Transient Gel Electrophoresis of a Spherical Colloidal Particle

Abstract

The general theory is developed for the time-dependent transient electrophoresis of a weakly charged spherical colloidal particle with an electrical double layer of arbitrary thickness in an uncharged or charged polymer gel medium. The Laplace transform of the transient electrophoretic mobility of the particle with respect to time is derived by considering the long-range hydrodynamic interaction between the particle and the polymer gel medium on the basis of the Brinkman–Debye–Bueche model. According to the obtained Laplace transform of the particle’s transient electrophoretic mobility, the transient gel electrophoretic mobility approaches the steady gel electrophoretic mobility as time approaches infinity. The present theory of the transient gel electrophoresis also covers the transient free-solution electrophoresis as its limiting case. It is shown that the relaxation time for the transient gel electrophoretic mobility to reach its steady value is shorter than that of the transient free-solution electrophoretic mobility and becomes shorter as the Brinkman screening length decreases. Some limiting or approximate expressions are derived for the Laplace transform of the transient gel electrophoretic mobility.

Transient dynamic electrophoresis of a spherical colloidal particle

“…Figure 1 shows that the magnitude of the transient dynamic electrophoretic mobility μ ( t ) first increases monotonically and then exhibits a damped oscillation with the frequency ω of the applied oscillating electric field, approaching its final value μ (∞), unlike the case where a step electric field is applied. In the case of a step electric field, μ ( t ) approaches monotonically increasing function of time t without oscillation [1–22].…”

“…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].…”

“…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]. 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.…”