The startup of electrophoretic motion in a suspension of spherical colloidal particles, which may be charged with constant zeta potential or constant surface charge density, due to the sudden application of an electric field is analytically examined. The unsteady modified Stokes equation governing the fluid velocity field is solved with unit cell models. Explicit formulas for the transient electrophoretic velocity of the particle in a cell in the Laplace transforms are obtained as functions of relevant parameters. The transient electrophoretic mobility is a monotonic decreasing function of the particle-to-fluid density ratio and in general a decreasing function of the particle volume fraction, but it increases and decreases with a raise in the ratio of the particle radius to the Debye length for the particles with constant zeta potential and constant surface charge density, respectively. On the other hand, the relaxation time in the growth of the electrophoretic mobility increases substantially with an increase in the particle-to-fluid density ratio and with a decrease in the particle volume fraction but is not a sensitive function of the ratio of the particle radius to the Debye length. For specified values of the particle volume fraction and particle-to-fluid density ratio in a suspension, the relaxation times in the growth of the particle mobility in transient electrophoresis and transient sedimentation are equivalent.

中文翻译：

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具有任意双电层的带电粒子悬浮液中的瞬态电泳

分析检查了由于突然施加电场而可能以恒定 zeta 电位或恒定表面电荷密度带电的球形胶体颗粒悬浮液中电泳运动的启动。控制流体速度场的非定常修正斯托克斯方程用晶胞模型求解。在拉普拉斯变换中，细胞中粒子的瞬时电泳速度的显式公式作为相关参数的函数获得。瞬态电泳迁移率是颗粒与流体密度比的单调递减函数，通常是颗粒体积分数的递减函数，但对于具有恒定 zeta 电位和恒定表面电荷密度的粒子，它分别随着粒子半径与德拜长度之比的增加而增加和减少。另一方面，电泳迁移率增长中的弛豫时间随着颗粒与流体密度比的增加和颗粒体积分数的降低而显着增加，但不是颗粒比的敏感函数半径到德拜长度。对于悬浮液中颗粒体积分数和颗粒与流体密度比的指定值，瞬态电泳和瞬态沉降中颗粒迁移率增长的弛豫时间是等效的。电泳迁移率增长中的弛豫时间随着粒子与流体密度比的增加和粒子体积分数的降低而显着增加，但不是粒子半径与德拜长度之比的敏感函数. 对于悬浮液中颗粒体积分数和颗粒与流体密度比的指定值，瞬态电泳和瞬态沉降中颗粒迁移率增长的弛豫时间是等效的。电泳迁移率增长中的弛豫时间随着粒子与流体密度比的增加和粒子体积分数的降低而显着增加，但不是粒子半径与德拜长度之比的敏感函数. 对于悬浮液中颗粒体积分数和颗粒与流体密度比的指定值，瞬态电泳和瞬态沉降中颗粒迁移率增长的弛豫时间是等效的。