Within the field of lab-on-a-chip systems large efforts are devoted to the development of onchip tools for particle handling and mixing in viscosity-dominated liquid flows on the sub-mm scale. One technology involves ultrasound with frequencies in the MHz range, which leads to wavelengths of the order of 0.1–1 mm suitable for mm-sized microchambers. Due to the nonlinearity of the governing acoustofluidic equations, second-order effects will induce steady forces on fluids and suspended particles through the effects known as acoustic streaming and acoustic radiation force. We extend the basic perturbation approach for treating these effects in systems at resonance in various geometries. The first-order eigenmodes are used as source terms for the time-averaged viscous second-order equations. The theory is applied to explain experimental results on aqueous microbead solutions in silicon-glass microchips.

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