Solvent flow in osmosis and hydraulics: network thermodynamics and representation by bond graphs

A tutorial introduction to network thermodynamics and bond graphs as a modeling technique for any physiochemical system is presented with a particular emphasis on reaction diffusion systems. It combines the generality of nonequilibrium thermodynamics with the advantages of a graph theory. It is applied to the representation of osmotic and hydraulic flows across a semipermeable membrane on the basis of the solvent diffusion theory of osmosis. This theory allows for an easy derivation of the van't Hoff law of osmotic pressure from the Fick law of diffusion. Molar flows and volume flows are transformed into one another by transducers, the modulus of which is the partial molar volume of water, in such a way that power is conserved by a reciprocal transformation between the chemical potential and the pressure. Osmotic and hydraulic resistances are calculated, and their dependence on pore size is estimated.