Transient Electrophoresis of a Cylindrical Colloidal Particle

Abstract

We develop the theory of transient electrophoresis of a weakly charged, infinitely long cylindrical colloidal particle under an application of a transverse or tangential step electric field. Transient electrophoretic mobility approaches steady electrophoretic mobility with time. We derive closed-form expressions for the transient electrophoretic mobility of a cylinder without involving numerical inverse Laplace transformations and the corresponding time-dependent transient Henry functions. The transient electrophoretic mobility of an arbitrarily oriented cylinder is also derived. It is shown that in contrast to the case of steady electrophoresis, the transient Henry function of an arbitrarily oriented cylinder at a finite time is significantly smaller than that of a sphere with the same radius and mass density as the cylinder so that a cylinder requires a much longer time to reach its steady mobility than the corresponding sphere.

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.…”

“…This condition, however, should be modified for a hydrophobic surface, because the molecules of a hydrophobic surface interact only weakly with the molecules in the surrounding liquid medium so that there should be a hydrodynamically slipping of the liquid on the hydrophobic surface. For a hydrophobic surface, the slip boundary condition should be employed [19–25]. Kobayashi [26] analyzed the measured steady electrophoretic mobility of polystyrene particles, showing that good agreement between a theory of Gopmandal et al.…”

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].…”