Mass flow rate control in a cylindrical capillary by an AC electric field at high zeta potential

Abstract

In the present study we obtain the mass flow rate characteristics in a cylindrical capillary due to a time-periodic electric field at high zeta potential, extending the conventional thin electrical double layer limit. The capillary cross section is divided into two regimes, the high potential regime (near surface region), and the low potential regime (capillary central line region). To obtain the potential distribution inside the capillary, the nonlinear part of the Poisson-Boltzmann equation is approximated by a linear function for the low potential regime and by an exponential function for high potential regime. Using the approximated potential distributions, the governing electro-hydrodynamic equation is then solved semi-analytically, where the imposed electric field and the velocity field is assumed to have the form which consist of a steady state term and a time-periodic term. A theoretical investigation on the mass flow rate, the phase difference is carried out on the basis of pulsation frequency, electric double layer thickness and the relative capillary radius. Moreover, this study is extended for triangular and trapezoidal shaped pulsation of the electric field. From the signature characteristics of the mass flow rate and the electric field, the "inverse" problem is also solved, that is, the desired electric field is obtained from a given mass flow rate.