FINITE-DIFFERENCE SOLUTION OF ELECTROKINETIC FLOW THROUGH MICROFLUIDIC PIPE

Abstract

The study of electro-viscous effects in steady, fully developed, pressure-driven flow of non-Newtonian fluids through a two dimensional cylindrical microchannel have been investigated numerically by solving the Poisson—Boltzmann and the momentum Navier-Stokes equations (with additional electrical body force term) using a finite difference method by writing code on C. The pipe wall is considered to have uniform surface charge density and the liquid is assumed to be a symmetric 1:1 electrolyte solution with bulk ion concentration. Electro-viscous resistance reduces the velocity adjacent to the wall, relative to the velocity on the axis and increases the pressure gradient. The effect is shown to be greater when the liquid is shear-thinning, and less when it is shear-thickening, than it is for Newtonian flow. For overlapping electrical double layers and elevated, surface charge density, the electroviscous reduction in the near wall velocity can form an almost stationary (zero shear) layer there when the liquid is shear-thinning. In that case, the liquid behaves approximately as if it is flowing through a channel of reduced diameter or of increased viscosity. The induced axial electrical field shows only a weak dependence on the power-law index with the dependence being greatest for shear-thinning liquids than the Newtonian fluids. This field exhibits a local maximum as surface charge density increases from zero, even though the corresponding electrokinetic resistance increases monotonically. The magnitude of the electroviscous effect on the apparent viscosity, as measured by the ratio of the apparent and physical consistency indices, decreases monotonically as the power-law index increases. Thus, overall, the electroviscous effect is stronger in shear-thinning, and weaker in shear-thickening liquids, than it is when the liquid is Newtonian. This study is presented for the case of Newtonian fluids distribution of EDL potential and its effect on flow field and pressure drop for fixed volumetric flow rate for the various values of surface charge density and inverse of Debye-Hukle parameters (K) and also presented the distribution of electrical field strength.