DNS of Nonlinear Electrophoresis

A numerical modelling of electrophoresis of dielectric particle is proposed under low and moderate homogeneous electric fields. As surface charge at the surface of the particle increases, nonlinear effects associated with surface conduction become more prominent. Current analytical methodologies addressing this issue employ asymptotic techniques, necessitating the establishment of effective boundary conditions. Consequently, solutions within the thin boundary layer, which substantially contribute to the emergence of nonlinear phenomena, are overlooked. While the asymptotic approach is capable of capturing principal effects, it falls short in providing a comprehensive understanding of the complete picture with non-linear effects. Our numerical modelling, incorporating a full formulation, is designed to bridge this knowledge gap. The numerical algorithm is tested in this work for the case of dielectric particle and can be readily extended to other particle types by altering the boundary conditions. The proposed method can be effortlessly generalized for various particle categories, such as ion-selective, flexible, biological, Janus particles, and those with hydrophobic surfaces. It operates without constraints concerning Debye, Dukhin, and Péclet numbers, which are associated with the emergence of nonlinear effects. The numerical algorithm was validated using an analytical solution for a weak electric field and experimental results for moderate and high electric fields. It was found that the electric field intensity and the surface charge density on the particle have the most significant impact on the emergence of non-linear effects. When there is a high degree of non-linearity, a structure of thin boundary layers nested within one another forms around the particle’s surface. In particular, the formation of a space charge region (SCR) around a non-conducting surface was discovered. It was previously believed that SCR only forms around surfaces with ion-exchange properties.