Droplet Electrophoresis with Internal Free Ions: Effect of Permittivity Changes in the Electric Double Layer

Droplet electrophoresis (EP) is of interest in biological systems, microfluidics, and separation techniques. We investigate EP of an oil droplet that contains free ions and is stabilized in an electrolyte solution through an amphoteric surfactant. The presence of mobile ions within the droplet leads to the creation of a distinct nonzero space charge density inside the droplet and consequently, formation of an inner EDL inside the droplet in addition to the traditionally considered outside EDL. While we assume the permittivity inside the inner EDL to remain constant, we consider both the case of constant and variable permittivity in the outer EDL. Our findings demonstrate a change in the droplet direction of motion in the electric field when transitioning from acidic to alkaline pH, regardless of permittivity and ionic strength in both oil and electrolyte. We further find a significant reduction in the magnitude of droplet velocity in the case of a variable permittivity due to reduction of the local space charge density within the EDL surrounding the droplet. When decreasing the viscosity ratio of the oil to the electrolyte, in all cases we find a reduction in droplet velocity. This decline is attributed mostly to the formation and strength of a vortex around the droplet. We finally demonstrate that with constant permittivity in the outer EDL, the variation in κa_outer has a more significant effect on the droplet's EP velocity than altering κa_inner. However, in cases where the body forces inside of the droplet dominate, minor changes in the outer electrolyte concentration have no influence on the droplet motion, which is relevant for biological colloids that can contain significant free internal charges. Our results are important for the manipulation of biological colloids, water and waste treatment such as lubricant removal from processing streams.