Microorganisms are able to overcome the thermal randomness of their surroundings by harvesting energy to navigate in viscous fluid environments. In a similar manner, synthetic colloidal microswimmers are capable of mimicking complex biolocomotion by means of simple self-propulsion mechanisms. Although experimentally the speed of active particles can be controlled by e.g. self-generated chemical and thermal gradients, an in-situ change of swimming direction remains a challenge. In this work, we study self-propulsion of half-coated spherical colloids in critical binary mixtures and show that the coupling of local body forces, induced by laser illumination, and the wetting properties of the colloid, can be used to finely tune both the colloid's swimming speed and its directionality. We experimentally and numerically demonstrate that the direction of motion can be reversibly switched by means of the size and shape of the droplet(s) nucleated around the colloid, depending on the particle radius and the fluid's ambient temperature. Moreover, the aforementioned features enable the possibility to realize both negative and positive phototaxis in light intensity gradients. Our results can be extended to other types of half-coated microswimmers, provided that both of their hemispheres are selectively made active but with distinct physical properties.
Spontaneous segregation of run-and-tumble particles with different velocities in microchannels is investigated by numerical simulations. Self-propelled particles are known to accumulate in the proximity of walls. Here we show how fast particles expel slower ones from the wall leading to a segregated state. The mechanism is understood as a function of particle velocities, particle density, or channel width. In the presence of an external fluid flow, particles with two different velocities segregate due to their different particle fluxes. Promising applications can be found in the development of…
We study the collective dynamics of self-propelled rods in an inhomogeneous motility field. At the interface between two regions of constant but different motility, a smectic rod layer is spontaneously created through aligning interactions between the active rods, reminiscent of an artificial, semi-permeable membrane. This "active membrane" engulfes rods which are locally trapped in low-motility regions and thereby further enhances the trapping efficiency by self-organization, an effect which we call "self-encapsulation". Our results are gained by computer simulations of self-propelled rod mod…
Phase diagram of the phenomenon of motility induced phase separation (MIPS) for a collection of self-propelled interacting disks is explored using Langevin dynamics simulation with particular emphasis on disk wall softness and the range of interaction amongst disks. We bring out important changes in the MIPS phase diagram both due to softness and inertia of the disks. Specifically, we show that overdamped softer disks phase separate while MIPS becomes possible only for harder disks in the inertial limit. Unlike most of the earlier studies on MIPS which consider hard-core disks, our findings ma…
We study the behaviour of interacting self-propelled particles, whose self-propulsion speed decreases with their local density. By combining direct simulations of the microscopic model with an analysis of the hydrodynamic equations obtained by explicitly coarse graining the model, we show that interactions lead generically to the formation of a host of patterns, including moving clumps, active lanes and asters. This general mechanism could explain many of the patterns seen in recent experiments and simulations.
We study a robust model of self-propelled rods interacting via volume exclusion and show that its collective dynamics encompasses both that of the corresponding Vicsek-style model (where local alignment is the sole interaction), and motility-induced phase separation (which occurs when repulsion is dominant). These results unify these heretofore largely disconnected bodies of knowledge on dry active matter and clarify the nature of the various phases involved.
We use coarse-grained molecular dynamics simulations to study the motility of a 2D vesicle containing self-propelled rods, as a function of the vesicle bending rigidity and the number density, length, and activity of the enclosed rods. Above a threshold value of the rod length, distinct dynamical regimes emerge, including a dramatic enhancement of vesicle motility characterized by a highly persistent random walk. These regimes are determined by clustering of the rods within the vesicle; the maximum motility state arises when there is one long-lived polar cluster. We develop a scaling theory th…
Many biological systems consist of self-motile and passive agents both of which contribute to overall functionality. However, there are very few studies of the properties of such mixtures. Here we formulate a model for mixtures of self-motile and passive agents and show that the model gives rise to three different dynamical phases: a disordered mesoturbulent phase, a polar flocking phase, and a vortical phase characterized by large-scale counterrotating vortices. We use numerical simulations to construct a phase diagram and compare the statistical properties of the different phases of the mode…
Self-propelled particles include both self-phoretic synthetic colloids and various micro-organisms. By continually consuming energy, they bypass the laws of equilibrium thermodynamics. These laws enforce the Boltzmann distribution in thermal equilibrium: the steady state is then independent of kinetic parameters. In contrast, self-propelled particles tend to accumulate where they move more slowly. They may also slow down at high density, for either biochemical or steric reasons. This creates positive feedback which can lead to motility-induced phase separation (MIPS) between dense and dilute f…
Designing microscopic and nanoscopic self-propelled particles and characterising their motion has become a major scientific challenge over the past decades. To this purpose, phoretic effects, namely propulsion mechanisms relying on local field gradients, have been the focus of many theoretical and experimental studies. In this review, we adopt a tutorial approach to present the basic physical mechanisms at stake in phoretic motion, and describe the different experimental works that lead to the fabrication of active particles based on this principle. We also present the collective effects obser…
We numerically and experimentally study the segregation dynamics in a binary mixture of microswimmers which move on a two-dimensional substrate in a static periodic triangular-like light intensity field. The motility of the active particles is proportional to the imposed light intensity and they possess a motility contrast, i.e., the prefactor depends on the species. In addition, the active particles also experience a torque aligning their motion towards the direction of the negative intensity gradient. We find a segregation of active particles near the intensity minima where typically one spe…
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. Non-monotonic evolutions are shown to arise from delayed avalanches towards the dilute phase combined with the emergence of a transient particle front.
Worm-like filaments that are propelled homogeneously along their tangent vector are studied by Brownian dynamics simulations. Systems in two dimensions are investigated, corresponding to filaments adsorbed to interfaces or surfaces. A large parameter space covering weak and strong propulsion, as well as flexible and stiff filaments is explored. For strongly propelled and flexible filaments, the free-swimming filaments spontaneously form stable spirals. The propulsion force has a strong impact on dynamic properties, such as the rotational and translational mean square displacement and the rate …
Active particles which are self-propelled by converting energy into mechanical motion represent an expanding research realm in physics and chemistry. For micron-sized particles moving in a liquid ("microswimmers"), most of the basic features have been described by using the model of overdamped active Brownian motion. However, for macroscopic particles or microparticles moving in a gas, inertial effects become relevant such that the dynamics is underdamped. Therefore, recently, active particles with inertia have been described by extending the active Brownian motion model to active Langevin dyn…
We investigate the dynamical coupling between the motion and the deformation of a single self-propelled domain based on two different model systems in two dimensions. One is represented by the set of ordinary differential equations for the center of gravity and two tensor variables characterizing deformations. The other is an active cell model which has an internal mechanism of motility and is represented by the partial differential equation for deformations. Numerical simulations show a rich variety of dynamics, some of which are common to the two model systems. The origin of the similarity a…
Minimal models of self-propelled particles with short-range volume exclusion interactions have been shown to exhibit signatures of phase separation. Here I show that the observed interfacial stability and fluctuations in motility-induced phase separations (MIPS) can be explained by modeling the microscopic dynamics of the active particles in the interfacial region. In addition, I demonstrate the validity of the Gibbs-Thomson relation in MIPS, which provides a functional relationship between the size of a condensed drop and its surrounding vapor concentration. As a result, the coarsening dynami…
We derive a dynamical field theory for self-propelled particles subjected to generic torques and forces by explicitly coarse-graining their microscopic dynamics, described by a many-body Fokker-Planck equation. The model includes both intrinsic torques inducing self-rotation, as well as interparticle torques leading to, for instance, the local alignment of particles' orientations. Within this approach, although the functional form of the pairwise interactions does not need to be specified, one can directly map the parameters of the field theory onto the parameters of particle-based models. We …
Starting from a microscopic model of self-propelled hard spheres we use tools of non-equilibrium statistical mechanics and the kinetic theory of hard spheres to derive a Smoluchowski equation for interacting Active Brownian particles. We illustrate the utility of the statistical mechanics framework developed with two applications. First, we derive the steady state pressure of the hard sphere active fluid in terms of the microscopic parameters and second, we identify the critical density for the onset of motility-induced phase separation in this system. We show that both these quantities agree …
We present a comprehensive study of a model system of repulsive self-propelled disks in two dimensions with ferromagnetic and nematic velocity alignment interactions. We characterize the phase behavior of the system as a function of the alignment and self-propulsion strength, featuring orientational order for strong alignment and Motility-Induced Phase Separation (MIPS) at moderate alignment but high enough self-propulsion. We derive a microscopic theory for these systems yielding a close set of hydrodynamic equations from which we perform a linear stability analysis of the homogenous disorder…
We show that memory, in the form of underdamped angular dynamics, is a crucial ingredient for the collective properties of self-propelled particles. Using Vicsek-style models with an Ornstein-Uhlenbeck process acting on angular velocity, we uncover a rich variety of collective phases not observed in usual overdamped systems, including vortex lattices and active foams. In a model with strictly nematic interactions the smectic arrangement of Vicsek waves giving rise to global polar order is observed. We also provide a calculation of the effective interaction between vortices in the case where a …
We propose a reciprocal, self-propelled model swimmer at intermediate Reynolds numbers ($Re$). Our swimmer consists of two unequal spheres that oscillate in antiphase generating nonlinear steady streaming (SS) flows. We show computationally that the SS flows enable the swimmer to propel itself, and also switch direction as $Re$ increases. We quantify the transition in the swimming direction by collapsing our data on a critical $Re$ and show that the transition in swimming directions corresponds to the reversal of the SS flows. Based on our findings, we propose that SS can be an important physi…
Active agents - like phoretic particles, bacteria, sperm, and cytoskeletal filaments in motility assays - show a large variety of motility-induced collective behaviors, such as aggregation, clustering and phase separation. The behavior of dense suspensions of phoretic particles and of bacteria during biofilm formation is determined by two principle physical mechanisms: (i) volume exclusion (short-range steric repulsion) and (ii) quorum sensing (longer-range reduced propulsion due to alteration of the local chemical environment). To systematically characterize such systems, we study semi-penetr…
Self-propelled particles can spontaneously form dense phases from a dilute suspension in a process referred to as motility-induced phase separation. The properties of the out-of-equilibrium structures that are formed are governed by the specifics of the particle interactions and the strength of the activity. Thus far, most studies into the formation of these structures have focused on spherical colloids, dumbbells, and rod-like particles endowed with various interaction potentials. Only a few studies have examined the collective behavior of more complex particle shapes. Here, we increase the g…
A wide range of experimental systems including gliding, swarming and swimming bacteria, in-vitro motility assays as well as shaken granular media are commonly described as self-propelled rods. Large ensembles of those entities display a large variety of self-organized, collective phenomena, including formation of moving polar clusters, polar and nematic dynamic bands, mobility-induced phase separation, topological defects and mesoscale turbulence, among others. Here, we give a brief survey of experimental observations and review the theoretical description of self-propelled rods. Our focus is …
Active matter physics has been developed with various types of self-propelled particles, including those with polar and bipolar motility and beyond. However, the bipolar motions experimentally realized so far have been either random along the axis or periodic at intrinsic frequencies. Here we report another kind of bipolar active particles, whose periodic bipolar self-propulsion is set externally at a controllable frequency. We used Quincke rollers -- dielectric particles suspended in a conducting liquid driven by an electric field -- under an AC electric field instead of the usually used DC f…
We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square-displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behaviour adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher order powers in time for the MSD. …
Suitable asymmetric microstructures can be used to control the direction of motion in microorganism populations. This rectification process makes it possible to accumulate swimmers in a region of space or to sort different swimmers. Here we study numerically how the separation process depends on the specific motility strategies of the microorganisms involved. Crucial properties such as the separation efficiency and the separation time for two bacterial strains are precisely defined and evaluated. In particular, the sorting of two bacterial populations inoculated in a box consisting of a series…
Active matter systems provide fascinating examples of pattern formation and collective motility without counterparts in equilibrium systems. Here, we employ Brownian dynamics simulations to study the collective motion and self-organization in systems of self-propelled semiflexible filaments, inspired by the gliding motility of \textit{filamentous Cyanobacteria}. Specifically, we investigate the influence of stochastic direction reversals on the patterns. We explore pattern formation and dynamics by modulating three relevant physical parameters, the bending stiffness, the activity, and the reve…
Active systems, or active matter, are self-driven systems which live, or function, far from equilibrium - a paradigmatic example which we focus on here is provided by a suspension of self-motile particles. Active systems are far from equilibrium because their microscopic constituents constantly consume energy from the environment in order to do work, for instance to propel themselves. The nonequilibrium nature of active matter leads to a variety of non-trivial intriguing phenomena. An important one which has recently been the subject of intense interest among biological and soft matter physici…
In many biological systems, the curvature of the surfaces cells live on influence their collective properties. Curvature should likewise influence the behavior of active colloidal particles. We show using molecular simulation of self-propelled active particles on surfaces of Gaussian curvature (both positive and negative) that curvature sign and magnitude can alter the system's collective behavior. Curvature acts as a geometrical lens and shifts the critical density of motility-induced phase separation (MIPS) to lower values for positive curvature and higher values for negative curvature, whic…
We study a strongly interacting crowded system of self-propelled stiff filaments by event-driven Brownian dynamics simulations and an analytical theory to elucidate the intricate interplay of crowding and self-propulsion. We find a remarkable increase of the effective diffusivity upon increasing the filament number density by more than one order of magnitude. This counter-intuitive 'crowded is faster' behavior can be rationalized by extending the concept of a confining tube pioneered by Doi and Edwards for highly entangled crowded, passive to active systems. We predict a scaling theory for the…
Motility-induced phase separation (MIPS) arises generically in fluids of self-propelled particles when interactions lead to a kinetic slowdown at high densities. Starting from a continuum description of scalar active matter, akin to a generalized Cahn-Hilliard equation, we give a general prescription for the mean densities of coexisting phases in flux-free steady states that amounts, at a hydrodynamics scale, to extremizing an effective free energy. We illustrate our approach on two well-known models: self-propelled particles interacting either through a density-dependent propulsion speed or v…
Collective behavior of self-propelled particles is observed on a microscale for swimmers such as sperm and bacteria as well as for protein filaments in motility assays. The properties of such systems depend both on their dimensionality and the interactions between their particles. We introduce a model for self-propelled rods in two dimensions that interact via a separation-shifted Lennard-Jones potential. Due to the finite potential barrier, the rods are able to cross. This model allows us to efficiently simulate systems of self-propelled rods that effectively move in two dimensions but can oc…
Growing, Buckling, and Swirling: motility from polymerization
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）；Center for Computational Biology, Flatiron Institute（计算生物学中心，平顿研究所）；Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）
The collective behavior of self-propelled particles (SPPs) under the combined effects of a circularly patterned substrate and circular confinement is investigated through coarse-grained molecular dynamics simulations of polarized and disjoint ring polymers. The study is performed over a wide range of values of the SPPs packing fraction $\barϕ$, motility force $F_D$, and area fraction of the patterned region. At low packing fractions, the SPPs are excluded from the system's center and exhibit a vortical motion that is dominated by the substrate at intermediate values of $F_D$. This exclusion zo…
In recent single-particle tracking (SPT) measurements on {\it Listeria monocytogenes} motility {\em in vitro}, the actin-based stochastic dynamics of the bacterium movement is analyzed statistically (Kuo and McGrath, 2000). The mean-square displacement (MSD) of the detrended trajectory exhibit a linear behavior; it has been suggested that a corresponding analysis for the Brownian ratchet model (Peskin, Odell, & Oster, 1993) leads to a non-monotonic MSD. A simplified version of the Brownian ratchet, when its motion is limited by the bacterium movement, is proposed and analyzed stochastically. A…
We study a system of self-propelled disks that perform run-and-tumble motion, where particles can adopt more than one internal state. One of those internal states can be transmitted to another particle if the particle carrying this state maintains physical contact with another particle for a finite period of time. We refer to this process as a reaction process and to the different internal states as particle species making an analogy to chemical reactions. The studied system may fall into an absorbing phase, where due to the disappearance of one of the particle species no further reaction can …
Active particles with their characteristic feature of self-propulsion are regarded as the simplest models for motility in living systems. The accumulation of active particles in low activity regions has led to the general belief that chemotaxis requires additional features and at least a minimal ability to process information and to control motion. We show that self-propelled particles display chemotaxis and move into regions of higher activity, if the particles perform work on passive objects, or cargo, to which they are bound. The origin of this cooperative chemotaxis is the exploration of t…
Minimal models of active Brownian colloids consisting of self-propelled spherical particles with purely repulsive interactions have recently been identified as excellent quantitative testing grounds for theories of active matter and have been the subject of extensive numerical and analytical investigation. These systems do not exhibit aligned or flocking states, but do have a rich phase diagram, forming active gases, liquids and solids with novel mechanical properties. This article reviews recent advances in the understanding of such models, including the description of the active gas and its …
Suspensions of self-propelled bodies generate a unique mechanical stress owing to their motility that impacts their large-scale collective behavior. For microswimmers suspended in a fluid with negligible particle inertia, we have shown that the virial `swim stress' is a useful quantity to understand the rheology and nonequilibrium behaviors of active soft matter systems. For larger self-propelled organisms like fish, it is unclear how particle inertia impacts their stress generation and collective movement. Here, we analyze the effects of finite particle inertia on the mechanical pressure (or …
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 sel…
