Computational modeling of impinging viscoelastic droplets

A numerical study on the impingement and spreading of an isothermal viscoelastic droplet on a solid surface is presented in this work. The time-dependent incompressible Navier-Stokes equations are used to describe the fluid flow in the liquid droplet, whereas the viscoelasticity in the moving droplet is described by the Giesekus constitutive equation. A finite element scheme with the arbitrary Lagrangian-Eulerian (ALE) approach is proposed to solve the coupled time-dependent incompressible Navier-Stokes equation and the Giesekus constitutive equation in a time-dependent domain. In addition, a three-field formulation based on the Local Projection Stabilization (LPS) is used in the numerical scheme. The stabilized scheme allows us to use equal order interpolation spaces for the velocity and the viscoelastic stress, whereas inf-sup stable finite elements are used for the velocity and the pressure. The coupled system is solved by a monolithic approach in a 3D-axisymmetric configuration. In addition to the mesh convergence study, parametric studies of the Weissenberg number, Newtonian solvent ratio, polymeric viscosity, Reynolds number and the equilibrium contact angle are performed to demonstrate the effects of viscoelasticity on the flow dynamics of the droplet on wetting surfaces. The numerical study shows that the wetting diameter of the droplet increases with an increase in the viscoelasticity of the fluid. Further, the viscoelastic effects during the spreading process increases with an increase in the Reynolds number. Moreover, the viscoelastic effects on the flow dynamics are not influenced by the equilibrium contact angle.