Brownian dynamics simulations of planar mixed flows of polymer solutions at finite concentrations

TL;DR

This study uses Brownian dynamics simulations with periodic boundary conditions to analyze how shear and extension flows affect polymer chain size and viscosity at finite concentrations, revealing a critical mixedness parameter dividing shear and extension dominance.

Contribution

The paper introduces a multi-chain Brownian dynamics simulation method for planar mixed flows, incorporating finite concentrations and excluded volume effects, and identifies a critical mixedness parameter for flow dominance.

Findings

Existence of a critical mixedness parameter $oldsymbol{ ext{chi}_c}$ separating shear and extension dominated flows.

Flow strength and mixedness parameter significantly influence polymer size and viscosity.

Simulation results align with theoretical predictions for flow behavior in polymer solutions.

Abstract

Periodic boundary conditions for planar mixed flows are implemented in the context of a multi-chain Brownian dynamics simulation algorithm. The effect of shear rate $\dot{\gamma}$, and extension rate $\dot{\epsilon}$, on the size of polymer chains, $\left<R_e^2\right>$, and on the polymer contribution to viscosity, $\eta$, is examined for solutions of FENE dumbbells at finite concentrations, with excluded volume interactions between the beads taken into account. The influence of the mixedness parameter, $\chi$, and flow strength, $\dot{\Gamma}$, on $\left<R_e^2\right>$ and $\eta$, is also examined, where $\chi \rightarrow 0$ corresponds to pure shear flow, and $\chi \rightarrow 1$ corresponds to pure extensional flow. It is shown that there exists a critical value, $\chi_\text{c}$, such that the flow is shear dominated for $\chi < \chi_\text{c}$, and extension dominated for $\chi > \chi_\text{c}$.