The role of fluid inertia on streamwise velocity and vorticity pattern in curved microfluidic channels

Abstract

Recently, we introduced a secondary Dean flow in curved rectangular microchannels by applying the finite volume scheme with a SIMPLE (semi-implicit method for pressure-linked equations) algorithm for the pressure-driven electrokinetic transport (Yun et al., 2010). This framework is based on the theoretical model coupled with the full Poisson-Boltzmann, Navier-Stokes, and the Nernst-Planck principle of net charge conservation. To explore intensively the effect of fluid inertia on the secondary flow, both the applied pressure drop Delta p/L and the channel curvature WIR(c) are changed for three kinds of rectangular channel cross section with considering the electric double layer and fluid slip condition. Simulation results exhibit that the square channel (i.e., channel aspect ratio similar or equal to 1) gets the higher axial velocity, compared to the others. The change of its skewed velocity profile from inward to outward was found with increasing fluid inertia caused by increasing Delta p/L, due to the reduced spanwise pressure gradient. The curvature introduces the presence of pairs of counter-rotating vortices perpendicular to the flow direction. Although the square channel shows a different feature of very close pattern in the vorticity profile, the total magnitude of average vorticity increases commonly in all cases with increasing either Delta p/L or WIR(c), providing scaling relations with the almost same value of exponent 2. It is obvious that the role of fluid inertia should explicitly be understood for a precise design of microfluidic chips taking arbitrary channel aspect ratios.