Exact results for sheared polar active suspensions with variable liquid crystalline order

TL;DR

This paper derives exact analytical solutions for sheared polar active liquid crystals with variable polarization, revealing non-zero stress at zero strain and providing insights into their macroscopic rheological behavior.

Contribution

It presents the first exact solutions for the polarization, density, and velocity fields in sheared polar active suspensions with variable order.

Findings

Non-zero shear stress at zero strain rate.

Analytic solutions match numerical results for finite systems.

System behavior depends on boundary conditions and size.

Abstract

We consider a confined sheared active polar liquid crystal with a uniform orientation and study the effect of variations in the magnitude of polarization. Restricting our analysis to one-dimensional geometries, we demonstrate that with asymmetric boundary conditions, this system is characterized, macroscopically, by a linear shear stress vs. shear strain relationship that does not pass through the origin: At a zero strain rate, the fluid sustains a non-zero stress. Analytic solutions for the polarization, density, and velocity fields are derived for asymptotically large or small systems and are shown by comparison with precise numerical solutions to be good approximations for finite-size systems.