Numerical Modeling of Flow through Foam Nodes within the Dry and Wet Limits

We present a numerical simulation using three-dimensional microscale models to illustrate flow dynamics through different foam geometries. These were designed to represent the flow with various liquid volume fractions throughout the Plateau border (PB) and node system within the "dry" limit and throughout the two nodes and PB system within the "wet" limit. Most surfaces in the models involve a gas-liquid interface. Here, the stress-balance boundary condition was applied to achieve coupling between the surface and bulk. The three-dimensional Navier-Stokes equation along with the continuity equation was solved using the finite volume approach, and a qualitative evaluation of flow velocities in different foam geometries was obtained. The numerical results were validated against the available experimental results for foam permeabilities in the nodes and PBs. Discrepancies were expected between the simulated and empirical values as the latter values were obtained by considering only the viscous losses in the PBs. Furthermore, the scaled resistance to flow for varying gas-liquid interface mobilities and liquid fractions was studied. The individual geometrical characteristics of the node and PB components were compared to investigate the PB- and node-dominated flow regimes numerically. Additionally, more accurate information was obtained for comparing the average flow velocities within the node-PB and the two-node-PB systems, providing a better understanding of the effect of a gas-liquid interface on foam flow. We eventually show that when the foam geometry is correctly described, the relative effect of the geometrical factors of the PB and node components of system models can be evaluated, allowing a numerical flow simulation with a unique parameter-the Boussinesq number (B_o).