We show using theory and experiments that a small particle moving along an elastic membrane through a viscous fluid is repelled from the membrane due to hydro-elastic forces. The viscous stress field produces an elastic disturbance leading to particle-wave coupling. We derive an analytic expression for the particle trajectory in the lubrication limit, bypassing the construction of the detailed velocity and pressure fields. The normal force is quadratic in the parallel speed, and is a function of the tension and bending resistance of the membrane. Experimentally, we measure the normal displacement of spheres sedimenting along an elastic membrane and find quantitative agreement with the theoretical predictions with no fitting parameters. We experimentally demonstrate the effect to be strong enough for particle separation and sorting. We discuss the significance of these results for bio-membranes and propose our model for membrane elasticity measurements.
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