 Flow-dependent migration beyond an equilibrium polymer depletion sketch

An equilibrium polymer-depletion profile describes how chain conformations and wall exclusion affect concentration without imposed flow. It is not, by itself, a prediction of the concentration field in a flowing polymer solution.

Flow deforms and orients polymers, and hydrodynamic interactions with a nearby wall can produce cross-stream migration. Brownian diffusion opposes the resulting concentration gradients. In a simplified one-dimensional description with constant diffusivity, $J_z=c{v}_{\mathrm{mig}}-D{\partial }_{z}c$ shows why a steady profile requires migration and diffusion information in addition to the equilibrium depletion length. A rigid-polymer calculation in simple shear predicts migration away from the wall and a flow-dependent depletion layer; this is a specified model, not a universal direction for every polymer and flow.^[ref]