Geometry of thresholdless active flow in nematic microfluidics

Abstract

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 nonuniform 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 nonvanishing Gaussian curvature must necessarily experience a nonvanishing active force. This general conclusion follows from a key result of differential geometry: Geodesics must converge or diverge on surfaces with nonzero Gaussian curvature. We derive the conditions under which such curvatureinduced 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 nonplanar 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.

Dynamic states of swimming bacteria in a nematic liquid crystal cell with homeotropic alignment

“…The director distortions created by swimming bacteria are generally three-dimensional, containing splay, bend, and twist. As shown theoretically [59,60] for active nematics, mixed splay-bend causes flows for arbitrary small levels of activity (swimming speed and concentration of bacteria in our case). Green et al [60] suggested an expression for the active force driving these flows, µ  ⋅ -´(ˆ) f n n n n .…”

“…As shown theoretically [59,60] for active nematics, mixed splay-bend causes flows for arbitrary small levels of activity (swimming speed and concentration of bacteria in our case). Green et al [60] suggested an expression for the active force driving these flows, µ  ⋅ -´(ˆ) f n n n n . Recent experiments with bacteria swimming in an LCLC with the mixed splay-bend do indeed show rectified active flows with bacteria swimming in unipolar fashion.…”

Topology of Three-Dimensional Active Nematic Turbulence Confined to Droplets

“…ζ onset is the activity for the onset of vortex flow, which we determine numerically by a linear fit of the angular momentum dependence on activity. Note that such emergence of active flows in confined and defect systems is known to depend on the symmetry and profile of the equilibirum (noactivity) structure [16,27,54]. When the active nematic passes to the active turbulence regime, the average magnitude of the angular momentum gradually saturates with activity, which again signifies the break up of the regular defect dynamics.…”

Command of active matter by topological defects and patterns

“…Liquid crystals were also used by Guillamat et al (16) as an adjacent layer to an aqueous dispersion of active microtubules to align their active flows. Theoretical models of active systems with orientational order predict that a non-uniform director might cause polar flows (17,18); in particular, Green, Toner and Vitelli (GTV)…”