Transient electrophoresis of a spherical colloidal particle with a slip surface

Abstract

We derive the general expression for the transient electrophoretic mobility of a spherical colloidal particle with a slip surface in an electrolyte solution. From the general mobility expression, we derive an analytic mobility expression, which is applicable for low particle zeta potentials and arbitrary Debye length. This expression corresponds to the time‐dependent transient Henry function.

Transient dynamic electrophoresis of a spherical colloidal particle

“…The fundamental electrokinetic equations for the liquid flow velocity, which can be expressed as u(r, t)e −iωt = (u r (r, t), u θ (r, t), u ϕ (r, t))e −iωt at position r(r, θ, ϕ) and time t and the velocity v j (r, t)e −iωt of jth ionic species of concentration n j (r, t), are similar to those for the usual dynamic electrophoresis of a sphere in a stationary oscillating electric field, namely, Ref. [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].…”

“…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]. These theoretical studies deal with the transient electrophoresis of various types of colloidal particles, including a spherical particle [1, 4, 6, 7, 9, 12, 15–17], 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].…”

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

“…This idealization is valid only at the macroscopic length scale [58][59][60] and can be applied to hydrophilic surfaces. In the case of hydrophobic surfaces, the molecules of the surface interact weakly with the molecules in the surrounding fluid [61]. For that reason, we should consider the velocity slip and spin velocity slip at the surface.…”