Rheological signatures in limit cycle behaviour of dilute, active, polar liquid crystalline polymers in steady shear

Mechanogeometry of nanowrinkling in cholesteric liquid crystal surfaces

Biological plywoods are multifunctional fibrous composites materials, ubiquitous in nature. The chiral fibrous organization is found in chitin (insects), cellulosics (plants), and collagen I (cornea and bone of mammals) and is a solid analog of that of cholesteric liquid crystals. The surface and interfaces of plywoods are distinguished by hierarchical topographies and nanowrinkling. In this paper, we present a theory to model the emergence of these surfaces and interfaces using liquid crystal-based shape equations that directly connect material properties with geometric wrinkling. The model applies to liquid crystal precursors of the plywood solid analoges. We focus on wrinkling geometry, wrinkling mechanics, and the mechanogeometry relationships that underlie multifunctionality ubiquitous in biological surfaces. Scaling wrinkling laws that connect mechanical pressures and stresses to folding and bending are formulated and quantified. A synthesis of the connections between mechanics and geometry is achieved using the topology of stress curves and curvature of the wrinkles. Taken together the results show that anchoring is a versatile surface morphing mechanism with a rich surface bending stress field, two ingredients behind many potential multifunctionalities.

Nonideal rheology of semidilute bacterial suspensions

The rheology of semidilute bacterial suspensions is studied with the tools of kinetic theory, considering binary interactions, going beyond the ideal gas approximation. Two models for the interactions are considered, which encompass both the steric and short-range interactions. In these, swimmers can either align polarly regardless of the state previous to the collision, or they can align axially, ending up antiparallel if the relative angle between directors is large. In both cases, it is found that an ordered phase develops when increasing the density, where the shear stress oscillates with large amplitudes, when a constant shear rate is imposed. This oscillation disappears for large shear rates in a continuous or discontinuous transition, depending on if the aligning is polar or axial, respectively. For pusher swimmers these nonlinear effects can produce an increase on the shear stress, contrary to the prediction of a viscosity reduction made for the dilute regime with the ideal gas approximation.

Microfluidic rheology of active particle suspensions: Kinetic theory

We analyze the effective rheology of a dilute suspension of self-propelled slender particles confined between two infinite parallel plates and subject to a pressure-driven flow. We use a continuum kinetic model to describe the configuration of the particles in the system, in which the disturbance flows induced by the swimmers are taken into account, and use it to calculate estimates of the suspension viscosity for a range of channel widths and flow strengths typical of microfluidic experiments. Our results are in agreement with previous bulk models, and in particular, demonstrate that the effect of activity is strongest at low flow rates, where pushers tend to decrease the suspension viscosity whereas pullers enhance it. In stronger flows, dissipative stresses overcome the effects of activity leading to increased viscosities followed by shear-thinning. The effects of confinement and number density are also analyzed, and our results confirm the apparent transition to superfluidity reported in recent experiments on pusher suspensions at intermediate densities. We also derive an approximate analytical expression for the effective viscosity in the limit of weak flows and wide channels, and demonstrate good agreement between theory and numerical calculations.

Role of the active viscosity and self-propelling speed in channel flows of active polar liquid crystals

We study channel flows of active polar liquid crystals (APLCs) focusing on the role played by the active viscosity (β) and the self-propelling speed (ω) on the formation and long time evolution of spontaneous flows using a continuum model. First, we study the onset of spontaneous flows by carrying out a linear stability analysis on two special steady states subject to various physical boundary conditions. We identify a single parameter b1, proportional to a linear combination of the active viscosity and the self-propelling speed, and inversely proportional to a Frank elastic constant, the solvent viscosity, and the liquid crystal relaxation time. We show that the active viscosity and the self-propelling speed influence the onset of spontaneous flows through b1 in that for any fixed value of the bulk activity parameter ζ, large enough |b1| can suppress the spontaneous flow. We then follow spontaneous flows in long time to further investigate the role of β and ω on spatial-temporal structures in the nonlinear regime numerically. The numerical study demonstrates a strong correlation between the most unstable eigenfunction obtained from the linear analysis and the terminal steady state or the persistent, traveling wave structure, revealing the genesis of flow and orientational structures in the active matter system. In the nonlinear regime, a nonzero b1 facilitates the formation of traveling waves in the case of boundary anchoring (the Dirichlet boundary condition) so long as the linear stability analysis predicts an onset of spontaneous flows; in the case of the free boundary condition (the Neumann boundary condition), a stable, spatially homogeneous tilted state always emerges in the presence of two active effects. Finally, we note that various fully out-of-plane spatio-temporal structures can emerge in long time dynamics depending on the boundary condition as well as the initial state of the polarity vector field.

Perspectives in active liquid crystals

Active soft matter is a young, growing field, with potential applications to a wide variety of systems. This Theme Issue explores this emerging new field by highlighting active liquid crystals. The collected contributions bridge theory to experiment, mathematical theories of passive and active nematics, spontaneous flows to defect dynamics, microscopic to continuum levels of description, spontaneous activity to biological activation. While the perspectives offered here only span a small part of this rapidly evolving field, we trust that they might provide the interested reader with a taste for this new class of non-equilibrium systems and their rich behaviour.