  "Active nematics" are orientationally ordered but apolar fluids composed of
interacting constituents individually powered by an internal source of energy.
When activity exceeds a system-size dependent threshold, spatially uniform
active apolar fluids undergo a hydrodynamic instability leading to spontaneous
macroscopic fluid flow. Here, we show that a special class of spatially
non-uniform configurations of such active apolar fluids display laminar (i.e.,
time-independent) flow even for arbitrarily small activity. We also show that
two-dimensional active nematics confined on a surface of non-vanishing Gaussian
curvature must necessarily experience a non-vanishing active force. This
general conclusion follows from a key result of differential geometry:
geodesics must converge or diverge on surfaces with non-zero Gaussian
curvature. We derive the conditions under which such curvature-induced active
forces generate "thresholdless flow" for two-dimensional curved shells. We then
extend our analysis to bulk systems and show how to induce thresholdless active
flow by controlling the curvature of confining surfaces, external fields, or
both. The resulting laminar flow fields are determined analytically in three
experimentally realizable configurations that exemplify this general
phenomenon: i) toroidal shells with planar alignment, ii) a cylinder with
non-planar boundary conditions, and iii) a "Frederiks cell" that functions like
a pump without moving parts. Our work suggests a robust design strategy for
active microfluidic chips and could be tested with the recently discovered
"living liquid crystals".
