Towards the computation of viscous flow resistance of a liquid bridge

Flow within thick liquid films present owing to capillary effects in the pore space is of key importance in many multiphase flow applications in porous media, for example, drying or oil recovery processes. The viscous resistance to the flow is a key parameter for modelling fluid transport in such situations. It is well known for liquid films wetting the corners of tubes of polygonal cross-section. In this latter case, the liquid films shape is simple and can be readily obtained. The situation is much more involved when considering a realistic pore space, as in a packing of spherical particles, for example. In this case, X-ray tomography observations have shown that most of the liquid is confined around contact points between particles at intermediate liquid saturation. Nonetheless, a connectivity of all the liquid bridges throughout the particle packing can exist, allowing liquid transport across the porous medium. The ultimate goal of the present research is to provide the viscous flow resistance for such capillary liquid cluster of complex shape. As a first step in this direction, we present in this paper direct numerical simulation of the Stokes flow in liquid bridges obtained between two cylindrical pillars confined between two hori- zontal plates. The liquid bridge shape is obtained under conditions of hydrostatic equilibrium thanks to the Surface Evolver software. Then simulations of the viscous flow within the bridge are performed using Comsol Multiphysics® Creeping flow solver