Driving forces coupled diffusion processes

Thermo-osmosis (or ihcrmo diffusion) is a process where a porous or nonporous membrane separates two phases different in temperature. Because of the temperature difference, a volume flux exists from the warm side to the cold side until thermodynamic equilibrium is attained. This has been described as an example of coupled flow in chapter IV. There is a considerable difference between thermo-osmosis and membrane distillation, because the membrane determines the separation performance in the former process, whereas in the latter case the membrane is just a barrier between two non-wettable liquids and the selectivity is determined by the vapour-liquid equilibrium. However, the temperature difference is the driving force in both processes. 

For diffusion in isothermal multicomponent systems the generalized driving force was written as a linear function of the relative velocities (m/ — My). In the general case, we must allow for coupling between the processes of heat and mass transfer and write constitutive relations for and q in terms of the (m — My) and V(l/r). With this allowance, the complete expression for the conductive heat flux is... 

Numerous fluxes obey the empirical relationship in Eq. 1, such as the flux of electric charges in a conductor (Ohm s law), molecular diffusion (Fick s law), conduction of heat (Fourier s law), or flow of water in an aquifer (Darcy s law). For two or more simultaneous transport fluxes, the driving forces of one may affect the other, resulting in mutually dependent fluxes in a coupled process ... 

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