Active viscoelastic nematics with partial degree of order

Continuum models of active nematic gels have proved successful to describe a number of biological systems consisting of a population of rodlike motile subunits in a fluid environment. However, in order to get a thorough understanding of the collective processes underlying the behaviour of active biosystems, the theoretical underpinnings of these models still need to be critically examined. To this end, we derive a minimal model based on a nematic elastomer energy, where the key parameters have a simple physical interpretation and the irreversible nature of activity emerges clearly. The interplay between viscoelastic material response and active dynamics of the microscopic constituents is accounted for by material remodelling. Partial degree of order and defect dynamics is included as a result of the kinematic coupling between the nematic elastomer shape-tensor and the orientational ordering tensor $\bQ$. In a simple one-dimensional channel geometry, we use linear stability analysis to show that even in the isotropic phase the interaction between flow-induced local nematic order and activity results in a spontaneous flow of particles