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Numerical modelling of flow through foam’s node

Anazadehsayed, Abdolhamid, Rezaee, Nastaran, Naser, Jamal
Journal of colloid and interface science 2017 v.504 pp. 485-491
equations, foams, mathematical models, mixing
In this work, for the first time, a three-dimensional model to describe the dynamics of flow through geometric Plateau border and node components of foam is presented. The model involves a microscopic-scale structure of one interior node and four Plateau borders with an angle of 109.5 from each other. The majority of the surfaces in the model make a liquid-gas interface where the boundary condition of stress balance between the surface and bulk is applied. The three-dimensional Navier-Stoke equation, along with continuity equation, is solved using the finite volume approach. The numerical results are validated against the available experimental results for the flow velocity and resistance in the interior nodes and Plateau borders. A qualitative illustration of flow in a node in different orientations is shown. The scaled resistance against the flow for different liquid-gas interface mobility is studied and the geometrical characteristics of the node and Plateau border components of the system are compared to investigate the Plateau border and node dominated flow regimes numerically. The findings show the values of the resistance in each component, in addition to the exact point where the flow regimes switch. Furthermore, a more accurate effect of the liquid-gas interface on the foam flow, particularly in the presence of a node in the foam network is obtained. The comparison of the available numerical results with our numerical results shows that the velocity of the node-PB system is lower than the velocity of single PB system for mobile interfaces. That is owing to the fact that despite the more relaxed geometrical structure of the node, constraining effect of merging and mixing of flow and increased viscous damping in the node component result in the node-dominated regime. Moreover, we obtain an accurate updated correlation for the dependence of the scaled average velocity of the node-Plateau border system on the liquid-gas interface mobility described by Boussinesq number.