Numerical modelling of flow through nodes in foams within the “dry” limit in the presence of solid particles

Abstract

We present three-dimensional models and associated numerical simulations using the Navier-Stokes and continuity equations, and we illustrate the dynamics related to flow within different foam geometries where silica particles are present in the foam. The effects of partially hydrophobic particles and hydrophilic nanoparticles on foams were studied. A microscale design was used to create models for a Plateau border and node system and for a two-nodes and Plateau border system, both within the “dry” limit, with various liquid and particle volume fractions. The influence of hydrophobic silica particles on foam drainage and permeabilities was examined through numerical simulations. The velocity profiles, particle agglomerations and particle distributions in the Plateau borders and nodes were simulated. The results obtained show that at the Plateau border scale, slow drainage occurs in the presence of deposited solid particles, and there is resultant insoluble agglomeration. The results were investigated and compared with those found in the literature, and a qualitative similarity was noted. It was observed through analysis that the presence of solid particles in foam elevates interfacial rigidity, resulting in a Plateau border-dominated regime, and thus influencing the mobility losses in the foam network. Finally, microscopic interfacial forces between semi-stagnant settled hydrophilic nanoparticles become dominant, causing agglomeration.