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Finite element simulation of a liquid droplet deformation: the influence of slip coefficient on the moving contact points

by Ganesan, Sashikumaar., Tobiska, Lutz..

Series: 2005-21, Preprints

65M60 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
65M50 Mesh generation and refinement
76D05 ~Navier-Stokes equations
76D45 Capillarity (surface tension)

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.

Navier-Stokes equations, finite elements, free surface flow, ALE approach, contact angle, Laplace-Beltrami operator