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# Three-Dimensional Finite Element Modeling of Particle Motion under the Influence of Acoustic Radiation Force in Microchannel

**S.M. Zareei, M. Jamshidian, Sh. Sepehrirahnama and S. Ziaei-Rad**

**Modares Mechanical Engineering, Volume 19, Issue 2, February 2019, Pages 483-490**

**ABSTRACT**

Acoustofluidics, the study of acoustics in microfluidic systems, is the basis for analyzing many laboratory applications including the separation of particles, particle sorting, cleaning, and mixing multiphase systems. In this research, a three-dimensional finite element model for particle motion under acoustic radiation force in acoustic microchannels is developed and the interaction of the incident waves with a suspended particle in microchannel is investigated. Using finite element method, the first-order fields due to an applied standing wave are initially calculated and, then, the acoustic radiation force is directly calculated from the second-order perturbation equations. The simulation results for radiation force are first verified against the analytical solution in the Rayleigh limit and, then, examined beyond this limit, for which there is no explicit analytical solution. In addition, the quasi-static motion of a particle under the influence of an applied acoustic standing wave in microchannel is simulated. For simulating particle motion, the acoustic stress on particle surface is calculated and transferred as an input to the laminar flow equations. Then, the drag force is estimated based on the shear stress due to the flow around the particle. The simulation results demonstrate that the particle velocity depends on its position with respect to the wave node at the center of the microchannel. As the particle approaches to the center of microchannel, its velocity decreases until it stops at the center of microchannel.

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