Lubrication theory for free-surface flows with finite slopes and fluxes

It is known that free-surface flows with small slopes can be described by classical lubrication theory. By replacing the assumption of quasi-parallel flows with local wedge flows, the classical lubrication theory has been generalized to the situation with finite surface slopes and vanishing fluxes, e.g., steady capillary flows with moving contact lines. In this work, this theory is further extended by imposing the contribution of finite fluxes, which can be modeled by a source/sink flow in a wedge. The resulting lubrication equation is used to investigate the surface morphologies observed in dip coating of an inclined plate, including the Landau-Levich-Derjaguin film, dimple and capillary shock. Dependence of these structures on the inclination angle and relative speed with respect to the plate is discussed in detail. Numerical solutions of the lubrication equation agree well with available asymptotic theory.

Automated summary

It has been discovered that classical lubrication theory can be used to describe free-surface flows with small slopes. By modifying the theory to include finite surface slopes and vanishing fluxes, this study examines surface morphologies observed in dip coating of an inclined plate. The results show that the structures, such as films, dimples, and capillary shocks, depend on the inclination angle and relative speed of the plate. Numerical solutions agree well with existing asymptotic theory.