Thermodynamics and hydrodynamics of chemical gels

We have developed a framework of thermodynamics and hydrodynamics of chemically crosslinked gels. Our framework of thermodynamics is analogous to that of binary fluid mixtures, except that the former includes a variable describing the deformation of the solid portion (network) of gels. The framework of the hydrodynamics is based on the theory of hydrodynamics of systems with broken symmetry and on the assumption of local equilibrium. In the present framework we assume that there is no plastic flow of solid portions of gels, an assumption which leads to the identification of the order-parameter field with the displacements of the material composing the solid portion. We also investigated the symmetry properties of the Onsager coefficients for this system with an emphasis on the relation to the metric tensor describing the deformation of the solid portion of gels. We investigated the limit of incompressibility of both the solid and the fluid portion of gels, as well as some other special cases of isotropic deformations, isothermal processes and the states with quasi-mechanical equilibrium. Our framework presents a generalization of Darcy's law to the deformed systems and introduces the osmotic stress tensor