The flow of dilute polymer solution in a narrow channel. II. Plane Poiseuille flow

Abstract

As an extension of the previous paper, we derive a similar theory for the plane Poiseuille flow of a dilute polymer solution. The strict enforcement of reflective boundary conditions allows an approximate solution to the Fokker–Planck–Kolmogorov equation to be obtained which is found to be consistent with solutions obtained by Galerkin methods and Monte Carlo simulation. The approximate theory also allows us to derive analytical expressions for the slip velocity and the effective viscosity which are again consistent with the plane Couette flow results derived in the previous paper. The theory is also extended to the nonlinear Warner spring model via Monte Carlo simulation.