Transient electrophoresis of a conducting spherical particle embedded in an electrolyte‐saturated Brinkman medium

Abstract

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 ζ‐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 ζ‐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.

Transient electrophoresis of a spherical colloidal particle with a slip surface

“…This information is practically important in the efficient design of measurement systems of steady-state electrophoresis. Although there are a lot of theoretical studies on transient electrophoresis [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], these studies deal with colloidal particles with a no-slip surface and can be applied to particles with a hydrophilic surface when the particles are immersed in an aqueous electrolyte solution. The no-slip boundary condition is valid for a hydrophilic surface, because the molecules of the surface strongly interact with the molecules in the surrounding liquid medium.…”

Electrophoresis analysis of a hydrophobic spherical particle in a micropolar electrolyte solution

“…Recently, researchers have investigated the electrophoretic motion of hard spherical particles embedded in a porous electrolyte medium in the literature. For instance, Sherief et al [35] studied the problem of the time-dependent electrophoretic motion of a charged spherical particle embedded in an arbitrary electrolyte solution-saturated porous medium. Ragab [36] used the unit cell model to analyze the unsteady electrophoretic motion of a suspension of charged spherical particles in an arbitrary electrolyte solution through a porous medium.…”

“…Therefore, our work contributes to the existing literature on the electrophoresis flow of viscous fluids and porous media, for example, Refs. [22,23,25,27,30,35], by considering microstructure fluids under a micropolar model with a slippage surface. The novelty of the present investigation lies in our study of the electrophoresis phenomenon of a micropolar model with a slippage surface, taking into account the spin velocity slips due to microrotation, in addition to the traditional velocity slip, and considering the full range of electrical particle conductivity.…”

Transient dynamic electrophoresis of a spherical colloidal particle

“…Morrison [1,2] and Ivory [3,4] initiated the theory of transient electrophoresis, which was advanced particularly by Keh and his coworkers [5-7, 9, 10, 14-16] and further developed by other researchers [8,[11][12][13][17][18][19][20][21][22]. These theoretical studies deal with the transient electrophoresis of various types of colloidal particles, including a spherical particle [1,4,6,7,9,12,[15][16][17], a cylindrical particle [2,20], a permselective particle [8], a porous or soft particle [14,19], a particle in a gel medium [11-13, 17, 21], and a spherical particle with a slip surface [22]. These studies deal with the case in which a static electric field is suddenly applied at time t = 0, and after that, that is, t > 0, the applied field does not vary with time, that is, a step electric field is applied.…”