Accurate statistics of a flexible polymer chain in shear flow

TL;DR

This paper provides exact analytical results for the behavior of a flexible polymer chain in shear flow, including tumbling time distribution and end-to-end vector statistics, validated by simulations.

Contribution

It derives exact and accurate analytical expressions for polymer tumbling times and end-to-end vector distributions in shear flow, especially at high shear rates.

Findings

Tumbling time distribution decays exponentially with a calculated constant α.

The constant α is approximately 0.324 at high shear rates, matching simulations.

Exact distribution functions for polymer length and orientation are derived.

Abstract

We present exact and analytically accurate results for the problem of a flexible polymer chain in shear flow. Under such a flow the polymer tumbles, and the probability distribution of the tumbling times $\tau$ of the polymer decays exponentially as $\sim \exp(-\alpha \tau/\tau_0)$ (where $\tau_0$ is the longest relaxation time). We show that for a Rouse chain, this nontrivial constant $\alpha$ can be calculated in the limit of large Weissenberg number (high shear rate) and is in excellent agreement with our simulation result of $\alpha \simeq 0.324$. We also derive exactly the distribution functions for the length and the orientational angles of the end-to-end vector of the polymer.