The time-dependent electrophoresis of an infinitely cylindrical particle in an electrolyte solution, saturated in a charged porous medium after the sudden application of a transverse or tangential step electric field, is investigated semi-theoretically with an arbitrary double-layer thickness in an arbitrary direction relative to the cylinder. The time-dependent modified Brinkman equation with an electric force term, which governs the fluid flow field, is used to model the porous medium and is solved by using the Laplace transform technique. Explicit formulas, for the time-dependent electrophoretic velocity of the cylindrical particle in Laplace’s transform domain, have been derived for both axially and transversely when the uniform electric fields are imposed. They can also be linearly superimposed for an arbitrarily oriented relative to the electric field. Semi-analytical results for the electrophoretic velocities are presented as functions of the dimensionless elapsed time, the ratio of the particle radius to the Debye length, the particle-to-medium density ratio, and the permeability parameter of the porous medium. The results demonstrate, in general, that the growth of the electrophoretic velocities with the time scale are more slower for high permeability, and the effect of the relaxation time for unsteady electrophoresis is found to be negligible, regardless of the thickness of the double layer, the relative mass density or the permeability of the medium. The normalized transient electrophoretic velocities exhibit a consistent upward trend as the ratio of the particle radius to the Debye screening length increases. Conversely, they display a consistent downward trend as the particle-to-fluid density ratio increases, while all other parameters remain constant. The effect of the relaxation time for the transient electrophoresis is much more important for a cylindrical particle than for a spherical particle due to its smaller specific surface area.

在突然施加横向或切向阶跃电场后，对电解质溶液中无限圆柱形颗粒在带电多孔介质中饱和的时间依赖性电泳进行了半理论研究，在任意方向上具有任意双层厚度相对于气缸。具有控制流体流场的电力项的瞬态修正 Brinkman 方程用于对多孔介质进行建模，并使用拉普拉斯变换技术进行求解。当施加均匀电场时，已经导出了拉普拉斯变换域中圆柱形粒子的轴向和横向电泳速度的显式公式。它们还可以线性叠加以相对于电场任意定向。电泳速度的半解析结果呈现为无量纲经过时间、颗粒半径与德拜长度之比、颗粒与介质密度比以及多孔介质渗透性参数的函数。结果表明，一般来说，对于高磁导率，电泳速度随时间尺度的增长更慢，并且发现弛豫时间对非稳态电泳的影响可以忽略不计，无论双层的厚度如何，介质的相对质量密度或渗透性。随着粒子半径与德拜筛选长度之比的增加，归一化瞬态电泳速度表现出一致的上升趋势。相反，随着颗粒与流体密度比的增加，它们表现出一致的下降趋势，而所有其他参数保持不变。由于其较小的比表面积，弛豫时间对瞬时电泳的影响对于圆柱形颗粒比对于球形颗粒更重要。