Two-Dimensional Numerical Analyses of Acoustophoresis Phenomena in Microfluidic Channel With Microparticle-Suspended, Viscous, Moving Fluid Medium

Abstract

Microfluidic, acoustophoretic separation of cells and microparticles has gained significant interest since it can offer a high-throughput, high-efficient, label-free, continuous separation. However, the designs of state-of-the-art, acoustophoretic separation devices have been mainly derived from a simplistic, one-dimensional (1-D), analytical acoustic model in a “static” fluid medium. Therefore, it is not possible to consider the effects of 2-D or 3-D geometries, “moving” fluid media, and viscous boundary layers that can significantly influence cell/microparticle motions in reality. Here, a 2-D numerical modeling procedure for analyzing the acoustophoretic microparticle motion in microfluidic channels is presented to address the aforementioned deficiencies. Here, the mass and momentum conservation equations and the state equation are decomposed into zeroth-, first-, and second-order governing equations by using a perturbation method. Then, zeroth-, first-, and second-order acoustic pressures are calculated by applying a sixth-order finite difference method to the decomposed governing equations with appropriate boundary conditions under an acoustic excitation. In particular, non-reflective boundary conditions are derived for the first- and second-order governing equations and applied at the ends of a microchannel. The acoustophoretic force calculated by integrating the acoustic pressure over the surface of a rigid microparticle along with viscous drag force is then applied to the Newton’s equation of motion to analyze the acoustophoretic motion of the microparticle. By comparing numerical and 1-D analytical microparticle motions, the proposed numerical modeling procedure is validated for a 1-D plane-wave-like excitation case. It is also shown that numerically-predicted microparticle behavior is quite different from that of the 1-D analytical model for a 2-D acoustic excitation case in a realistic microchannel. Additionally, the effects of the microparticle’s size and density on its acoustophoretic motions are studied.