Network Based Modelling of Transport Phenomena in Solid and Fluid Phases of Open Cell Foams: Construction of Graphs

From 3D X-ray computed images and using iMorph software, two graphs are derived from the solid and fluid networks of open-cell foams. The graphs are constructed based on the foam structure, which satisfies Plateau's laws. We have defined two types of graphs: 1) the representative graphs of solid and fluid phase networks: The graph of the solid phase is, intuitively, constructed by associating vertices to nodes and edges to struts. For the graph of the fluid phase, vertices are associated with porous cells and edges to throats at the interface of two cells. 2) the coupling graph is related to transfer phenomena between the fluid and solid phases: It is constructed by associating effective edges, which connect a vertex of the solid graph with an adjacent vertex of the fluid graph. The graphs lead to discrete element representation (topology preserving) with geometrical information of the foam structure. Physical variables can be attributed to the discrete objects called cell complex: internal energy to finite volume, heat flux to surface/interface, driving force to edge, and temperature to node. This alternative modeling approach based on graphs is promising for heterogeneous systems with large sizes as it reduces the computational complexity of conventional finite element meshing.