A finite element model for dynamic wetting on flexible solids using arbitrary Lagrangian Eulerian (ALE) mesh motion

摘要

Dynamic Wetting is an important phenomena observed in many industrial applications. Computational techniques for tracking the location of a contact line on rigid solids are well established. A viscous stress singularity can arise at a dynamic contact line due to a double-valued velocity at the contact line in the liquid domain. This viscous stress singularity is often relieved using the Navier slip condition. Tracking the location of a contact line on a flexible solid is more challenging because the substrate deformation changes as the contact line slides across the solid surface. Also, an additional singularity can arise in the elastic stress singularity due to surface tension acting as a line force at the contact line. Arbitrary Lagrangian Eulerian (ALE) mesh motion enables tracking the motion of a contact line on a flexible solid by decoupling the mesh motion and the motion of the underlying solid or liquid. This paper will present a Finite Element formulation for solving for fluid structural interactions between a viscous liquid and an elastic solid with dynamic wetting on the elastic solid surface. Boundary conditions have been developed to conserve mass and momentum along the fluid-solid interface and in the vicinity of the dynamic contact line. The elastic stress singularity is relieved by distributing the line force over a finite contact region; to ensure that the deformation near the contact line is insensitive to motion of the contact line, the size of elements adjacent to the contact line are fixed. This model has been used to predict meniscus location in the upstream gap of a slot coaler as a prototype flow for modeling dynamic wetting on flexible solids. The results show that, generally, higher substrate flexibility leads to less displacement of the meniscus from its static location.