Start‐up Brinkman electrophoresis of a dielectric sphere for Happel and Kuwabara models

Abstract

The starting electrophoresis in a charged porous continuum response of a homogeneous suspension of spherical particles to the sudden application of an external electric field is analyzed semianalytically through the use of a unit cell model. The electric double layer in the porous Brinkman medium surrounding each sphere is assumed to be thin but finite, and the effect of dynamic electroosmosis within it is included. The field equation for the fluid outside the double layers is solved based on the unit cell model under the start-up Brinkman model. Expressions of the time-dependent electrophoretic and settling velocities of the particle in the Laplace transform as functions of the permeability, the relative mass density, the electrokinetic particle radius, and the volume fraction of the particles are performed for two different boundary conditions at the fictitious surface of the cell. Numerical results indicate that the timescale for the development of electrophoresis and sedimentation is small for a high permeability, an assemblage of spheres through a dielectric porous medium with a higher particle volume fraction and a smaller particle to porous fluid density ratio; the electrophoretic mobility is a monotonically increasing function of the electrokinetic radius of the sphere at any instant. The start-up of electrophoretic mobility decreases with an increase in the particle volume fraction at a small value of the particle-to-medium density ratio, but it may increase as the particle volume fraction increases at a large value of this density. The particle interaction effect in a swarm on the time-dependent electrophoresis is much smaller than that on the starting sedimentation of the particles. The detailed comparison of the results of the cell model with different boundary conditions at the virtual surface of the cell is obtained and illustrated graphically.

Micropolar fluid flow through the membrane composed of impermeable cylindrical particles coated by porous layer under the effect of magnetic field

“…Similar types of investigations can be found in the work . Saad has discussed the problem of unsteady electrophoresis and sedimentation of group of charged particles through the Brinkman porous medium using Happel and Kuwabara cell model techniques.…”

Transient dynamic electrophoresis of a spherical colloidal particle

“…There are a lot of theoretical studies on the transient electrophoresis of a colloidal particle in an electrolyte solution under the application of a step electric field . 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].…”

“…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.…”

“…Transient electrophoresis, which is a response of a colloidal particle to a suddenly applied electric field, is not only of theoretical interest but also has practical importance in designing efficient measurement systems for steady‐state electrophoresis. There are a lot of theoretical studies on the transient electrophoresis of a colloidal particle in an electrolyte solution under the application of a step electric field [1–22]. 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, 11–13, 17–22].…”

Transient Electrophoresis of a Cylindrical Colloidal Particle

“…Transient electrophoresis is the time-dependent unsteady response of a charged colloidal particle in an electrolyte solution to an applied step electric field [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. It is often required to determine the time necessary for the velocity of a particle to approach its steady value when an electric field is applied to the particle.…”