Investigation of the interfacial instability between a newtonian fluid and a polymeric fluid under the influence of an electric field for microfluidics applications

Abstract

Microfluidic devices are widely used in various industries as they provide many advantages such as easy control of chemical reactions, heat and mass transfer, short analysis time and consumption of chemicals in small amounts. Reactions are either carried in homogeneous phase in a microchannel or in a batch reactor such as a small crucible or a micro droplet, which is also known as digital microfluidics. In micro length scale, the flow regime is laminar, which makes mixing or formation of mono dispersed micro sized droplets difficult. Electrohydrodynamics is an effective method for efficient mixing when two miscible liquids are used and for generating uniform droplets in microchannels when two immiscible liquids are used. The electric field causes the flat interface to deflect, i.e., to become unstable. The aim of this study is to theoretically and numerically analyze the stability of the interface between a Newtonian fluid and a non-Newtonian fluid under the effect of an electric field applied normal to the interface. The fluids under the effect of pressure-driven flow are assumed to be immiscible, incompressible, and leaky-dielectric. Linear stability analysis is conducted to observe the behavior of the system under the electric field and to show the effects of system parameters such as Reynolds number, applied potential, physical and electrical properties of the fluids, elasticity of the polymer. As a result, it is found that decreasing the permittivity ratio or increasing any of the Weissenberg number, the thickness ratio, the viscosity ratio, the conductivity ratio or the Reynolds number have a stabilizing effect; whereas increasing the dimensionless parameter S, the ratio of fluid to electric time scale does not affect the maximum growth rate but decreases the critical wavenumber. Moreover, increasing the electric number, i.e., increasing the applied voltage could be stabilizing or destabilizing depending on the selected parameters.