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 ${\Psi }_2$ for small shear rates. It is found that the mean-field (consistent preaveraging) approximation for hydrodynamic interactions (HI) produces an unphysical positive ${\Psi }_2$, while inclusion of fluctuations in HI leads to a negative value for ${\Psi }_2$, in agreement with experimental evidence.