How Flow Changes Polymer Depletion in a Slit

TL;DR

This paper presents a theoretical model combining two-fluid and self-consistent field theories to predict how fluid flow influences polymer depletion in a slit, considering solvent conditions and flow rates.

Contribution

It introduces a novel combined theoretical approach to analyze polymer depletion dynamics under flow in confined geometries.

Findings

Analytic expression for steady-state polymer concentration profiles in weak flow and narrow slit.

Time evolution of concentration profiles computed for various flow rates and solvent conditions.

Reveals the interplay between depletion, solvent quality, slit width, and flow strength.

Abstract

A theoretical model is developed for predicting dynamic polymer depletion effects under the influence of fluid flow. The results are established by combining the two-fluid model and the self-consistent field theory. We consider a uniform fluid flow across a slit containing a solution with polymer chains. The two parallel and infinitely long walls are permeable to solvent only and the polymers do not adsorb to these walls. For a weak flow and a narrow slit in Theta-solvent conditions, an analytic expression is derived to describe the steady state polymer concentration profiles. In both Theta- and good-solvents, we compute the time evolution of the concentration profiles for various flow rates characterized by the Peclet number. The model reveals the interplay of depletion, solvent condition, slit width, and relative strength of the fluid flow.