COUPLED 2025

Finite Element Simulations of Capillary Flow in Fibrous Microstructures

  • Bruchon, Julien (Mines Saint-Étienne)
  • Moulin, Nicolas (Mines Saint-Étienne)
  • Drapier, Sylvain (Mines Saint-Étienne)

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In the context of structural composite manufacturing processes, this work provides a finite element (FE) framework for the simulation of capillary flow in 2D fibrous microstructures. The computational domain, an elementary domain in which fibers are represented by circular holes, consists of two subdomains, a liquid resin and the air, separated by a moving interface, in a level-set framework. Based on triangular mesh elements, the Stokes equations are solved using a continuous and piecewise linear approximation of the velocity and pressure fields. The resulting FE formulation is then stabilized using a Variational Multi-Scale technique, the ASGS method. Surface tensions and surface energies are accounted for by Laplace's law at the liquid/air (zero isovalue of the level set function), liquid/fibers, and air/fibers (portions of the mesh boundary) interfaces without calculating curvature. The mechanical equilibrium at the triple points results naturally from this approach. In addition, the pressure space is enriched on the elements crossed by the resin/air interface to accurately capture the pressure discontinuity due to surface tension. The enrichment does not change the number of degrees of freedom. Finally, flows in two types of microstructures, hexagonal and random microstructures, are studied in terms of permeability and capillary pressure. References Y. Liu, N. Moulin, J. Bruchon, P.-J. Liotier et S. Drapier: Towards voids formation and permeability predictions in LCM processes: A computational bifluid-solid mechanics framework dealing with capillarity and wetting issues. Compte Rendus de Mécanique, 344(4-5):236–250, 2016. J. Bruchon, Y. Liu et N. Moulin: Finite element setting for fluid flow simulations with natural enforcement of the triple junction equilibrium. Computers & Fluids, 171:103–121, 2018. L. Chevalier, J. Bruchon, N. Moulin, P.-J. Liotier et S. Drapier: Accounting for local capillary effects in two-phase flows with relaxed surface tension formulation in enriched finite elements. Comptes Rendus Mécanique, 346(8):617–633, 2018.