Rouse model with fluctuating internal friction

TL;DR

This paper introduces an exactly solvable bead-spring-dashpot chain model incorporating internal friction, revealing complex rheological behaviors such as shear-thickening and shear-thinning in polymer solutions.

Contribution

It provides a numerical solution for chains with more than two beads, demonstrating the effects of internal friction on rheological properties and comparing with semi-analytical approximations.

Findings

Internal friction causes non-monotonous viscosity variation.

Shear-thickening occurs after initial shear-thinning.

Higher internal friction lowers the shear rate for shear-thickening onset.

Abstract

A coarse-grained bead-spring-dashpot chain model with the dashpots representing the presence of internal friction, is solved exactly numerically, for the case of chains with more than two beads. Using a decoupling procedure to remove the explicit coupling of a bead's velocity with that of its nearest neighbors, the governing set of stochastic differential equations are solved with Brownian dynamics simulations to obtain material functions in oscillatory and steady simple shear flow. Simulation results for the real and imaginary components of the complex viscosity have been compared with the results of previously derived semi-analytical approximations, and the difference in the predictions are seen to diminish with an increase in the number of beads in the chain. The inclusion of internal friction results in a non-monotonous variation of the viscosity with shear rate, with the occurrence of continuous shear-thickening following an initial shear-thinning regime. The onset of shear-thickening in the first normal stress coefficient is pushed to lower shear rates with an increase in the internal friction parameter.