Chiral active matter: microscopic ‘torque dipoles’ have more than one hydrodynamic description

Abstract

Many biological systems, such as bacterial suspensions and actomyosin networks, form polar liquid crystals. These systems are 'active' or far-from-equilibrium, due to local forcing of the solvent by the constituent particles. In many cases the source of activity is chiral; since forcing is internally generated, some sort of 'torque dipole' is then present locally. But it is not obvious how 'torque dipoles' should be encoded in the hydrodynamic equations that describe the system at the continuum level: different authors have arrived at contradictory conclusions on this issue. In this work, we resolve the paradox by presenting a careful derivation, from linear irreversible thermodynamics, of the general equations of motion of a single-component chiral active fluid with spin degrees of freedom. We find that there is no unique hydrodynamic description for such a fluid in the presence of torque dipoles of a given strength. Instead, at least three different hydrodynamic descriptions emerge, depending on whether we decompose each torque dipole as two point torques, two force pairs, or one point torque and one force pair-where point torques create internal angular momenta of the chiral bodies (spin), whereas force pairs impart centre of mass motion that contributes to fluid velocity. By considering a general expansion of the Onsager coefficients, we also derive a new shear-elongation parameter and crosscoupling viscosity, which can lead to unpredicted phenomena even in passive polar liquid crystals. Finally, elimination of the angular variables gives an effective polar hydrodynamics with renormalized active stresses, viscosities and kinetic coefficients. Remarkably, this can include a direct contribution of chiral activity to the equation of motion for the polar order parameter, which survives even in 'dry' active systems where the fluid velocity is set to zero.

Layered Chiral Active Matter: Beyond Odd Elasticity

“…This microscale drive manifests itself macroscopically as nonequilibrium currents and forces [10][11][12][13][14][15][16][17][18][19]. Continuum hydrodynamic theories of fluid [20], liquid-crystalline and crystalline phases [7,8,14,16,[21][22][23] of active matter have been constructed including extensions with chiral asymmetry [9,[24][25][26][27][28][29][30][31][32]. In this paper, we construct theories of layered active chiral systems.…”

“…where d = 2 corresponds to a thin film of 3D chiral material with a distinguished normal taken to be along N ≡ +ŷ, thus inheriting uniquely the two-dimensional antisymmetric tensor ε with components ε ij = ikj N k . Though here written as an antisymmetric stress (σ c ) ij can be given in an equivalent symmetric form and is allowed in momentum-conserving systems [31,[41][42][43]. A Swift-Hohenberg free-energy functional F [41,44] allows model H * to describe the dynamics of spatially modulated states ψ = ψ 0 +ψ 1 where ψ 1 , with zero spatial average, represents a modulation with wavelength 2π/q s about a uniform background ψ 0 .…”

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

“…To account for the chemical reactions, we introduce the chemical coordinate n , which is (half) the difference between the local number density of product molecules and that of the fuel molecules. Because the active system is a part of a large nonequilibrium system that relaxes (slowly) towards equilibrium, the explicit dynamics of n can be deduced from LIT [ 21 , 52 , 56 , 57 , 58 ], in which the thermodynamic fluxes are written as a linear combination of the thermodynamic forces. Identifying and as the current and the thermodynamic force associated with , respectively, LIT states that (in the absence of noise) where is the Onsager matrix.…”

“…Although the scheme to embed SPDEs within thermodynamically consistent description is not unique a priori, our framework provides a minimal approach to do so without LIT. Interestingly, LIT is also the starting point for a large class of active field theories, known as active gels, which have been extremely successful in capturing the dynamics of complex biological systems, such as acto-myosin networks and living tissues [ 55 , 56 , 58 , 66 ].…”

“…[ 18 ], and extending it to fields (see also [ 21 , 30 ]), we write the functional FPE with where , and we define similarly to of Equation ( 1 ): Requiring that the stationary solution of the functional FPE, Equation ( A2 ), is , the flux must have the form [ 21 , 30 ]: This yields the following relations: Using Equation ( A3 ) and substituting Equation ( A5 ) into Equation ( A6 ), we finally obtain the spurious drift in the Stratonovich convention, Note that can be defined as symmetric, in which case, it is the square root of [ 18 ]. Note also that the choice of different time-discretisation schemes only affects the dissipative part of the generalized mobility matrix (its symmetric part ), while its reactive part (the antisymmetric part) [ 21 , 58 ] contributes a term that is unaffected by time-discretisation. Importantly, and as explained in detail in Section 3.3 and Section 4.2 , there are problems with the continuous description of the spurious drift, specifically in cases where …”