Steady flow of ionic liquid through a cylindrical microfluidic contraction–expansion pipe: Electroviscous effects and pressure drop

Abstract

Electroviscous effects in steady, pressure-driven flow of a symmetric 1:1 electrolyte in a cylindrical microfluidic 4:1:4 contraction–expansion at low Reynolds number are investigated numerically by solving the field equations using a finite volume method. Predicted profiles of electrical potential, charge distribution, pressure drop and apparent viscosity are qualitatively similar to those for the slit-like contraction–expansion studied previously by the authors. However, the changes in electrical potential and pressure drop along the channel are greater than those for a corresponding slit-like geometry. The apparent viscosity is lower in the cylindrical contraction–expansion than it is in the equivalent slit-like geometry, whereas the converse is found for uniform channels except when the electrical double layers (EDLs) overlap. As for the slit-like case, a simple model is developed to calculate the pressure drop, and hence the apparent viscosity, by adding the pressure drops over the inlet, outlet and contracted sections of the channel (based on the fully developed flow in a uniform pipe), and an extra pressure drop due to contraction–expansion using the low Reynolds number analytical solution for a circular orifice. For the parameter range considered, the predictions of the simple model overestimate the apparent viscosity by up to 5 – 12 % compared with that obtained by a finite volume numerical solution. The differences become smaller when the thickness of the EDL or the surface charge density are reduced.