Numerical analysis of layer and bridging adsorption of flexible polymers in porous media

We report a study of the flow of polymers solutions through porous media using traveling wave and numerical analysis. We consider flow regimes where layer adsorption of (short) undeformed chains and bridging adsorption of (long) stretched ones occurs either separately or simultaneously. The model for polymer transport taking into account these phenomena was found earlier to reduce to a system of four partial differential equations, describing respectively polymer mass conservation, bridging probability conservation, layer adsorption kinetics and bridging adsorption kinetics. In this study, we show that at short times the above quantities are concave-upward decaying functions of distance which develop to traveling wave for sufficiently long times. This corresponds to a progressive saturation of adsorption towards the inlet of the porous sample. In the case of simultaneous layer and bridging adsorption, the concentration profile exhibits an unusual superposition of traveling waves, consistent with a slower propagation of the bridging adsorption wave with respect to the layer adsorption one. This shows that flow induces a separation of short and long chains.