Time-dependent free surface Stokes flow with a moving contact line. II. Flow over wedges and trenches

We consider the problem of a viscous liquid film with a moving contact line flowing under the influence of a body force over a substrate that includes a convex wedge or a trench. The time evolution of the liquid film profile is obtained by the numerical technique developed in part I. The effect of the capillary number Ca and the contact angle phi on the interaction between the dynamic contact line and topography is studied for both rectangular wedges and trenches of various widths and depths. Our results show that for smaller Ca the liquid film is pushed further along the wedge wall, resulting in a greater "runout'' length before the film separates into a drop. When the wedge is the initial step down of a trench of finite depth and width, this runout length provides an upper bound on the depth of trenches that can be coated. For flows that reach the trench floor, details of the further development of the surface profile determine whether the liquid successfully coats the surface. We explore for various Ca and phi the dimensions of trenches that can be coated. (C) 2004 American Institute of Physics.