Non-equilibrium chemical potential and polymer extraction from a porous matrix

The influence of a flow on the transfer of a polymer solution from a porous matrix to a flowing fluid is analysed. Since the flow modifies the free energy of the solution, through stretching and orientation of the macromolecules, the thermodynamic driving force for polymer transport is modified with respect to that of a quiescent fluid. The consequences of this modification for the extraction of a polymer from a porous matrix are explored in detail, and the formal results are explicitly illustrated by means of a specific solution. For the particular example analysed here, of possible interest in oil extraction or in microfluidic problems, the non-equilibrium effects may yield a reduction of the order of 10% of the extraction rate.