Mechanical model of fiber morphogenesis in the liver

We give a description of fibroblast cell diffusion in a soft tissue, paying special attention to the coupling of force, matter and microforce balance laws through a suitable dissipation principle. To this end we cast our framework into a multi-level schematics, comprising both kinematics and kinetics, which is based on a characterization of the free energy. This way we lay down first a force balance law, where force and stress fields are defined as power conjugate quantities to velocity fields and their gradients, then we give a species molar balance law, with chemical potential test fields, as power conjugate quantities to the rate of change of species concentration, and finally a microforce balance law. The main feature of this framework is the constitutive expression for the chemical potential which turns out to be split in a natural way into a term derived from the homogeneous convex part of the free energy and an active external chemical potential giving rise to the spinodal decomposition. The active part of the chemical potential is given an expression depending on the cell density and resembling the one defined in [29], where it is meant to characterize an upward cell diffusion induced by cell motility.