Finite element setting for fluid flow simulations with natural enforcement of the triple junction equilibrium. (30th July 2018)

• Record Type: Journal Article
• Authors: Bruchon, J.; Liu, Y.; Moulin, N.
• Is Part Of: Computers & fluids. Volume 171(2018)
• Page Start: 103
• Page End: 121
• Publication Date: 2018-07-30
• Subjects: Stabilised finite elements -- Mesh adaptation -- Pressure enrichment -- Surface operators -- Surface tension -- Laplace's law; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2018.06.007
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: This paper presents a framework for simulating capillary-driven flows. Triple junction condition is taken into account naturally in the weak formulation. The contact-angle is not explicitly calculated. A stabilized finite element setting is proposed. Surface curvature may not be well defined everywhere. Abstract: Capillary phenomena are involved in many industrial processes, especially those dealing with composite manufacturing. However, their modelling is still challenging. Therefore, a finite element setting is proposed to better investigate this complex issue. The variational formulation of a liquid–air Stokes' system is established, while the solid substrate is described through boundary conditions. Expressing the weak form of Laplace's law over liquid–air, liquid–solid and air–solid interfaces, leads to a natural enforcement of the mechanical equilibrium over the wetting line, without imposing explicitly the contact-angle itself. The mechanical problem is discretised by using finite elements, linear both in velocity and pressure, stabilised with a variational multiscale method, including the possibility of enrichment of the pressure space. The moving interface is captured by a Level-Set methodology, combined with a mesh adaptation technique with respect to both pressure and level-set fields. Our methodology can simulate capillary-driven flows in 2D and 3D with the desired precision: droplet spreading, droplet coalescence, capillary rise. In each case, the equilibrium state expected in terms of velocity, pressure and contact angle is reached.