In this study, the time-dependent electrophoretic motion of a conducting spherical particle embedded in an arbitrary electrolyte solution saturated porous medium is investigated. The porous medium is uniformly charged and the embedded hard particle is charged with constant -potential or constant surface charge density. The unsteady modified Brinkman equation with an electric force term, which governs the fluid velocity field, is used to model the porous medium and is solved by Laplace's transform technique. An analytical expression for the electrophoretic velocity of the spherical particle is obtained in Laplace transform domain as a function of the relevant parameters, and its inversion is obtained through numerical techniques. Also, in this study, the steady-state electrophoretic velocity is obtained analytically as linear functions of -potential (or surface density charge) and the fixed charge density. The steady-state electrophoretic velocity is displayed graphically for various relevant parameters and compered with the available data in the literature. Also, the numerical values of the transient electrophoretic velocity are plotted versus the nondimensional elapsed time and discussed for different values of the Debye length parameter, density ratio, permeability of the porous medium, and for high and nonconducting particles.

中文翻译：

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嵌入电解质饱和布林克曼介质中的导电球形粒子的瞬态电泳

在这项研究中，研究了嵌入任意电解质溶液饱和多孔介质中的导电球形粒子的时间依赖性电泳运动。多孔介质均匀带电，嵌入的硬质颗粒带电常数- 潜在的或恒定的表面电荷密度。控制流体速度场的带有电力项的非定常修正 Brinkman 方程用于模拟多孔介质，并通过拉普拉斯变换技术求解。在拉普拉斯变换域中得到了球形粒子电泳速度与相关参数的关系的解析表达式，并通过数值技术得到了它的反演。此外，在本研究中，稳态电泳速度是通过分析获得的线性函数 - 电位（或表面密度电荷）和固定电荷密度。稳态电泳速度以图形方式显示各种相关参数，并与文献中的可用数据进行比较。此外，还绘制了瞬态电泳速度的数值与无量纲经过时间的关系图，并讨论了德拜长度参数、密度比、多孔介质的渗透性以及高和非导电粒子的不同值。