Membrane phenomena in nonisothermal systems .1. Theory

Theoretical equations for the thermoosmosis and thermal membrane potential across a charged membrane were derived using a set comprising the energy flux and the coupled logarithmic temperature-difference force as a dissipation function of irreversible processes. In order to obtain phenomenological equations in discontinuous systems by integrating phenomenological equations in continuous systems, it was assumed that temperature and total chemical potential are continuous at the interface between the membrane and the external solution. The new equations were compared with approximate equations derived previously from a set comprising the entropy flux and the coupled temperature-difference force as the dissipation function. Moreover, an equation for the thermal membrane potential was also derived using an alternative method by summing two parts: the equilibrium potential differences between the membrane and the external solutions on both sides of the membrane (two Donnan potentials) and the thermal-diffusion potential in the membrane.