Predictive models for moving contact line flows
Modeling flows with moving contact lines poses the formidable challenge that the usual assumptions of Newtonian fluid and no-slip condition give rise to a well-known singularity. This singularity prevents one from satisfying the contact angle condition to compute the shape of the fluid-fluid interface, a crucial calculation without which design parameters such as the pressure drop needed to move an immiscible 2-fluid system through a solid matrix cannot be evaluated. Some progress has been made for low Capillary number spreading flows. Combining experimental measurements of fluid-fluid interfaces very near the moving contact line with an analytical expression for the interface shape, we can determine a parameter that forms a boundary condition for the macroscopic interface shape when Ca much les than l. This parameter, which plays the role of an "apparent" or macroscopic dynamic contact angle, is shown by the theory to depend on the system geometry through the macroscopic length scale. This theoretically established dependence on geometry allows this parameter to be "transferable" from the geometry of the measurement to any other geometry involving the same material system. Unfortunately this prediction of the theory cannot be tested on Earth.