Joakim Stenhammar

Continuum Theory of Phase Separation Kinetics for Active Brownian Particles

Active Brownian particles (ABPs), when subject to purely repulsive interactions, are known to undergo activity-induced phase separation broadly resembling an equilibrium (attraction-induced) gas-liquid coexistence. Here we present an accurate continuum theory for the dynamics of phase-separating ABPs, derived by direct coarse graining, capturing leading-order density gradient terms alongside an effective bulk free energy. Such gradient terms do not obey detailed balance; yet we find coarsening dynamics closely resembling that of equilibrium phase separation. Our continuum theory is numerically compared to large-scale direct simulations of ABPs and accurately accounts for domain growth kinetics, domain topologies, and coexistence densities.

Pressure and Phase Equilibria in Interacting Active Brownian Spheres

We derive a microscopic expression for the mechanical pressure P in a system of spherical active Brownian particles at density ρ. Our exact result relates P, defined as the force per unit area on a bounding wall, to bulk correlation functions evaluated far away from the wall. It shows that (i) P(ρ) is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to P, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; and (iii) P is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles and show that the densities at coexistence do not satisfy a Maxwell construction on P.

Light-induced self-assembly of active rectification devices

Self-propelled particles that swim in response to light can self-assemble microfluidic rectification devices under nonuniform illumination. Self-propelled colloidal objects, such as motile bacteria or synthetic microswimmers, have microscopically irreversible individual dynamics—a feature they share with all living systems. The incoherent behavior of individual swimmers can be harnessed (or “rectified”) by microfluidic devices that create systematic motions that are impossible in equilibrium. We present a computational proof-of-concept study showing that such active rectification devices could be created directly from an unstructured “primordial soup” of light-controlled motile particles, solely by using spatially modulated illumination to control their local propulsion speed. Alongside both microscopic irreversibility and speed modulation, our mechanism requires spatial symmetry breaking, such as a chevron light pattern, and strong interactions between particles, such as volume exclusion, which cause a collisional slowdown at high density. Together, we show how these four factors create a novel, many-body rectification mechanism. Our work suggests that standard spatial light modulator technology might allow the programmable, light-induced self-assembly of active rectification devices from an unstructured particle bath.

Electric multipole moment fluctuations in polar liquids.

A general expression for the distribution of the fluctuating 2(l)-pole moment M(l) of a spherical sample of dielectric material is derived on the basis of dielectric theory combined with statistical mechanics. The formulas are compared with results from computer simulations of a weakly coupled Stockmayer fluid and the agreement is shown to be excellent. Furthermore, we calculate the size of the coupling, quantified through the free energy of solvation A(solv), of the fluctuating electric moments to a surrounding dielectric medium. It turns out that the contribution to A(solv) from each fluctuating electric moment actually increases with increasing order l of the moment, resulting in a formally infinite free energy of solvation. We also present a correction to A(solv) for molecular media, which shows that the molecular nature of the surrounding medium effectively suppresses the divergence in the solvation free energy.

Some comments and corrections regarding the calculation of electrostatic potential derivatives using the Ewald summation technique

A review of the literature on the calculation of electrostatic potentials, fields, and field gradients in systems consisting of charges and dipoles using the Ewald summation technique is presented. Discrepancies between the previous formulas are highlighted, and an error in the derivation of the reciprocal contributions to the electrostatic field and field gradient is corrected. The new formulas for the field and field gradient are shown to exhibit a termwise identity with the ones for the electrostatic energy.

Nondielectric long-range solvation of polar liquids in cubic symmetry

Long-range solvation properties of strongly coupled dipolar systems simulated using the Ewald and reaction field methods are assessed by using electric fluctuation formulas for a dielectric medium. Some components of the fluctuating electric multipole moments are suppressed, whereas other components are favored as the boundary of the simulation box is approached. An analysis of electrostatic interactions in a periodic cubic system suggests that these structural effects are due to the periodicity embedded in the Ewald method. Furthermore, the results obtained using the reaction field method are very similar to those obtained using the Ewald method, an effect which we attribute to the use of toroidal boundary conditions in the former case. Thus, the long-range solvation properties of polar liquids simulated using either of the two methods are nondielectric in their character.

Effects of different boundary conditions on the long-range structure of polar liquids

The long-range order in strongly coupled dipolar systems has been studied using large-scale simulations for systems containing up to 100 000 particles. It is found that the boundary conditions used strongly influence the result. It is found that a periodic system modeled with the minimum image approximation yields an artificial order, whereas the same system described using the Ewald summation technique is slightly less long-range ordered, as compared to the results obtained from studies on a non-periodical spherical droplet. Analytical expressions together with scaling considerations suggest that dipolar systems are structured on all length scales. However, more extensive studies are needed to fully assess the impact of using different boundary conditions on the long-range structure of polar liquids.

Role of Correlations in the Collective Behavior of Microswimmer Suspensions

In this Letter, we study the collective behavior of a large number of self-propelled microswimmers immersed in a fluid. Using unprecedentedly large-scale lattice Boltzmann simulations, we reproduce the transition to bacterial turbulence. We show that, even well below the transition, swimmers move in a correlated fashion that cannot be described by a mean-field approach. We develop a novel kinetic theory that captures these correlations and is nonperturbative in the swimmer density. To provide an experimentally accessible measure of correlations, we calculate the diffusivity of passive tracers and reveal its nontrivial density dependence. The theory is in quantitative agreement with the lattice Boltzmann simulations and captures the asymmetry between pusher and puller swimmers below the transition to turbulence.

Nonequilibrium dynamics of mixtures of active and passive colloidal particles

We develop a mesoscopic field theory for the collective nonequilibrium dynamics of multicomponent mixtures of interacting active (i.e., motile) and passive (i.e., nonmotile) colloidal particles with isometric shape in two spatial dimensions. By a stability analysis of the field theory, we obtain equations for the spinodal that describes the onset of a motility-induced instability leading to cluster formation in such mixtures. The prediction for the spinodal is found to be in good agreement with particle-resolved computer simulations. Furthermore, we show that in active-passive mixtures the spinodal instability can be of two different types. One type is associated with a stationary bifurcation and occurs also in one-component active systems, whereas the other type is associated with a Hopf bifurcation and can occur only in active-passive mixtures. Remarkably, the Hopf bifurcation leads to moving clusters. This explains recent results from simulations of active-passive particle mixtures, where moving clusters and interfaces that are not seen in the corresponding one-component systems have been observed. (Less)

Bulk simulation of polar liquids in spherical symmetry

Molecular simulations of strongly coupled dipolar systems of varying size have been carried out, using particles confined inside a dielectric cavity and an image charge approach to treat the dielectric response from the surroundings. A simple method using penalty functions was employed to create an isotropic and homogeneous distribution of particles inside the cavity. The dielectric response of the molecular system was found to increase as the number of particles N was increased. Nevertheless, a significant surface effect remained even for the largest systems (N=10,000), manifesting itself through a decrease in the dielectric constant of the system as the confining surface was approached. The surface effect was significantly reduced by using a negative dielectric constant of the surrounding dielectric medium, although accomplishing a full dielectric solvation of the molecular system was not possible.