Langevin approach to polymers in flow

A Gaussian polymer chain in simple shear flow is studied using Langevin equations. Incorporating hydrodynamic interactions to first order in {ε}==4-d (d is the spatial dimensionality) with the aid of field-theoretic methods, we solve these nonlinearly coupled kinetic equations for polymer-solvent dynamics and analytically evaluate the second normal stress coefficient Ψ₂ for small shear rates. It is found that the mean-field (consistent preaveraging) approximation for hydrodynamic interactions (HI) produces an unphysical positive Ψ₂, while inclusion of fluctuations in HI leads to a negative value for Ψ₂, in agreement with experimental evidence.