A continuum hydrodynamic model has been used to characterize flowing
active nematics. The behavior of such a system subjected to a
weak steady shear is analyzed. We explore the director structures and
flow behaviors of the system in flow-aligning and flow tumbling regimes.
Combining asymptotic analysis and numerical simulations, we extend previous
studies to give a complete characterization of the steady states for both contractile and
extensile particles in flow-aligning and flow-tumbling regimes. Another
key prediction of this work is the role of the system size on the steady
states of an active nematic system: if the system size is small, the velocity
and the director angle files for both flow-tumbling contractile and extensile
systems are similar to those of passive nematics; if the system is big, the
velocity and the director angle files for flow-aligning contractile systems
and tumbling extensile systems are akin to sheared passive cholesterics while
they are oscillatory for flow-aligning extensile and tumbling contractile systems.