05-21
Finite element simulation of a liquid droplet deformation: the influence of slip coefficient on the moving contact points
by Ganesan, Sashikumaar.; Tobiska, Lutz.
Preprint series: 05-21, Preprints
- MSC:
- 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
- 65M50 Mesh generation and refinement
- 76D05 Navier-Stokes equations, See also {35Q30}
- 76D45 Capillarity, See also {76B45}
Abstract: A newly developed numerical scheme is used to investigate the influence of the slip coefficient on the fluid flow and contact points for a liquid droplet deformation on a solid surface in a two-dimensional setting. The model accounts for the viscosity, gravity, surface tension and contact angle. A variational form for the curvature and ALE approach are used to represent the surface tension continuously over the free surface. An explicit term is derived in the finite element formulation to include the contact angle. The results for two-dimensional droplet are presented to illustrate the effects of slip coefficient on different droplet sizes and impact velocities. Simulations are performed until the droplet comes into the equilibrium state (sessile state). Results shows that the equilibrium state is uniquely determined by the given equilibrium contact angle. It is found that the slip coefficient is highly influencing the flow dynamics and the sequence of spreading and recoiling but different slip coefficients lead to the same equilibrium shape at the stationary limit. A rebound effect is also observed for the free-slip condition. The total mass loss in the entire simulation is less-than one percent illustrating the accuracy of the scheme.
Keywords: Navier-Stokes equations, finite elements, free surface flow, ALE approach, contact angle, Laplace-Beltrami operator
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