Thermodynamic theory of thermo-osmosis

Let us consider an adiabatically insulated multicomponent system, divided into two subsystems I and II by a porous barrier or a membrane (Fig. 3.1). 

Let us suppose that chemical reactions can occur in the two chambers. Chambers I and II having volumes and F are maintained at temperatures and (r = r d-AT), pressures and (P =P + AP), AT and AP represent the temperature 

the change of mass of component k and energy in reservoir I is given by 

Similarly, dU and the change of internal energy U in reservoir I, is given by 

The changes in the masses of k, caused by chemical reaction, are related by the relation 

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Thermodynamic theory of thermo-osmosis of gaseous non-reacting mixtures... 

On combining Eq. (3.123) with Eq. (3.122), Eq. (3.188) is obtained. It thus follows that the kinetic theory of thermo-osmosis is consistent with the thermodynamic theory of thermo-osmosis. 

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