Hydrodynamic Theory Of Films And Moving Contact Lines On Solid Surfaces

The motion of liquid films and contact lines on solid surfaces is widely encountered in daily life and industrial applications.Studies of these problems are challenging due to the multi-scale feature and stress singularity of moving contact lines.The evolution and flow regime of the entrained films are also worth exploring.In this thesis,we investigate the behavior of contact lines and films by theoretical analysis and numerical computations.The main contents are as follows:(1)Based on lubrication theory,we study the relationship between the speed and the interface shape in the vicinity of contact lines.Under different meniscus convexities and directions of contact line movement,the liquid film morphology connecting the macro-scale and micro-scale transition area is given,and the ana-lytical relationship between the apparent contact angle and the contact line speed is presented.Our theory is verified with the numerical solution of the lubrication equation,and in particular reduces to the theory of Eggers(2005b)for receding contact lines and concave menisci.The present theory is then applied to processes of drop spreading and retracting.(2)We study the critical speed of wetting transition of dip coating problem based on the generalized lubrication theory.We prove mathematically that the generalized lubrication equation can be transformed into the classical lubrication equation near the moving contact line.According to this transformation,the general vis-cosity ratio and contact angle in the physical space(especially for the water entry problem)can be reduced to a problem with a single phase and small contact angles in the transformed space.When the solution in the transformed space returns to the physical space,we obtain an analytical formula for the critical speed of wetting transition for general values of the viscosity ratio and the contact angle.(3)The thick film produced after wetting transition in dip coating is studied based on lubrication theory.The thick film is a structure formed under the balance of gravity and viscous force,and its upper end is connected to a receding contact line.We use the asymptotic matching method to present an analytical formula for the dewetting speed of the contact line.For the case where the plate is inclined and the liquid viscosity is small,we use perturbation method to analyse the influence of the plate inclination and the inertial effect on the dewetting speed.(4)We explore the evolution of the liquid film on a spherical surface based on lu-brication theory.Through finite element method and theoretical analysis,the evolution of the liquid film on a spherical surface under the balance of gravity,surface tension and viscous force is studied.Results show that at the late stage of evolution the liquid film on the spherical surface can be divided into four regions from top to bottom:a thin film,a ridge ring,a dimple ring and a pendent drop.Each zone is characterized by a unique mechanism.The pendent drop on the bottom is quasi-static,while films in the other zones follow different scaling laws.(5)Based on the lubrication theory,the process of spreading and retracting of the droplet on spherical surfaces is studied.Through finite element method and theoretical analysis,the contact line motion on the sphere is studied.We obtain a formula linking the contact line speed and the macroscopic interface morphology through asymptotic matching.This formula is valid for the whole process of droplet spreading and the late stage of droplet retracting,and reduces to the result for flat walls when the sphere approaches a plane.We also discover that the retracting process is slower than the spreading process,and the response of the macroscopic interface is slow during the retracting process.