Classical Nucleation Theory for Active Fluid Phase Separation.

Classical Nucleation Theory (CNT), linking rare nucleation events to the free-energy landscape of a growing nucleus, is central to understanding phase-change kinetics in passive fluids. Nucleation in nonequilibrium systems is much harder to describe because there is no free energy, but instead a dynamics-dependent quasipotential that typically must be found numerically. Here we extend CNT to a class of active phase-separating systems governed by a minimal field-theoretic model (Active Model B+). In the small noise and supersaturation limits that CNT assumes, we compute analytically the quasipotential, and hence, nucleation barrier, for liquid-vapor phase separation. Crucial to our results, detailed balance, although broken microscopically by activity, is restored along the instanton trajectory, which in CNT involves the nuclear radius as the sole reaction coordinate.

Interface Roughening in Nonequilibrium Phase-Separated Systems.

Interfaces of phase-separated systems roughen in time due to capillary waves. Because of fluxes in the bulk, their dynamics is nonlocal in real space and is not described by the Edwards-Wilkinson or Kardar-Parisi-Zhang (KPZ) equations, nor their conserved counterparts. We show that, in the absence of detailed balance, the phase-separated interface is described by a new universality class that we term |q|KPZ. We compute the associated scaling exponents via one-loop renormalization group and corroborate the results by numerical integration of the |q|KPZ equation. Deriving the effective interface dynamics from a minimal field theory of active phase separation, we finally argue that the |q|KPZ universality class generically describes liquid-vapor interfaces in two- and three-dimensional active systems.

Erratum: Capillary Interfacial Tension in Active Phase Separation [Phys. Rev. Lett. 127, 068001 (2021)].

This corrects the article DOI: 10.1103/PhysRevLett.127.068001.

The Royal Society RAMP modelling initiative.

Normally, science proceeds following a well-established set of principles. Studies are done with an emphasis on correctness, are submitted to a journal editor who evaluates their relevance, and then undergo anonymous peer review by experts before publication in a journal and acceptance by the scientific community via the open literature. This process is slow, but its accuracy has served all fields of science well. In an emergency situation, different priorities come to the fore. Research and review need to be conducted quickly, and the target audience consists of policymakers. Scientists must jostle for the attention of non-specialists without sacrificing rigour, and must deal not only with peer assessment but also with media scrutiny by journalists who may have agendas other than ensuring scientific correctness. Here, we describe how the Royal Society coordinated efforts of diverse scientists to help model the coronavirus epidemic. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Capillary Interfacial Tension in Active Phase Separation.

In passive fluid-fluid phase separation, a single interfacial tension sets both the capillary fluctuations of the interface and the rate of Ostwald ripening. We show that these phenomena are governed by two different tensions in active systems, and compute the capillary tension σ_{cw} which sets the relaxation rate of interfacial fluctuations in accordance with capillary wave theory. We discover that strong enough activity can cause negative σ_{cw}. In this regime, depending on the global composition, the system self-organizes, either into a microphase-separated state in which coalescence is highly inhibited, or into an "active foam" state. Our results are obtained for Active Model B+, a minimal continuum model which, although generic, admits significant analytical progress.

Hydrodynamically Interrupted Droplet Growth in Scalar Active Matter.

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.

Constitutive Model for Time-Dependent Flows of Shear-Thickening Suspensions.

We develop a tensorial constitutive model for dense, shear-thickening particle suspensions subjected to time-dependent flow. Our model combines a recently proposed evolution equation for the suspension microstructure in rate-independent materials with ideas developed previously to explain the steady flow of shear-thickening ones, whereby friction proliferates among compressive contacts at large particle stresses. We apply our model to shear reversal, and find good qualitative agreement with particle-level, discrete-element simulations whose results we also present.

Dynamic clustering and re-dispersion in concentrated colloid-active gel composites.

We study the dynamics of quasi-two-dimensional concentrated suspensions of colloidal particles in active gels by computer simulations. Remarkably, we find that activity induces a dynamic clustering of colloids even in the absence of any preferential anchoring of the active nematic director at the particle surface. When such an anchoring is present, active stresses instead compete with elastic forces and re-disperse the aggregates observed in passive colloid-liquid crystal composites. Our quasi-two-dimensional "inverse" dispersions of passive particles in active fluids (as opposed to the more common "direct" suspensions of active particles in passive fluids) provide a promising route towards the self-assembly of new soft materials.

Competing chemical and hydrodynamic interactions in autophoretic colloidal suspensions.

At the surfaces of autophoretic colloids, slip velocities arise from local chemical gradients that are many-body functions of particle configuration and activity. For rapid chemical diffusion, coupled with slip-induced hydrodynamic interactions, we deduce the chemohydrodynamic forces and torques between colloids. For bottom-heavy particles above a no-slip wall, the forces can be expressed as gradients of a nonequilibrium potential which, by tuning the type of activity, can be varied from repulsive to attractive. When this potential has a barrier, we find arrested phase separation with a mean cluster size set by competing chemical and hydrodynamic interactions. These are controlled, in turn, by the monopolar and dipolar contributions to the active chemical surface fluxes.

Dynamic Vorticity Banding in Discontinuously Shear Thickening Suspensions.

It has recently been argued that steady-state vorticity bands cannot arise in shear thickening suspensions because the normal stress imbalance across the interface between the bands will set up particle migrations. In this Letter, we develop a simple continuum model that couples shear thickening to particle migration. We show by linear stability analysis that homogeneous flow is unstable towards vorticity banding, as expected, in the regime of negative constitutive slope. In full nonlinear computations, we show, however, that the resulting vorticity bands are unsteady, with spatiotemporal patterns governed by stress-concentration coupling. We furthermore show that these dynamical bands also arise in direct particle simulations, in good agreement with the continuum model.

Mixtures of Blue Phase Liquid Crystal with Simple Liquids: Elastic Emulsions and Cubic Fluid Cylinders.

We numerically investigate the behavior of a phase-separating mixture of a blue phase I liquid crystal with an isotropic fluid. The resulting morphology is primarily controlled by an inverse capillary number, χ, setting the balance between interfacial and elastic forces. When χ and the concentration of the isotropic component are both low, the blue phase disclination lattice templates a cubic array of fluid cylinders. For larger χ, the isotropic phase arranges primarily into liquid emulsion droplets which coarsen very slowly, rewiring the blue phase disclination lines into an amorphous elastic network. Our blue phase-simple fluid composites can be externally manipulated: an electric field can trigger a morphological transition between cubic fluid cylinder phases with different topologies.

Active viscoelastic matter: from bacterial drag reduction to turbulent solids.

A paradigm for internally driven matter is the active nematic liquid crystal, whereby the equations of a conventional nematic are supplemented by a minimal active stress that violates time-reversal symmetry. In practice, active fluids may have not only liquid-crystalline but also viscoelastic polymer degrees of freedom. Here we explore the resulting interplay by coupling an active nematic to a minimal model of polymer rheology. We find that adding a polymer can greatly increase the complexity of spontaneous flow, but can also have calming effects, thereby increasing the net throughput of spontaneous flow along a pipe (a "drag-reduction" effect). Remarkably, active turbulence can also arise after switching on activity in a sufficiently soft elastomeric solid.

Phase separation and rotor self-assembly in active particle suspensions.

Adding a nonadsorbing polymer to passive colloids induces an attraction between the particles via the "depletion" mechanism. High enough polymer concentrations lead to phase separation. We combine experiments, theory, and simulations to demonstrate that using active colloids (such as motile bacteria) dramatically changes the physics of such mixtures. First, significantly stronger interparticle attraction is needed to cause phase separation. Secondly, the finite size aggregates formed at lower interparticle attraction show unidirectional rotation. These micro-rotors demonstrate the self-assembly of functional structures using active particles. The angular speed of the rotating clusters scales approximately as the inverse of their size, which may be understood theoretically by assuming that the torques exerted by the outermost bacteria in a cluster add up randomly. Our simulations suggest that both the suppression of phase separation and the self-assembly of rotors are generic features of aggregating swimmers and should therefore occur in a variety of biological and synthetic active particle systems.

Discontinuous shear thickening without inertia in dense non-Brownian suspensions.

A consensus is emerging that discontinuous shear thickening (DST) in dense suspensions marks a transition from a flow state where particles remain well separated by lubrication layers, to one dominated by frictional contacts. We show here that reasonable assumptions about contact proliferation predict two distinct types of DST in the absence of inertia. The first occurs at densities above the jamming point of frictional particles; here, the thickened state is completely jammed and (unless particles deform) cannot flow without inhomogeneity or fracture. The second regime shows strain-rate hysteresis and arises at somewhat lower densities, where the thickened phase flows smoothly. DST is predicted to arise when finite-range repulsions defer contact formation until a characteristic stress level is exceeded.

Filling an emulsion drop with motile bacteria.

We have measured the spatial distribution of motile Escherichia coli inside spherical water droplets emulsified in oil. At low cell concentrations, the cell density peaks at the water-oil interface; at increasing concentration, the bulk of each droplet fills up uniformly while the surface peak remains. Simulations and theory show that the bulk density results from a "traffic" of cells leaving the surface layer, increasingly due to cell-cell scattering as the surface coverage rises above ∼10%. Our findings show similarities with the physics of a rarefied gas in a spherical cavity with attractive walls.

Chemotactic clusters in confined run-and-tumble bacteria: a numerical investigation.

We present a simulation study of pattern formation in an ensemble of chemotactic run-and-tumble bacteria, focussing on the effect of spatial confinement, either within traps or inside a maze. These geometries are inspired by previous experiments probing pattern formation in chemotactic strains of E. coli under these conditions. Our main result is that a microscopic model of chemotactic run-and-tumble particles which themselves secrete a chemoattractant is able to reproduce the main experimental observations, namely the formation of bacterial aggregates within traps and in dead ends of a maze. Our simulations also demonstrate that stochasticity plays a key role and leads to a hysteretic response when the chemotactic sensitivity is varied. We compare the results of run-and-tumble particles with simulations performed with a simplified version of the model where the active particles are smooth swimmers which respond to chemotactic gradients by rotating towards the source of chemoattractant. This class of models leads again to aggregation, but with quantitative and qualitative differences in, for instance, the size and shape of clusters.

Spontaneous motility of passive emulsion droplets in polar active gels.

We study by computer simulations the dynamics of a droplet of passive, isotropic fluid, embedded in a polar active gel. The latter represents a fluid of active force dipoles, which exert either contractile or extensile stresses on their surroundings, modelling for instance a suspension of cytoskeletal filaments and molecular motors. When the polarisation of the active gel is anchored normal to the droplet at its surface, the nematic elasticity of the active gel drives the formation of a hedgehog defect; this defect then drives an active flow which propels the droplet forward. In an extensile gel, motility can occur even with tangential anchoring, which is compatible with a defect-free polarisation pattern. In this case, upon increasing activity the droplet first rotates uniformly, and then undergoes a discontinuous nonequilibrium transition into a translationally motile state, powered by bending deformations in the surrounding active medium.

Intracellular facilitated diffusion: searchers, crowders, and blockers.

In bacteria, regulatory proteins search for a specific DNA-binding target via "facilitated diffusion": a series of rounds of three-dimensional diffusion in the cytoplasm, and one-dimensional (1D) linear diffusion along the DNA contour. Using large scale Brownian dynamics simulations we find that each of these steps is affected differently by crowding proteins, which can either be bound to the DNA acting as a road block to the 1D diffusion, or freely diffusing in the cytoplasm. Macromolecular crowding can strongly affect mechanistic features such as the balance between three-dimensional and 1D diffusion, but leads to surprising robustness of the total search time.

Colloidal templating at a cholesteric-oil interface: assembly guided by an array of disclination lines.

We simulate colloids (radius R ~ 1 µm) trapped at the interface between a cholesteric liquid crystal and an immiscible oil at which the helical order (pitch p) in the bulk conflicts with the orientation induced at the interface, stabilizing an ordered array of disclinations. For a weak anchoring strength W of the director field at the colloidal surface, this creates a template, favoring particle positions either on top of or midway between defect lines, depending on α=R/p. For small α, optical microscopy experiments confirm this picture, but for larger α no templating is seen. This may stem from the emergence at moderate W of a rugged energy landscape associated with defect reconnections.

Modeling the relaxation of polymer glasses under shear and elongational loads.

Glassy polymers show "strain hardening": at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time. This can be explained by a minimal nonfactorable model combining flow-induced melting of a glass with the buildup of stress carried by strained polymers. Within this model, liquefaction of segmental motion permits strong flow that creates polymer-borne stress, slowing the deformation enough for the segmental (or solvent) modes then to re-vitrify. Here, we present new results for the corresponding behavior under step-stress shear loading, to which very similar physics applies. To explain the unloading behavior in the extensional case requires introduction of a "crinkle factor" describing a rapid loss of segmental ordering. We discuss in more detail here the physics of this, which we argue involves non-entropic contributions to the polymer stress, and which might lead to some important differences between shear and elongation. We also discuss some fundamental and possibly testable issues concerning the physical meaning of entropic elasticity in vitrified polymers. Finally, we present new results for the startup of steady shear flow, addressing the possible role of transient shear banding.