Cross-stream-line migration in confined flowing polymer solutions: Theory and simulation

Abstract

Theory and Brownian dynamics (BD) simulations are used to study cross-stream migration in confined dilute flowing polymer solutions, using bead-spring chain and dumbbell models for the polymer molecules. Different degrees of confinement are explored, from a chain above a single wall to slits whose widths 2h are much bigger than the polymer contour length L and radius of gyration Rg (2h⪢L⪢Rg), much bigger than the radius of gyration but comparable with the contour length (2h∼L>Rg), and comparable with the polymer radius of gyration (2h∼Rg). The results show that except in the latter case, polymer chains migrate in shear flow away from the confining surfaces due to the hydrodynamic interactions between chains and walls. In contrast, when 2h∼Rg, the chain migration in flow is toward the walls. This is a steric effect, caused by extension of the chain in the flow direction and corresponding shrinkage of the chains in the confined direction; here the hydrodynamic effects of each wall cancel one another out. Considering the polymer chain as a Stokeslet-doublet (point-force-dipole) as in a previously developed kinetic theory captures the correct far-field (relative to the walls) behavior. Once a finite-size dipole is used, the theory improves its near-wall predictions. In the regime 2h∼L>Rg, the results are significantly affected by the level of discretization of the polymer chain, i.e., number of springs, because the spatial distribution of the forces exerted by the chain on the fluid acts on the scale of the channel geometry.