Geometric pumping induced by shear flow in dilute liquid crystalline polymer solutions

TL;DR

This paper explores how shear flow can induce geometric pumping in dilute liquid crystalline polymer solutions, revealing non-zero time-integrated currents even with zero average shear, through theoretical analysis and simulations.

Contribution

It derives a Berry-like curvature-based expression for nonlinear rheology under time-dependent shear flow, connecting geometric effects to polymer orientation and stress.

Findings

Time-integrated angular velocity and stress are non-zero with zero average shear.

Theoretical predictions are confirmed by numerical simulations.

Nonadiabatic effects depend on shear modulation speed.

Abstract

We investigate nonlinear rheology of dilute liquid crystalline polymer solutions under time dependent two-directional shear flow. We analyze the Smoluchowski equation, which describes the dynamics of the orientation of a liquid crystalline polymer, by employing technique of the full counting statistics. In the adiabatic limit, we derive the expression for time integrated currents generated by a Berry-like curvature. Using this expression, it is shown that the expectation values of the time-integrated angular velocity of a liquid crystalline polymer and the time-integrated stress tensor are generally not zero even if the time average of the shear rate is zero. The validity of the theoretical calculations is confirmed by direct numerical simulations of the Smoluchowski equation. Nonadiabatic effects are also investigated by simulations and it is found that the time-integrated stress tensor depends on the speed of the modulation of the shear rate if we adopt the isotropic distribution as an initial state.