Multi-species dynamical density functional theory for microswimmers: Derivation, orientational ordering, trapping potentials, and shear cells

Internal sites of actuation and activation in thin elastic films and membranes of finite thickness

Functionalized thin elastic films and membranes frequently feature internal sites of net forces or stresses. These are, for instance, active sites of actuation, or rigid inclusions in a strained membrane that induce counterstress upon externally imposed deformations. We theoretically analyze the geometry of isotropic, flat, thin, linearly elastic films or membranes of finite thickness, laterally extended to infinity. At the mathematical core of such characterizations are the fundamental solutions for localized force and stress singularities associated with corresponding Green's functions. We derive such solutions in three dimensions and place them into the context of previous two-dimensional calculations. To this end, we consider both no-slip and stress-free conditions at the top and/or bottom surfaces. We provide an understanding for why the fully free-standing thin elastic membrane leads to diverging solutions in most geometries and compare these situations to the truly two-dimensional case. A no-slip support of at least one of the surfaces stabilizes the solution, which illustrates that the divergences in the fully free-standing case are connected to global deformations. Within the aforementioned framework, our results are important for associated theoretical characterizations of thin elastic films, whether supported or free-standing, and of membranes subject to internal or external forces or stresses.

Intrinsic statistical separation of subpopulations in heterogeneous collective motion via dimensionality reduction

Collective motion of locally interacting agents is found ubiquitously throughout nature. The inability to probe individuals has driven longstanding interest in the development of methods for inferring the underlying interactions. In the context of heterogeneous collectives, where the population consists of individuals driven by different interactions, existing approaches require some knowledge about the heterogeneities or underlying interactions. Here, we investigate the feasibility of identifying the identities in a heterogeneous collective without such prior knowledge. We numerically explore the behavior of a heterogeneous Vicsek model and find sufficiently long trajectories intrinsically cluster in a principal component analysis-based dimensionally reduced model-agnostic description of the data. We identify how heterogeneities in each parameter in the model (interaction radius, noise, population proportions) dictate this clustering. Finally, we show the generality of this phenomenon by finding similar behavior in a heterogeneous D'Orsogna model. Altogether, our results establish and quantify the intrinsic model-agnostic statistical disentanglement of identities in heterogeneous collectives.

Mixtures of self-propelled particles interacting with asymmetric obstacles

In the presence of an obstacle, active particles condensate into a surface "wetting" layer due to persistent motion. If the obstacle is asymmetric, a rectification current arises in addition to wetting. Asymmetric geometries are therefore commonly used to concentrate microorganisms like bacteria and sperms. However, most studies neglect the fact that biological active matter is diverse, composed of individuals with distinct self-propulsions. Using simulations, we study a mixture of "fast" and "slow" active Brownian disks in two dimensions interacting with large half-disk obstacles. With this prototypical obstacle geometry, we analyze how the stationary collective behavior depends on the degree of self-propulsion "diversity," defined as proportional to the difference between the self-propulsion speeds, while keeping the average self-propulsion speed fixed. A wetting layer rich in fast particles arises. The rectification current is amplified by speed diversity due to a superlinear dependence of rectification on self-propulsion speed, which arises from cooperative effects. Thus, the total rectification current cannot be obtained from an effective one-component active fluid with the same average self-propulsion speed, highlighting the importance of considering diversity in active matter.

Active Brownian particles in external force fields: Field-theoretical models, generalized barometric law, and programmable density patterns

We investigate the influence of external forces on the collective dynamics of interacting active Brownian particles in two as well as three spatial dimensions. Via explicit coarse graining, we derive predictive models, i.e., models that give a direct relation between the models' coefficients and the bare parameters of the system, that are applicable for space- and time-dependent external force fields. We study these models for the cases of gravity and harmonic traps. In particular, we derive a generalized barometric formula for interacting active Brownian particles under gravity that is valid for low to high concentrations and activities of the particles. Furthermore, we show that one can use an external harmonic trap to induce motility-induced phase separation in systems that, without external fields, remain in a homogeneous state. This finding makes it possible to realize programmable density patterns in systems of active Brownian particles. Our analytic predictions are found to be in very good agreement with Brownian dynamics simulations.

Wetting dynamics by mixtures of fast and slow self-propelled particles

We study active surface wetting using a minimal model of bacteria that takes into account the intrinsic motility diversity of living matter. A mixture of "fast" and "slow" self-propelled Brownian particles is considered in the presence of a wall. The evolution of the wetting layer thickness shows an overshoot before stationarity and its composition evolves in two stages, equilibrating after a slow elimination of excess particles. Nonmonotonic evolutions are shown to arise from delayed avalanches towards the dilute phase combined with the emergence of a transient particle front.

Perspective: New directions in dynamical density functional theory

Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.

Effect of boundaries on displacements and motion in two-dimensional fluid or elastic films and membranes

Thin fluid or elastic films and membranes are found in nature and technology, for instance, as confinements of living cells or in loudspeakers. When applying a net force, the resulting flows in an unbounded two-dimensional incompressible low-Reynolds-number fluid or displacements in a two-dimensional linearly elastic solid seem to diverge logarithmically with the distance from the force center, which has led to some debate. Recently, we have demonstrated that such divergences cancel when the total (net) force vanishes. Here, we illustrate that if a net force is present, the boundaries play a prominent role. Already a single no-slip boundary regulates the flow and displacement fields and leads to their decay to leading order inversely in distance from a force center and the boundary. In other words, it is the boundary that stabilizes the system in this situation, unlike the three-dimensional case, where an unbounded medium by itself is able to absorb a net force. We quantify the mobility and displaceability of an inclusion as a function of the distance from the boundary, as well as interactions between different inclusions. In the case of free-slip boundary conditions, a kinked boundary is necessary to achieve stabilization.

Mediated interactions between rigid inclusions in two-dimensional elastic or fluid films

Interactions between rigid inclusions in continuous three-dimensional linearly elastic solids and low-Reynolds-number viscous fluids have largely been quantified in the past. Prime example systems are given by functionalized elastic composite materials or fluid colloidal suspensions. Here, we address the significantly less frequently studied situation of rigid inclusions in two-dimensional elastic or low-Reynolds-number fluid films. We concentrate on the situation in which disklike inclusions remain well separated from each other and do not get into contact. Specifically, we demonstrate and explain that the logarithmic divergence of the associated Green's function is removed in the absence of net external forces on the inclusions, in line with physical intuition. For instance, this situation applies when only pairwise mutual interactions between the inclusions prevail. Our results will support, for example, investigations on membranes functionalized by appropriate inclusions, both of technical or biological origin, or the dynamics of active microswimmers in appropriately prepared thin films.

Diversity of self-propulsion speeds reduces motility-induced clustering in confined active matter

Self-propelled swimmers such as bacteria agglomerate into clusters as a result of their persistent motion. In 1D, those clusters do not coalesce macroscopically and the stationary cluster size distribution (CSD) takes an exponential form. We develop a minimal lattice model for active particles in narrow channels to study how clustering is affected by the interplay between self-propulsion speed diversity and confinement. A mixture of run-and-tumble particles with a distribution of self-propulsion speeds is simulated in 1D. Particles can swap positions at rates proportional to their relative self-propulsion speed. Without swapping, we find that the average cluster size L_c decreases with diversity and follows a non-arithmetic power mean of the single-component L_c's, unlike the case of tumbling-rate diversity previously studied. Effectively, the mixture is thus equivalent to a system of identical particles whose self-propulsion speed is the harmonic mean self-propulsion speed of the mixture. With swapping, particles escape more quickly from clusters. As a consequence, L_c decreases with swapping rates and depends less strongly on diversity. We derive a dynamical equilibrium theory for the CSDs of binary and fully polydisperse systems. Similarly to the clustering behaviour of one-component models, our qualitative results for mixtures are expected to be universal across active matter. Using literature experimental values for the self-propulsion speed diversity of unicellular swimmers known as choanoflagellates, which naturally differentiate into slower and faster cells, we predict that the error in estimating their L_cvia one-component models which use the conventional arithmetic mean self-propulsion speed is around 30%.

Collective excitations in active fluids: Microflows and breakdown in spectral equipartition of kinetic energy

The effect of particle activity on collective excitations in active fluids of microflyers is studied. With an in silico study, we observed an oscillating breakdown of equipartition (uniform spectral distribution) of kinetic energy in reciprocal space. The phenomenon is related to short-range velocity-velocity correlations that were realized without forming of long-lived mesoscale vortices in the system. This stands in contrast to well-known mesoscale turbulence operating in active nematic systems (bacterial or artificial) and reveals the features of collective dynamics in active fluids, which should be important for structural transitions and glassy dynamics in active matter.

Active mixtures in a narrow channel: motility diversity changes cluster sizes

The persistent motion of bacteria produces clusters with a stationary cluster size distribution (CSD). Here we develop a minimal model for bacteria in a narrow channel to assess the relative importance of motility diversity (i.e. polydispersity in motility parameters) and confinement. A mixture of run-and-tumble particles with a distribution of tumbling rates (denoted generically by α) is considered on a 1D lattice. Particles facing each other cross at constant rate, rendering the lattice quasi-1D. To isolate the role of diversity, the global average α stays fixed. For a binary mixture with no particle crossing, the average cluster size (Lc) increases with the diversity as lower-α particles trap higher-α ones for longer. At finite crossing rate, particles escape from the clusters sooner, making Lc smaller and the diversity less important, even though crossing can enhance demixing of particle types between the cluster and gas phases. If the crossing rate is increased further, the clusters become controlled by particle crossing. We also consider an experiment-based continuous distribution of tumbling rates, revealing similar physics. Using parameters fitted from experiments with Escherichia coli bacteria, we predict that the error in estimating Lc without accounting for polydispersity is around 60%. We discuss how to find a binary system with the same CSD as the fully polydisperse mixture. An effective theory is developed and shown to give accurate expressions for the CSD, the effective α, and the average fraction of mobile particles. We give reasons why our qualitative results are expected to be valid for other active matter models and discuss the changes that would result from polydispersity in the active speed rather than in the tumbling rate.

Dynamical Crystallites of Active Chiral Particles

One of the intrinsic characteristics of far-from-equilibrium systems is the nonrelaxational nature of the system dynamics, which leads to novel properties that cannot be understood and described by conventional pathways based on thermodynamic potentials. Of particular interest are the formation and evolution of ordered patterns composed of active particles that exhibit collective behavior. Here we examine such a type of nonpotential active system, focusing on effects of coupling and competition between chiral particle self-propulsion and self-spinning. It leads to the transition between three bulk dynamical regimes dominated by collective translative motion, spinning-induced structural arrest, and dynamical frustration. In addition, a persistently dynamical state of self-rotating crystallites is identified as a result of a localized-delocalized transition induced by the crystal-melt interface. The mechanism for the breaking of localized bulk states can also be utilized to achieve self-shearing or self-flow of active crystalline layers.

Effects of social distancing and isolation on epidemic spreading modeled via dynamical density functional theory

For preventing the spread of epidemics such as the coronavirus disease COVID-19, social distancing and the isolation of infected persons are crucial. However, existing reaction-diffusion equations for epidemic spreading are incapable of describing these effects. In this work, we present an extended model for disease spread based on combining a susceptible-infected-recovered model with a dynamical density functional theory where social distancing and isolation of infected persons are explicitly taken into account. We show that the model exhibits interesting transient phase separation associated with a reduction of the number of infections, and allows for new insights into the control of pandemics.

Towards an analytical description of active microswimmers in clean and in surfactant-covered drops

Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications.

Mechanical Coupling of Puller and Pusher Active Microswimmers Influences Motility

Active self-propelled colloidal populations induce time-dependent three-dimensional fluid flows, which alter the rheological (viscoelastic) properties of their fluidic media. Researchers have also studied passive colloids mixed with bacterial suspensions to understand the hydrodynamic coupling between active and passive colloids. With recent developments in biological cell-driven biohybrid microswimmers, different type biological microswimmer (e.g., bacteria and algae) populations need to interact fluidically with each other in the same fluidic media, while such interactions have not been studied experimentally yet. Therefore, we report the swimming behavior of two opposite types of biological microswimmer (active colloid) populations: Chlamydomonas reinhardtii (C. reinhardtii) algae (puller-type microswimmers) population in coculture with Escherichia coli (E. coli) bacteria (pusher-type microswimmers) population. We observed noticeable fluidic coupling deviations from the existing understanding of passive colloids mixed with bacterial suspensions previously studied in the literature. The fluidic coupling among puller- and pusher-type microswimmers led to nonequilibrium fluctuations in the fluid flow due to their opposite swimming patterns. Such coupling could be the main reason behind the shift in motility behaviors of these two opposite-type swimmer populations suspended in the same fluidic media.