On gel electrophoresis of dielectric charged particles with hydrophobic surface: A combined theoretical and numerical study

Abstract

A theoretical study on the gel electrophoresis of a charged particle incorporating the effects of dielectric polarization and surface hydrophobicity at the particle-liquid interface is made. A simplified model based on the weak applied field and low charge density assumption is also presented and compared with the full numerical model for a nonpolarizable particle to elucidate the nonlinear effects such as double layer polarization and relaxation as well as surface conduction. The main motivation of this study is to analyze the electrophoresis of the surface functionalized nanoparticle with tunable hydrophobicity or charged fluid drop in gel medium by considering the electrokinetic effects and hydrodynamic interactions between the particle and the gel medium. An effective medium approach, in which the transport in the electrolyte-saturated hydrogel medium is governed by the Brinkman equation, is adopted in the present analysis. The governing electrokinetic equations based on the conservation principles are solved numerically. The Navier-slip boundary condition along with the continuity condition of dielectric displacement are imposed on the surface of the hydrophobic polarizable particle. The impact of the slip length on the electrophoresis is profound for a thinner Debye layer, however, surface conduction effect also becomes significant for a hydrophobic particle. Impact of hydrophobicity and relaxation effects are higher for a larger particle. Dielectric polarization creates a reduction in its electrophoretic propulsion and has negligible impact at the thinner Debye length as well as lower gel screening length.

Transient Gel Electrophoresis of a Spherical Colloidal Particle

“…Now consider the case where the particle ζ potential is low, and the relative permittivity of ε p of the particle is much smaller than that of the electrolyte solution ε r (ε p « ε r ) so that ε p is practically equal to zero. In this case, Equations ( 33) and (34) give…”

“…When an external electric field is suddenly applied to a suspension of colloidal particles, the particle starts to move with a time-dependent transient electrophoretic mobility, which reaches steady electrophoretic mobility as time goes to infinity. While there are many theoretical studies on transient free-solution electrokinetics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], including transient electrophoresis of spherical hard particles [1,4,6,7,9,13,14,17], cylindrical hard particles [2,11,16] and soft particles (i.e., polyelectrolyte-coated particles) [12,15], and on steady gel electrophoresis including gel electrophoresis of spherical hard particles [18][19][20][21][22][23][24][25]28,[30][31][32]34,35], soft particles [26,27,…”