A simple constitutive model for a polymer flow near a polymer-grafted wall

Abstract

A simple constitutive model is proposed to describe a polymer flow near a polymer-grafted wall. The model is based on a generalization of the Rolie-Poly equation [A. E. Likhtman and R. S. Graham, J. Non-Newton. Fluid Mech. 114, 1–12 (2003)] to a “bulk+wall” system combined with a microscopic picture of the relaxation of the tethered chains. Different grafting regimes are considered, varying from nonoverlapping to strongly interacting tethered chains. Despite its simplicity, the model allows one to reproduce all the generic features of the flow. Different scaling regimes are predicted, in accord with earlier studies, and the transition between them is quantified. Special attention is paid to a careful comparison to available experimental data: a reasonable agreement is demonstrated and possible shortcomings of the model are discussed.