Gaussian approximation for finitely extensible bead-spring chains with hydrodynamic interaction

TL;DR

This paper develops a new mean-field model called FENE-PG that improves the Gaussian Approximation for finitely extensible bead-spring chains with hydrodynamic interactions, accurately predicting rheological behavior in complex flows.

Contribution

It introduces the FENE-PG spring force law, combining Gaussian Approximation with hydrodynamic interactions, enhancing accuracy over existing models.

Findings

Predictions match Brownian dynamics simulations well.

Quantitative agreement on coil-stretch hysteresis.

Diagonalization assumptions reduce computation time significantly.

Abstract

The Gaussian Approximation, proposed originally by Ottinger [J. Chem. Phys., 90 (1) : 463-473, 1989] to account for the influence of fluctuations in hydrodynamic interactions in Rouse chains, is adapted here to derive a new mean-field approximation for the FENE spring force. This "FENE-PG" force law approximately accounts for spring-force fluctuations, which are neglected in the widely used FENE-P approximation. The Gaussian Approximation for hydrodynamic interactions is combined with the FENE-P and FENE-PG spring force approximations to obtain approximate models for finitely-extensible bead-spring chains with hydrodynamic interactions. The closed set of ODE's governing the evolution of the second-moments of the configurational probability distribution in the approximate models are used to generate predictions of rheological properties in steady and unsteady shear and uniaxial extensional flows, which are found to be in good agreement with the exact results obtained with Brownian dynamics simulations. In particular, predictions of coil-stretch hysteresis are in quantitative agreement with simulations' results. Additional simplifying diagonalization-of-normal-modes assumptions are found to lead to considerable savings in computation time, without significant loss in accuracy.