Hydrodynamically Interrupted Droplet Growth in Scalar Active Matter

Abstract

Suspensions of spherical active particles often show microphase separation. At a continuum level, coupling their scalar density to fluid flow, there are two distinct explanations. Each involves an effective interfacial tension: the first mechanical (causing flow) and the second diffusive (causing Ostwald ripening). Here we show how the negative mechanical tension of contractile swimmers creates, via a self-shearing instability, a steady-state life cycle of droplet growth interrupted by division whose scaling behavior we predict. When the diffusive tension is also negative, this is replaced by an arrested regime (mechanistically distinct, but with similar scaling) where division of small droplets is prevented by reverse Ostwald ripening.

Hierarchical microphase separation in non-conserved active mixtures

“…[8][9][10]) This echoes studies of bacteria colonies whose phase separation (coarsening) is arrested by birth-and-death dynamics to give patterns on a finite length scale [11]. This suggests that, like the latter, the physics of biomolecular condensates can be captured schematically by 'active field theories' based on minimal, φ 4 -type ingredients [12][13][14][15][16][17].…”

“…It is known that this coupling can give further distinctive routes to microphase separation, for example when activity in effect reverses the sign of the interfacial tension that governs the stress exerted on the fluid at the boundary of the droplet (but without doing the same for the Ostwald currents). This happens when the droplet is made of so-called contractile material [13,15]. In this paper, we omit these further complications and consider only how to combine the types of physics already captured by Model AB and AMB+, in which there is no separate momentum conservation, and the reaction-diffusion dynamics of φ give a complete description of the pertinent physics.…”

Layered Chiral Active Matter: Beyond Odd Elasticity

“…A patternformation framework [33] offers a foolproof approach to the construction of the hydrodynamic equations for active cholesterics, equivalent to the traditional route [7,8] starting with the equations of motion for an orientation field and eliminating the fast degrees of freedom. Accordingly, we begin by extending [34,35] to define active model H* : the coupled dynamics of a pseudoscalar density ψ governed by a conservation law ∂ t ψ = −∇ • J and a momentum density ρv whose dynamics in the Stokesian regime is governed by ∇ • σ = 0, with current J = ψv − M ∇µ + J a + J c and stress tensor σ = −η[∇v + (∇v) T ] + σ ψ + pI − σ c − σ a , where subscripts a and c denote achiral active and chiral contributions respectively. Here M is a mobility, µ = δF/δψ is a chemical potential expressed in terms of a free-energy functional F [ψ], η is a viscosity, the passive force density −∇ • σ ψ = −ψ∇µ is the Onsager counterpart to ψv [36], and the pressure p imposes overall incompressibility ∇ • v = 0.…”

“…Here M is a mobility, µ = δF/δψ is a chemical potential expressed in terms of a free-energy functional F [ψ], η is a viscosity, the passive force density −∇ • σ ψ = −ψ∇µ is the Onsager counterpart to ψv [36], and the pressure p imposes overall incompressibility ∇ • v = 0. J a = λ 1 ψ∇ψ∇ 2 ψ + λ 2 ψ∇(∇ψ) 2 as familiar from active models B and H [34,35,[37][38][39][40]. In what follows we ignore the chiral currents J c , whose effects on the dynamics of layered states arise at sub-leading order in wavenumber [41].…”

“…In what follows we ignore the chiral currents J c , whose effects on the dynamics of layered states arise at sub-leading order in wavenumber [41]. The achiral active stress [34,35], in both two and three dimensions, is σ a = ζ H ∇ψ∇ψ while the chiral active stress is…”