Effect of substrate flexibility on dynamic wetting: a finite element model Original Research Article

Dynamic wetting plays an important role in coating processes. In this paper, we present a new finite element formulation that can predict the effect of substrate deformation on the location of the dynamic contact line. Our model solves for the fluid–structural interactions between an elastic solid and a viscous liquid with a dynamic contact line that can move across the deformable solid surface. Surface tension forces acting at the dynamic contact line pull outwards on the substrate and cause the formation of capillary ridge. To predict the shape of the capillary ridge and motion of dynamic contact line, our model uses arbitrary Lagrangian Eulerian (ALE) mesh motion in both fluid and solid phases, because ALE decouples the motion of solid and mesh points. In dynamic wetting of rigid solids it is known that a singularity arises at the dynamic wetting line due to a double-valued velocity. The singularity is often relieved by allowing a slip in a small contact region near the dynamic contact line. Dynamic wetting on flexible substrates involves a second singularity, which arises in the solid domain due to a line force acting at the contact line. The line force singularity is relieved by distributing the force over a finite contact region. Two ALE methods of mesh motion are implemented and compared. The variation of dynamic contact line position with respect to various parameters such as downstream pressure, contact angle, capillary number and elasticity number are presented for the finite element model and compared with an analytical model.