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.
