Electrokinetic transport of a non-conducting liquid droplet in a polyelectrolyte medium

Abstract

A numerical study on the electrophoresis of a liquid droplet embedded in a polyelectrolyte hydrogel 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 non-conducting. The dielectric polarization of the non-conducting droplet is also addressed in the present study. The impact of the surface conduction, double layer polarization, and relaxation effects on the electrophoresis of the non-conducting polarizable uniformly charged droplet is elucidated for a wide range of the gel volume charge density, Debye length, and drop viscosity and size. The presence of the gel immobile charge and slip velocity at the droplet surface leads to a stronger surface conduction, which precludes consideration of a simplified model based on the thin-layer assumption. Our numerical solutions at a low ζ-potential corresponding to a droplet of large viscosity, for which surface conduction is negligible- A gree well with the existing analytic solutions for a rigid colloid. The strong electroosmotic flow driven by the immobile charges of the gel medium creates a negatively charged drop in the hydrogel medium to translate along the direction of the applied field. Entrapment of the charged drop can be made by regulating the Debye length and volume charge density of the gel. The charged gel medium is found to be efficient in size-based sorting of the liquid drops.