Electrophoresis of hydrophobic and polarizable liquid droplets in hydrogel medium

Abstract

The emulsion droplet-hydrogel composite is a new class of biomaterial which finds potential application in several fields, including chemical, biological, food and pharmaceutical industries, as well as to controlled release drug in targeted location, etc. Besides, the electric field response of polarizable emulsion droplets quenched in hydrogel medium offers several Lab-on-a-Chip applications. Note that the gel electrophoresis of such droplets is advantageous compared to free-flow electrophoresis. Given the importance, a general theory of electrophoresis applicable for any hydrophobic and polarizable liquid droplets quenched in hydrogel medium is developed. Such a theory is also applicable for electric field response of emulsion droplets quenched in a hydrogel medium. The mathematical model is based on conservation principles of mass and momentum considering the hydrogel skeleton as soft polymeric material saturated with electrolytic solution. Within the Debye-Hückel electrostatic framework, we have derived a closed form analytical expression for electrophoretic mobility of hydrophobic and polarizable liquid droplets embedded in hydrogel skeleton. The derived general expression is further approximated with negligible error and the corresponding approximate form is found to be very convenient and can be easily programmed on a personal computer. Additionally we further deduce several closed form analytical expressions derived under various limits. Thus, the newly derived analytical results may be useful to the experimentalists to analyze and interpret their observations.