Improved understanding of the acoustophoretic focusing of dense suspensions in a microchannel

We provide improved understanding of acoustophoretic focusing of a dense suspension (volume fraction φ>10%) in a microchannel subjected to an acoustic standing wave using a proposed theoretical model and experiments. The model is based on the theory of interacting continua and utilizes a momentum transport equation for the mixture, continuity equation, and transport equation for the solid phase. The model demonstrates the interplay between acoustic radiation and shear-induced diffusion (SID) forces that is critical in the focusing of dense suspensions. The shear-induced particle migration model of Leighton and Acrivos, coupled with the acoustic radiation force, is employed to simulate the continuum behavior of particles. In the literature, various closures for the diffusion coefficient D_{φ}^{*} are available for rigid spheres at high concentrations and nonspherical deformable particles [e.g., red blood cells (RBCs)] at low concentrations. Here we propose a closure for D_{φ}^{*} for dense suspension of RBCs and validate the proposed model with experimental data. While the available closures for D_{φ}^{*} fail to predict the acoustic focusing of a dense suspension of nonspherical deformable particles like RBCs, the predictions of the proposed model match experimental data within 15%. Both the model and experiments reveal a competition between acoustic radiation and SID forces that gives rise to an equilibrium width w^{*} of a focused stream of particles at some distance L_{eq}^{*} along the flow direction. Using different shear rates, acoustic energy densities, and particle concentrations, we show that the equilibrium width is governed by Péclet number Pe and Strouhal number Stasw^{*}=1.4(PeSt)^{-0.5} while the length required to obtain the equilibrium-focused width depends on St as L_{eq}^{*}=3.8/(St)^{0.6}. The proposed model and correlations would find significance in the design of microchannels for acoustic focusing of dense suspensions such as undiluted blood.