A numerical study on the electrophoresis of a liquid droplet in an aqueous medium is made by considering the full set of governing equations based on the conservation principle. The surface of the droplet is considered to be charged, and the liquid filling the droplet is nonconducting. The dielectric polarization of the nonconducting droplet is also addressed in the present study. The impact of the surface conduction, double layer polarization, and relaxation effects creates a retardation on the electrophoresis. The occurrence of slip velocity at the droplet surface creates the surface conduction important even at weak electric field and a thin Debye layer for which the double layer polarization and relaxation may become small. The role of the surface conduction, which is measured through the Dukhin number, on the electrophoretic propulsion of the droplet is analyzed. Our numerical solutions for low charge density and thinner Debye length agree well with the existing simplified model and asymptotic analysis. However, a large discrepancy in mobility from these existing results occurs when the droplet size is bigger or droplet viscosity is lower than the suspended liquid medium. The variation of the electrophoretic mobility of a perfectly dielectric droplet as a function of the droplet viscosity, droplet size, and other electrokinetic parameters is analyzed. The dielectric polarization of the droplet and its impact on the electrophoresis are considered in the present work. The drag and the strength of the internal circulation are obtained.

We consider the electrophoresis of a charged colloid for a generalized situation in which the particle is considered to be polarizable and the surface exhibits hydrophobicity. The dielectric polarization of the particle creates a nonlinear dependence of the electrophoretic velocity on the applied electric field, and the core hydrophobicity amplifies the fluid convection in the Debye layer. Thus, a linear analysis is no longer applicable for this situation. The present analysis is based on the numerical solution of the nonlinear electrokinetic equations based on the Navier-Stokes-Nernst-Planck-Poisson equations coupled with the Laplace equation for the electric field within the dielectric particle. The hydrophobicity of the particle may influence its electric polarization by enhancing the convective transport of ions. The nonlinear effects, such as double-layer polarization and relaxation, are also influenced by the hydrophobicity of the particle surface. The present results compare well for a lower range of the applied electric field and surface charge density with the existing results for a perfectly dielectric particle with a hydrophobic surface based on the first-order perturbation analysis due to Khair and Squires [Phys. Fluids 21, 042001 (2009)PHFLE61070-663110.1063/1.3116664]. Dielectric polarization creates a reduction in particle electrophoretic velocity, and its impact is strong for a moderate range of Debye length. A quantitative measure of the nonlinear effects is demonstrated by comparing the electrophoretic velocity with an existing linear model.

The electrophoresis of a polyelectrolyte nanoparticle, whose charge condition depends on the salt concentration and pH of the suspended medium as well as the dielectric permittivity difference, is analyzed. The present nonlinear model for the electrophoresis of this pH-regulated polyelectrolyte (PE) particle is based on the consideration of full set of governing equations of fluid and ion transport coupled with the equation for electric field. The Born energy of the ions are incorporated to account for the difference in the dielectric permittivity of the PE and the electrolyte. The governing equations are computed numerically through a control volume approach. The nonlinear effects are highlighted by comparing with the existing linear model as well as results based on the first-order perturbation analysis valid for a weak applied field. The ion partitioning effect arising due to the difference in self energy of ions between the two media, have a strong impact on the mobility of the PE. The ion partitioning effect attenuates the penetration of counterions in the PE, which enhances the electric force and hence, results in a larger mobility of the PE. The nonlinear effects due to the double layer polarization and relaxation are intensified due to the ion partitioning effect. The ion partitioning effect influences the association/dissociation of PE functional group by tuning the hydrogen/hydroxide ions. Present study shows that the ion partitioning effect is profound for higher salt concentration and/or higher volume density of PE functional groups.

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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.