The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.
采用单元模型分析了在无盐溶液中带电球形颗粒悬浮液的电泳和电传导。针对相对较低的表面电荷密度或较高的颗粒体积分数的情况，对线性化的泊松-玻尔兹曼方程（适用于仅在颗粒周围包含反离子的流体中）和拉普拉斯方程进行求解，以分别得到平衡电势分布及其在外加电场作用下的微扰，同时对离子连续性方程和修正的斯托克斯方程进行求解，以得到电化学势能和流体流动场。推导出了颗粒电泳迁移率和悬浮液有效电导率的显式解析公式，并研究了颗粒间相互作用对这些输运性质的显著影响。标准化的zeta 电势、电泳迁移率和有效电导率随颗粒的标准化表面电荷密度的增加而单调增加，通常随颗粒体积分数的增加而减小，保持其他参数不变。在德拜-休克尔近似下，无盐悬浮液中归一化到表面电荷密度的电泳迁移率与颗粒半径与德拜屏蔽长度比和颗粒体积分数的依赖关系与含盐悬浮液中的相同，但无盐悬浮液中有效电导率随颗粒体积分数的变化与含电解质悬浮液中的变化有很大不同。
