  Active nematic fluids confined in narrow channels generate spontaneous flows
when the activity is sufficiently intense. Recently, it was shown that if the
molecular anchoring at the channel walls is conflicting flows are initiated
even in the zero activity limit. An analytical laminar velocity profile for
this specific configuration was derived within a simplified nematohydrodynamic
model in which the nematic order parameter is a fixed-magnitude unit vector n.
In this study we explore systematically active flows in this confined geometry
with a more general theoretical model that uses a second-rank tensor order
parameter Q to express both the magnitude and orientation of the nematic phase.
The Q-model allows for the presence of defects and biaxial, in addition to
uniaxial, molecular arrangements. Our aim is to provide a unified picture,
beyond the limiting regime explored previously, to serve as a guide for
potential microfluidic applications. We reveal how the nematic-flow coupling is
not only dependent on geometrical constraints but also highly sensitive to
material and flow parameters. We specifically stress the key role played by the
activity and the flow aligning parameter and we show that solutions depend on
two dimensionless parameters. We find that for large values of the activity
parameter the flow is suppressed for contractile particles while is either
sustained or suppressed for extensile particles depending on whether they tend
to align or tumble when subject to shear. We explain these distinct behaviors
by an argument based on the results of the stability analysis applied to
simpler configurations. We finally provide a numerical example of a biaxial
three-dimensional thresholdless active flow for which we show that biaxiality
is specially relevant for a weakly first-order isotropic-nematic phase
transition.
