Active nematic gels as active relaxing solids

I propose a continuum theory for active nematic gels, defined as fluids or suspensions of orientable rodlike objects endowed with active dynamics, that is based on symmetry arguments and compatibility with thermodynamics. The starting point is our recent theory that models (passive) nematic liquid crystals as relaxing nematic elastomers. The interplay between viscoelastic response and active dynamics of the microscopic constituents is naturally taken into account. By contrast with standard theories, activity is not introduced as an additional term of the stress tensor, but it is added as an external remodeling force that competes with the passive relaxation dynamics and drags the system out of equilibrium. In a simple one-dimensional channel geometry, we show that the interaction between nonuniform nematic order and activity results in either a spontaneous flow of particles or a self-organization into subchannels flowing in opposite directions.

Figure 1

Schematic representation of the channel geometry studied in the text.

Figure 2

Spontaneous flow. Vector plot of the solutions of Eqs. (27), with $a_0=2.5$, $\zeta =0.5$, and $L=1.1L_c$, where $L_c$ is given as in Eq. (29) $(n=1)$. Blue arrows represent the velocity field $v_x\left(z\right)$, while orange lines depict the director field.

Figure 3

Self-channeling. Vector plot of the solutions of Eqs. (27), with $a_0=2.5$, $\zeta =0.5$, and $L=1.4L_c$, where $L_c$ is given as in Eq. (29) $(n=1)$. Blue arrows represent the velocity field $v_x\left(z\right)$, while orange lines depict the director field.