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Capillary phenomena are involved in many industrial processes, especiallythose dealing with composite manufacturing. However, their modelling is stillchallenging. Therefore, a finite element setting is proposed to betterinvestigate this complex issue. The variational formulation of a liquid-airStokes system is established, while the solid substrate is described throughboundary conditions. Expressing the weak form of Laplace's law over liquid-air,liquid-solid and air-solid interfaces, leads to a natural enforcement of themechanical equilibrium over the wetting line, without imposing explicitly thecontact angle itself. The mechanical problem is discretized by using finiteelements, linear both in velocity and pressure, stabilized with a variationalmultiscale method, including the possibility of enrichment of the pressurespace. The moving interface is captured by a Level-Set methodology, combinedwith a mesh adaptation technique with respect to both pressure and level-setfields. Our methodology can simulate capillary-driven flows in 2D and 3D withthe desired precision: droplet spreading, droplet coalescence, capillary rise.In each case, the equilibrium state expected in terms of velocity, pressure andcontact angle is reached.

Finite element setting for fluid flow simulations with natural enforcement of capillary effects