Mechanical model of fiber morphogenesis in the liver

We give a description of fibroblast cell diffusion in a soft tis- sue, paying special attention to the coupling of force, matter and micro- force 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 decom- position. 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.