Contact line motion in the spreading of thin liquid films

The flow of thin liquid films spreading over a solid surface is investigated. In the models, a relation between the dynamic contact angle and the slip velocity at the contact line is imposed.;A lubrication model for a thin layer of liquid advancing over a dry, heated, inclined plate is first studied. The plate is at constant temperature, and the surface Biot number is specified. The steady state solution is obtained numerically. In addition, the steady state solution is studied analytically in the neighborhood of the contact line. A linear stability analysis about the steady state is then performed. The effects of gravity, thermocapillarity and contact line motion are discussed. In addition, a numerical simulation of two dimensional nonlinear evolution is presented.;A Karman-Pohlhausen method to include inertia is then used in the isothermal case. The steady state profiles of the film are obtained for this model. Their linear stability is again investigated. This theory gives improvement over the lubrication theory when compared to some recent experiments in which the Reynolds numbers are significantly larger than one.;A lubrication model with contact angle variations for the dynamics of a sheet of fluid with a dry spot is also examined. A three dimensional linear stability analysis from an axisymmetric equilibrium solution is performed. For axisymmetric holes, the nonlinear evolution equations are solved numerically in the quasi-steady state case and for the complete system. Predictions for the radial position and velocity of the contact line, as well as the shape of the interface, are obtained for axisymmetric holes near the unstable solution. The study of the evolution of axisymmetric holes is complemented by considering an initial profile that is not a solution to the static equation. In addition, the evolution of a non circular hole is considered in the quasi-steady limit.