Saturation-pressure relationships for two- and three-phase flow analogies for soft matter

Soft matter and porous media analogies are used to derive micro-scale informed pressure-saturation relationships for cell aggregates. These aggregates may consist of different cell types and an interstitial liquid. The extracellular matrix is the scaffold for these soft materials and is first taken as rigid. Extension to deformable material is also addressed. In tissue mechanics, micro-scale formulations are very often not sustainable from the computational point of view due to the complexity of the pore scale phase distributions and the large size of many problems of interest. Hence, models are formulated mainly at a larger scale, called the macro scale. We derive the relationships at that scale by exploiting theoretical results from two phase flow in porous media which incorporate information from the micro-scale. An example with an indirect validation of the obtained relationship is shown.