The breakdown of asymptotic hydrodynamic models of liquid spreading at increasing capillary number

Abstract

Complex hydrodynamics near the moving contact line control spreading of a fluid across a solid surface. In the confined region near the contact line, velocity gradients in the fluid are large and viscous forces control the shape of the fluid/fluid interface. The present model for liquid spreading describes the viscous effect on the dynamic interface shape to lowest order in capillary number, Ca. Using videomicroscopy and image analysis techniques, we have examined the shape of liquid/air interfaces very near moving contact lines for Ca≥0.10 where the interfaces are in capillary depression. We find that the theory correctly describes the data up to Ca=0.10 for distances from 20 to 400 μm from the contact line. As Ca increases, the model fails to describe the data in a region near the contact line, which grows as Ca increases. In this expanding region, the model predicts too large a curvature for the interface. We explore the origins of this breakdown by examining the fundamental assumptions of the model. The geometry-dependent part of the solution to O(1) in Ca is sufficient even at Ca=0.44. The breakdown of the model arises from the low order of the geometry-free part of the perturbation solution and/or contributions to the interface shape from the unique hydrodynamics very near the moving contact line.