(288g) Flow between a Cavity and a Flexible Wall: Lubrication Model and Finite-Element Calculations

Flows near deformable solid boundaries occur in a diverse range of settings including coating and printing processes, biological systems, and suspensions. In order to examine the effect of surface topography on the elastohydrodynamic interactions that arise in these flows, the flow between a rigid cavity and a flexible wall is studied using a lubrication model and finite-element calculations. In the lubrication model, Reynolds equation for the fluid is coupled to a model for a uniformly tensioned wall. The resulting nonlinear ordinary differential equations are then solved numerically to obtain pressure profiles and wall positions. When the wall tension is large relative to viscous forces, the wall hardly deforms and both a pressure mountain and valley are observed due to the gap change produced by the cavity topography. When the wall modulus and tension are small relative to viscous forces, the wall easily deforms and assumes a shape similar to that of the cavity. The pressure profiles are also dramatically altered and in some cases show only a valley without a mountain. Cavity shape is found to have a significant influence on both the pressure profiles and the wall deformation. In the finite-element calculations,equations for elliptic mesh generation are solved iteratively along with Stokes' equations. The equation describing the flexible wall is used to update its position during the iterations. Two different configurations are considered. In the first, flow passes through the gap between a moving flexible wall and a rigid cavity. In the second, flow driven by an externally applied pressure gradient passes through the gap between a stationary rigid wall and a cavity with a flexible bottom wall that can be deformed by an external pressure. The results for the first configuration indicate that the lubrication model yields good predictions of the pressure profile, position of the flexible wall, and flow rate. The results for the second configuration indicate that the flow pattern in the cavity is dramatically altered as the external pressure changes. Replacing the bottom of a cavity with a flexible wall and applying a time-periodic pressure to it may thus be a potentially useful way to improve mixing and heat/mass transport in the cavity.