Surfing its own wave: hydroelasticity of a particle near a membrane

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.

我们通过理论和实验表明，一个在黏性流体中沿着弹性膜移动的小颗粒会由于流体弹性力而被膜排斥。黏性应力场产生一种弹性扰动，导致颗粒 - 波耦合。我们在润滑极限下推导出了颗粒轨迹的解析表达式，无需构建详细的速度和压力场。法向力与平行速度呈二次方关系，并且是膜的张力和抗弯曲性的函数。在实验中，我们测量了沿弹性膜沉降的球体的法向位移，并发现与理论预测在没有拟合参数的情况下定量吻合。我们通过实验证明这种效应足以用于颗粒分离和分选。我们讨论了这些结果对生物膜的重要性，并提出了我们用于膜弹性测量的模型。