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.

中文翻译：

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带电粒子无盐悬浮液中的电泳和导电

采用晶胞模型分析了带电球形颗粒在无盐溶液中的电泳和导电现象。线性化 Poisson-Boltzmann 方程（适用于表面电荷密度相对较低或颗粒体积分数较高的情况）和 Laplace 方程分别求解平衡电势分布及其由施加的电场引起的扰动，在仅在粒子周围含有反离子的流体，分别求解了离子连续性方程和修正的斯托克斯方程，用于电化学势能和流体流场。得到了粒子的电泳迁移率和悬浮液的有效电导率的明确解析公式，粒子相互作用对这些传输特性的影响是显着而有趣的。缩放的 zeta 电位、电泳迁移率和有效电导率随着颗粒的缩放表面电荷密度的增加而单调增加，并且通常随着颗粒体积分数的增加而减小，保持彼此参数不变。在德拜-休克尔近似下，在无盐悬浮液中，用表面电荷密度归一化的电泳迁移率对颗粒半径与德拜屏蔽长度和颗粒体积分数之比的依赖性与含盐悬浮液中的相同。暂停，