Ratcheting viscous fluids in a vibrating channel

Abstract eng:
A laboratory experiment shows that fluid can be pumped from one end to another in a narrow channel with vibrating sawtooth walls. The phenomenon is referred to as ratcheting fluid. We here present a theory describing the mechanism of rectifying oscillatory momentum into steady motions and symmetry-breaking that lead to the directional pumping of fluids as observed. A ‘terrain-following’ theoretical framework is formulated using a conformal transformation to accurately resolve the Stokes boundary layer of oscillatory flows and boundary-driven effects. The theory correctly predicts the unidirectional pumping, clearly elucidating the working principle of this fluid rectifier: The nonlinear inertia rectifies the periodic fluctuations of the flow into a steady momentum flux, driving steady circulations against viscous resistance. The asymmetric wall geometry renders the steady circulations to be spatially biased, leading to the pumping. Various influences on the pumping rate are analyzed. Applications to viscoelastic flows will be discussed.

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