Theory of shear-induced migration in dilute polymer solutions near solid boundaries

Abstract

In this work, a continuum theory is developed for the behavior of flowing dilute polymer solutions near solid surfaces, using a bead-spring dumbbell model of the dissolved polymer chains. Hydrodynamic interactions between the chains and the wall lead to migration away from the wall in shear flow. At steady state, this hydrodynamic effect is balanced by molecular diffusion; an analytical expression for the resulting concentration profile is derived. It is shown that the depletion layer thickness is determined by the normal stresses that develop in flow and can be much larger than the size of the polymer molecule. The transient development of this depletion layer is also studied, as well as the spatial development downstream from an entrance. Numerical and similarity solutions in these cases show that the developing concentration profile generally displays a maximum at an intermediate distance from the wall.