Electric field-driven formation of particle concentration fronts in suspensions

Abstract

A distinct front, separating regions enriched with and depleted of particles, was recently observed in suspensions subjected to high-gradient ac electric fields and a set of theoretical model equations for the particle concentration, containing no fitting parameters, were developed [Kumar et al., 2004. Combined negative dielectrophoresis and phase separation in nondilute suspensions subject to a high-gradient ac electric field. Phys. Rev. E 69, 021402-1–10; Bennett et al., 2003. Combined field-induced dielectrophoresis and phase separation for manipulating particles in microfluidics. Appl. Phys. Lett. 83, 4866–4868]. Although the numerical solutions of these equations were found to be quantitatively consistent with the experimental observations, they did not provide sufficient information for elucidating the mechanism of the front formation due to the complexity of the equations. Here, we examine these equations analytically for the special case in which they admit a similarity solution and establish the existence of shock solutions to these equations. The shocks are shown to arise because of the rapid local growth of the suspension viscosity due to the field-driven particle accumulation in certain areas of the domain.