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Ultrasound makes fluids vibrate very quickly. Even though these vibrations are fast, their effects add up to create slow, steady motions that move tiny particles.
Two key pieces are at work: acoustophoresis, where sound pushes particles directly, and acoustic streaming, gentle circulating currents created by friction in the fluid. In this project, we develop a single theory that predicts how particles move across the full range of conditions seen in experiments, bringing together the frictionless (“inviscid”) acoustofluidic view and the friction-driven (“viscous streaming”) view. This unified picture reveals when drift or streaming dominates and how they interact, letting us design flows that carry, trap, or assemble particles. The results can guide lab-on-a-chip technologies to sort particles by size or material and to control transport in more complex settings where rapid vibrations ride on top of slower background currents.
When a fluid vibrates back and forth, tiny particles don’t just shake—they experience slow, steady pushes that can pull, repel, or re-orient them over many cycles. This paper builds a single, predictive picture for how two identical particles influence each other in such oscillatory flows.
The key idea is to separate fast vibrations from the slow, time-averaged effects and then combine two tools: compact “multipole” descriptions of the oscillatory flow and a symmetry principle (the Lorentz reciprocal theorem) that turns a hard problem into an efficient calculation. The result is a semi-analytic framework that recovers known simulations and yields simple formulas for how the net forces scale with particle spacing and driving frequency, including when the boundary layers around the particles don’t overlap. These insights clarify when particles attract, repel, or rotate relative to one another—guiding design of ultrasound-based sorting and assembly
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