For solutions it is known that the mass flux depends on the concentration gradient. However, according to the phase-space kinetic theory, there may also be a dependence on the velocity gradient as well (which cannot be allowed in the thermodynamics of irreversible processes [5a]).
That is, we now have to deal with second-order diffusion tensor, , that includes velocity gradients as well as the concentration gradient. For a steady shear flow, , and a dilute solution of Rouse chains, the diffusion tensor is given by:
As a result of the tensorial nature of , the diffusion flux is not in the same direction as the concentration gradient.
Another result that can be obtained from the phase-space kinetic theory is the general expression for the diffusion fluxes in a multicomponent mixture of polymers. For this situation, we have found that there is a relation, similar to the Maxwell-Stefan relations: