Lubrication 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. Reynolds equation for the fluid is coupled to a model for the wall which is backed by a series of springs and/or held by a uniform tension force. The resulting nonlinear ordinary differential equations are then solved numerically to obtain pressure profiles and wall positions. When the wall modulus or 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. The results suggest that surface topography may significantly modify the elastohydrodynamic interactions that arise in lubrication flows near deformable solid boundaries.
Bibliographical noteFunding Information:
This work was supported through the Industrial Partnership for Research in Interfacial and Materials Engineering of the University of Minnesota. S.K. also thanks the Shell Oil Company Foundation for support through its Faculty Career Initiation Funds program, and 3M for a Nontenured Faculty Award. We are grateful for resources from the University of Minnesota Supercomputing Institute.