Effect of Variable Permittivity on the Electrophoretic Mobility of a Droplet

Electrophoresis (EP) is the manipulation of charged droplets/particles with an electric field, enabling precise separation and characterization of particles/droplets or biomolecules. This technique can be employed in energy recovery and separation processes, for instance to break oil and water emulsions. In this work, we highlight the importance of considering variable permittivity in the electric double layer (EDL) around the droplet for a more comprehensive understanding of droplet EP. Acknowledging this variable permittivity is critical for optimizing the technique's efficiency and accuracy, as it directly influences droplet migration behavior and stability.

A numerical model describing an oil droplet containing dissolved ions in an electrolyte solution was developed. The formation of an EDL inside the droplet as a result of the interfacial charges was considered, which led to the emergence of a body force inside the droplet in addition to the external body force on the droplet, influencing the droplet mobility. The numerical simulations revealed that accounting for variable permittivity inside the EDL reduced the EDL thickness compared to assuming constant permittivity. Interestingly, depending on the ionic concentration within the droplet and the magnitude of the inner body force, the direction of droplet motion could deviate from its surface charge-based prediction. These findings have implications for various applications, including soil remediation and ion detection in chemistry.