Kinetic theory and simulations of active polar liquid crystalline polymers

Abstract

A kinetic model is derived for active polar liquid crystalline polymers, that is, ensembles of polar, large molecular weight, rigid rod, “swimmers” in a viscous solvent. The model couples polarity and particle-activation physics to the Doi–Hess theory for passive liquid crystalline polymers (LCP). Our model extends the polar hydrodynamic liquid crystal model of the Marchetti group to active large molecular weight rods at arbitrary equilibrium volume fractions. The Doi–Hess–Smoluchowski equation inherits contributions due to spatial inhomogeneity and translational diffusion of the rod number density, rod polarity and self-propulsion, and the hydrodynamic equations inherit additional extra stress contributions. By suppression of LCP physics, our model recovers kinetic and mesoscopic active suspension theories of athermal, polar and apolar, micron-scale swimmers. The authors' full orientation space, 2D physical space, Smoluchowski–Navier–Stokes solver is generalized to the new model and implemented on the full system of 125 nonlinear PDEs from which we explore the coupling of rotational and translational diffusion, nano-rod density gradients, polarity and self-propulsion, and flow feedback through polar and nematic stresses. For this paper, results are presented for the dilute regime where the stable passive isotropic phase is driven far from equilibrium by activation physics, the analog of non-Brownian active “pusher” suspensions. We present a rich family of excitable and stationary patterns, previously seen in Landau–de Gennes-type coarse-grained models of apolar and polar active nematics and boundary-driven passive nematics at semi-dilute concentrations where the passive isotropic state is unstable. We find fluctuating, periodic and stationary patterns, including 1D banded and diverse 2D patterns, tunable by the relative strengths of rotational and translational diffusivity with all other physical parameters held constant.