Wetting on flexible substrates: a finite element formulation

Wetting is an important phenomenon in industrial applications such as coating industry as it could affect the coating uniformity and production rate. In modeling dynamic wetting on rigid solids, one of the challenges is to relieve the singularity in the viscous stress arising at the dynamic contact line due to double valued velocity. The singularity arising at the contact line is a mathematical singularity and not a physical singularity and hence, needs to be relieved. There are several models to relieve the singularity but Navier slip condition is the most commonly used model. Modeling dynamic wetting on flexible substrates requires relieving singularities both in the solid and liquid domains. In the solid domain, a singularity arises due to the surface tension force, which acts as a line force at the dynamic contact line and in the liquid domain due to the double valued velocity. If the contact line is stationary, it is referred to as static contact line. Singularity in elastic stress arises at the static contact line on flexible solids due to surface tension force acting at a point. The objective of this thesis is to the give models for relieving the singularities, finite element formulation and mesh motion scheme needed for modeling wetting on flexible substrates. In dynamic wetting, the singularity in the solid domain is relieved by distributing the line force over a constant contact region and the singularity in the liquid domain is relieved by using the Navier slip condition. In static wetting, the singularity is relieved by using two boundary conditions at the contact line, namely, crease angle condition and distributed line force condition. Modeling dynamic wetting on flexible substrates requires an Arbitrary Lagrangian Eulerian (ALE) method of mesh motion because the displacements of the contact node and the displacements of the solid at the contact node are not equal. In the liquid domain, pseudo solid mesh motion is implemented for moving the mesh. In the solid domain, however, pseudo solid mesh motion leads to shearing and distortion of elements near the contact line. We have developed a mesh motion technique based on spines that reduces elemental distortion near the contact line and is chosen for the parametric study. The element size adjacent to the contact node along solid and liquid free surfaces needs to be fixed. This enables constant stress and hence, makes the trends of dynamic contact line position with change in elasticity number independent of mesh motion scheme chosen. The test problem for studying dynamic wetting is chosen to be the upstream end of slot coater. The contact line is sensitive to important parameters such as downstream pressure, contact angle, capillary number, and elasticity number. The significant contributions of this thesis are finite element formulations for modeling static and dynamic wetting on flexible substrates. These formulations could be extended for many practical problems. In modeling of static wetting on flexible substrates, it has been shown that Neumann’s triangle law of forces is not valid for flexible solids. The performances of rigid and flexible solids for prototype flow of upstream end of slot coater are presented. The formulation developed will be of significant use for problems, which involve wetting on flexible substrates.Ph.D., Chemical Engineering -- Drexel University, 200