dc Step response of induced-charge electro-osmosis between parallel electrodes at large voltages

Induced-charge electro-osmosis (ICEO) is important since it can be used for realizing high performance microfluidic devices. Here, we analyze the simplest problem of ion relaxation around a circular polarizable cylinder between parallel blocking electrodes in a closed cell by using a multiphysics coupled simulation technique. This technique is based on a combination of the finite-element method and finite-volume method for the Poisson-Nernst-Planck (PNP) equations having a flow term and the Stokes equation having an electric stress term. Through this analysis, we successfully demonstrate that on application of dc voltages, quadorapolar ICEO vortex flows grow during the charging time of the cylinder for both unbounded and bounded problems and decay during the charging time of the parallel electrodes only for the bounded problem using blocking electrodes. Further, by proposing a simple model that considers the two-dimensional (2D) PNP equations analytically, we successfully explain the step response time of the ICEO flow for the both unbounded and bounded problems. Furthermore, at low applied voltages, we find analytical formulations on steady diffused-ion problems and steady ICEO-flow problems and examine that our numerical results agree well with the analytical results. Moreover, by considering an ion-conserving condition with 2D Poisson-Boltzmann equations, we explain significant decrease of the maximum slip velocity at large applied voltages fairly well. We believe that our analysis will contribute greatly to the realistic designs of prospective high-performance microfluidic devices.