Interaction Dynamics of Two Particles Sedimenting Near a Flexible Elastic Membrane*

While the motion of a single particle near soft surfaces has been well-studied, the interactions between multiple particles in such environments are less understood. In this work, we experimentally investigate the behavior of two millimeter-sized particles settling under gravity near a soft membrane suspended in silicone oil. The particles are separated by the soft sheet and do not interact directly through the fluid. However, the deformation caused by each particle's movement breaks the symmetry of the flow around the other particle, leading to either repulsion or attraction based on their orientation and relative speed. The experimental findings are confirmed using numerical solutions of lubrication theory for the flow, coupled to membrane elasticity. We then gain analytic insight into the interactions using the Lorentz reciprocal theorem implemented in Fourier space. We examine how particle orientation, fluid viscosity, the membrane's tension, and its bending stiffness affect the interaction force. Our findings show that elastic interfaces lead to long-range elastohydrodynamic interactions between particles, even when they are on opposite sides of the interface.