Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
Phys Rev E. 2017 Nov;96(5-1):052606. doi: 10.1103/PhysRevE.96.052606. Epub 2017 Nov 21.
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.
我们提供了对在微通道中处于声驻波下的稠密悬浮液（体积分数φ>10%）的声聚焦的改进理解，这是使用提出的理论模型和实验实现的。该模型基于连续介质相互作用理论，并利用混合物的动量传输方程、连续性方程和固相传输方程。该模型展示了声辐射和剪切诱导扩散（SID）力之间的相互作用，这对于稠密悬浮液的聚焦至关重要。采用 Leighton 和 Acrivos 的剪切诱导颗粒迁移模型，并结合声辐射力，模拟颗粒的连续体行为。在文献中，对于高浓度刚性球体和低浓度非球形可变形颗粒（例如红细胞（RBC）），有各种用于扩散系数 D_{φ}^{}的封闭解。在这里，我们提出了一种用于 RBC 稠密悬浮液的 D_{φ}^{}封闭解，并通过实验数据验证了所提出的模型。虽然可用的 D_{φ}^{}封闭解无法预测非球形可变形颗粒（如 RBC）稠密悬浮液的声聚焦，但提出的模型的预测与实验数据吻合在 15%以内。模型和实验都揭示了声辐射和 SID 力之间的竞争，导致在沿流方向的某个距离 L_{eq}^{}处形成颗粒聚焦流的平衡宽度 w^{}。通过使用不同的剪切速率、声能密度和颗粒浓度，我们表明平衡宽度由 Péclet 数 Pe 和 Strouhal 数 St 控制，即 w^{}=1.4(PeSt)^{-0.5}，而获得平衡聚焦宽度所需的长度取决于 St，即 L_{eq}^{*}=3.8/(St)^{0.6}。所提出的模型和相关性将在设计用于声聚焦稠密悬浮液（如未稀释的血液）的微通道方面具有重要意义。
