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Implementation of surface tension with wall adhesion effects in a three-dimensional finite element model for fluid flow

Abstract : This paper addresses the finite element modelling of surface tension. The external stress vectors associated with surface tension are assumed proportional to the average curvature and oriented along the normal vector to the fluid surface. The issue of estimating the average curvature of a discretized surface is then discussed. It is proposed to use the surface divergence of a field of nodal normal vectors. Special attention is devoted to the calculation of the so-called consistent normal vectors. In the case of a surface composed of linear triangular facets, it is demonstrated that these normals are given at each node by the average of the normals of the surrounding facets, weighted by their surface. In order to account for wall adhesion effects, the method which consists in modifying the normal vectors at nodes in contact is discussed and extended to the three-dimensional case. In order to validate the approach, the three-dimensional finite element resolution of the equilibrium of a drop of liquid on a plane is treated.
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Michel Bellet. Implementation of surface tension with wall adhesion effects in a three-dimensional finite element model for fluid flow. Communications in Numerical Methods in Engineering, Wiley, 2001, 17 (8), pp.Pages 563-579. ⟨10.1002/cnm.430⟩. ⟨hal-00575977⟩

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