Pseudochemotactic drifts of artificial microswimmers

Active colloidal molecules in activity gradients

We consider a rigid assembly of two active Brownian particles, forming an active colloidal dimer, in a gradient of activity. We show analytically that depending on the relative orientation of the two particles the active dimer accumulates in regions of either high or low activity, corresponding to, respectively, chemotaxis and antichemotaxis. Certain active dimers show both chemotactic and antichemotactic behavior, depending on the strength of the activity. Our coarse-grained Fokker-Planck approach yields an effective potential, which we use to construct a nonequilibrium phase diagram that classifies the dimers according to their tactic behavior. Moreover, we show that for certain dimers a higher persistence of the motion is achieved similar to the effect of a steering wheel in macroscopic devices. This work could be useful for designing autonomous active colloidal structures which adjust their motion depending on the local activity gradients.

Dynamics of active particles with space-dependent swim velocity

We study the dynamical properties of an active particle subject to a swimming speed explicitly depending on the particle position. The oscillating spatial profile of the swim velocity considered in this paper takes inspiration from experimental studies based on Janus particles whose speed can be modulated by an external source of light. We suggest and apply an appropriate model of an active Ornstein Uhlenbeck particle (AOUP) to the present case. This allows us to predict the stationary properties, by finding the exact solution of the steady-state probability distribution of particle position and velocity. From this, we obtain the spatial density profile and show that its form is consistent with the one found in the framework of other popular models. The reduced velocity distribution highlights the emergence of non-Gaussianity in our generalized AOUP model which becomes more evident as the spatial dependence of the velocity profile becomes more pronounced. Then, we focus on the time-dependent properties of the system. Velocity autocorrelation functions are studied in the steady-state combining numerical and analytical methods derived under suitable approximations. We observe a non-monotonic decay in the temporal shape of the velocity autocorrelation function which depends on the ratio between the persistence length and the spatial period of the swim velocity. In addition, we numerically and analytically study the mean square displacement and the long-time diffusion coefficient. The ballistic regime, observed in the small-time region, is deeply affected by the properties of the swim velocity landscape which induces also a crossover to a sub-ballistic but superdiffusive regime for intermediate times. Finally, the long-time diffusion coefficient decreases as the amplitude of the swim velocity oscillations increases because the diffusion is mainly determined by those regions where the particles are slow.

Run with the Brownian Hare, Hunt with the Deterministic Hounds

We present analytic results for mean capture time and energy expended by a pack of deterministic hounds actively chasing a randomly diffusing prey. Depending on the number of chasers, the mean capture time as a function of the prey's diffusion coefficient can be monotonically increasing, decreasing, or attain a minimum at a finite value. Optimal speed and number of chasing hounds exist and depend on each chaser's baseline power consumption. The model can serve as an analytically tractable basis for further studies with bearing on the growing field of smart microswimmers and autonomous robots.

Thermotaxis of Janus particles

The interactions of autonomous microswimmers play an important role for the formation of collective states of motile active matter. We study them in detail for the common microswimmer-design of two-faced Janus spheres with hemispheres made from different materials. Their chemical and physical surface properties may be tailored to fine-tune their mutual attractive, repulsive or aligning behavior. To investigate these effects systematically, we monitor the dynamics of a single gold-capped Janus particle in the external temperature field created by an optically heated metal nanoparticle. We quantify the orientation-dependent repulsion and alignment of the Janus particle and explain it in terms of a simple theoretical model for the induced thermoosmotic surface fluxes. The model reveals that the particle's angular velocity is solely determined by the temperature profile on the equator between the Janus particle's hemispheres and their phoretic mobility contrast. The distortion of the external temperature field by their heterogeneous heat conductivity is moreover shown to break the apparent symmetry of the problem.

Chemotaxis of Cargo-Carrying Self-Propelled Particles

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 the activity gradient by the active particle when bound to a load, resulting in an average excess force on the load in the direction of higher activity. Using a new theoretical model, we capture the most relevant features of these active-passive dimers, and in particular we predict the crossover between antichemotactic and chemotactic behavior. Moreover, we show that merely connecting active particles to chains is sufficient to obtain the crossover from antichemotaxis to chemotaxis with increasing chain length. Such an active complex is capable of moving up a gradient of activity such as provided by a gradient of fuel and to accumulate where the fuel concentration is at its maximum. The observed transition is of significance to protoforms of life, enabling them to locate a source of nutrients even in the absence of any supporting sensomotoric apparatus.

Chemokinesis-driven accumulation of active colloids in low-mobility regions of fuel gradients

Many motile cells exhibit migratory behaviors, such as chemotaxis (motion up or down a chemical gradient) or chemokinesis (dependence of speed on chemical concentration), which enable them to carry out vital functions including immune response, egg fertilization, and predator evasion. These have inspired researchers to develop self-propelled colloidal analogues to biological microswimmers, known as active colloids, that perform similar feats. Here, we study the behavior of half-platinum half-gold (Pt/Au) self-propelled rods in antiparallel gradients of hydrogen peroxide fuel and salt, which tend to increase and decrease the rods' speed, respectively. Brownian Dynamics simulations, a Fokker-Planck theoretical model, and experiments demonstrate that, at steady state, the rods accumulate in low-speed (salt-rich, peroxide-poor) regions not because of chemotaxis, but because of chemokinesis. Chemokinesis is distinct from chemotaxis in that no directional sensing or reorientation capabilities are required. The agreement between simulations, model, and experiments bolsters the role of chemokinesis in this system. This work suggests a novel strategy of exploiting chemokinesis to effect accumulation of motile colloids in desired areas.

Stochastic resetting of active Brownian particles with Lorentz force

Equilibrium properties of a system of passive diffusing particles in an external magnetic field are unaffected by Lorentz force. In contrast, active Brownian particles exhibit steady-state phenomena that depend on both the strength and the polarity of the applied magnetic field. The intriguing effects of the Lorentz force, however, can only be observed when out-of-equilibrium density gradients are maintained in the system. To this end, we use the method of stochastic resetting on active Brownian particles in two dimensions by resetting them to the line x = 0 at a constant rate and periodicity in the y direction. Under stochastic resetting, an active system settles into a nontrivial stationary state which is characterized by an inhomogeneous density distribution, polarization and bulk fluxes perpendicular to the density gradients. We show that whereas for a uniform magnetic field the properties of the stationary state of the active system can be obtained from its passive counterpart, novel features emerge in the case of an inhomogeneous magnetic field which have no counterpart in passive systems. In particular, there exists an activity-dependent threshold rate such that for smaller resetting rates, the density distribution of active particles becomes non-monotonic. We also study the mean first-passage time to the x axis and find a surprising result: it takes an active particle more time to reach the target from any given point for the case when the magnetic field increases away from the axis. The theoretical predictions are validated using Brownian dynamics simulations.

Active Brownian Motion with Orientation-Dependent Motility: Theory and Experiments

Combining experiments on active colloids, whose propulsion velocity can be controlled via a feedback loop, and the theory of active Brownian motion, we explore the dynamics of an overdamped active particle with a motility that depends explicitly on the particle orientation. In this case, the active particle moves faster when oriented along one direction and slower when oriented along another, leading to anisotropic translational dynamics which is coupled to the particle's rotational diffusion. We propose a basic model of active Brownian motion for orientation-dependent motility. On the basis of this model, we obtain analytical results for the mean trajectories, averaged over the Brownian noise for various initial configurations, and for the mean-square displacements including their non-Gaussian behavior. The theoretical results are found to be in good agreement with the experimental data. Orientation-dependent motility is found to induce significant anisotropy in the particle displacement, mean-square displacement, and non-Gaussian parameter even in the long-time limit. Our findings establish a methodology for engineering complex anisotropic motilities of active Brownian particles, with a potential impact in the study of the swimming behavior of microorganisms subjected to anisotropic driving fields.

Rectification and separation of mixtures of active and passive particles driven by temperature difference

Transport and separation of binary mixtures of active and passive particles are investigated in the presence of temperature differences. It is found that temperature differences can strongly affect the rectification and separation of the mixtures. For active particles, there exists an optimal temperature difference at which the rectified efficiency is maximal. Passive particles are not propelled and move by collisions with active particles, so the response to temperature differences is more complicated. By changing the system parameters, active particles can change their directions, while passive particles always move in the same direction. The simulation results show that the separation of mixtures is sensitive to the system parameters, such as the angular velocity, the temperature difference, and the polar alignment. The mixed particles can be completely separated under certain conditions.

Enhanced motility in a binary mixture of active nano/microswimmers

It is often desirable to enhance the motility of active nano- or microscale swimmers such as, e.g., self-propelled Janus particles as agents of chemical reactions or weak sperm cells for better chances of successful fertilization. Here we tackle this problem based on the idea that motility can be transferred from a more active guest species to a less active host species. We performed numerical simulations of motility transfer in two typical cases, namely for interacting particles with a weak inertia effect, by analyzing their velocity distributions, and for interacting overdamped particles, by studying their effusion rate. In both cases, we detected motility transfer with a motility enhancement of the host species of up to a factor of four. This technique of motility enhancement can find applications in chemistry, biology and medicine.

Pseudo-chemotaxis of active Brownian particles competing for food

Active Brownian particles (ABPs) are physical models for motility in simple life forms and easily studied in simulations. An open question is to what extent an increase of activity by a gradient of fuel, or food in living systems, results in an evolutionary advantage of actively moving systems such as ABPs over non-motile systems, which rely on thermal diffusion only. It is an established fact that within confined systems in a stationary state, the activity of ABPs generates density profiles that are enhanced in regions of low activity, which is thus referred to as ‘anti-chemotaxis’. This would suggest that a rather complex sensoric subsystem and information processing is a precondition to recognize and navigate towards a food source. We demonstrate in this work that in non-stationary setups, for instance as a result of short bursts of fuel/food, ABPs do in fact exhibit chemotactic behavior. In direct competition with inactive, but otherwise identical Brownian particles (BPs), the ABPs are shown to fetch a larger amount of food. We discuss this result based on simple physical arguments. From the biological perspective, the ability of primitive entities to move in direct response to the available amount of external energy would, even in absence of any sensoric devices, encompass an evolutionary advantage.

Rectification of chiral active particles driven by transversal temperature difference

Rectification of chiral active particles driven by transversal temperature difference is investigated in a two-dimensional periodic channel. Chiral active particles can be rectified by transversal temperature difference. Transport behaviors are qualitatively different for different wall boundary conditions. For the sliding boundary condition, the direction of transport completely depends on the chirality of particles. The average velocity is a peaked function of angular velocity or temperature difference. The average velocity increases linearly with the self-propulsion speed, while it decreases monotonically with the increase in the packing fraction. For randomized boundary condition, the transport behaviors become complex. When self-propulsion speed is small, in contrast with the sliding boundary condition, particles move in the opposite direction. However, for large self-propulsion speed, current reversals can occur by continuously changing the system parameters (angular velocity, temperature difference, packing fraction, and width of the channel).

Colloidal Brazil nut effect in microswimmer mixtures induced by motility contrast

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 species is localized close to the minimum and the other one is centered around in an outer shell. For a very strong aligning torque, there is an exact mapping onto an equilibrium system in an effective external potential that is minimal at the intensity minima. This external potential is similar to (height-dependent) gravity such that one can define effective "heaviness" of the self-propelled particles. In analogy to shaken granular matter in gravity, we define a "colloidal Brazil nut effect" if the heavier particles are floating on top of the lighter ones. Using extensive Brownian dynamics simulations, we identify system parameters for the active colloidal Brazil nut effect to occur and explain it based on a generalized Archimedes' principle within the effective equilibrium model: heavy particles are levitated in a dense fluid of lighter particles if their effective mass density is lower than that of the surrounding fluid. We also perform real-space experiments on light-activated self-propelled colloidal mixtures which confirm the theoretical predictions.

A hydrodynamic-stochastic model of chemotactic ciliated microorganisms

Biological systems like ciliated microorganisms are capable of responding to the external chemical gradients, a process known as chemotaxis. In this process, the internal signaling network of the microorganism is triggered due to binding of the chemoattractant molecules with the receptors on the surface of the body. This can alter the activity at the surface of the microorganism. We study the chemotaxis of ciliated microorganisms using the chiral squirmer model, a spherical body with a surface slip velocity. In the presence of a chemical gradient, the coefficients of the slip velocity get modified resulting in a change in the path followed by the body. We observe that the strength of the gradient is not the only parameter which controls the dynamics of the body but also the adaptation time plays a very significant role in the success of chemotaxis. The trajectory of the body is smooth if we ignore the discreteness in the ligand-receptor binding which is stochastic in nature. In the presence of the latter, the path is not only irregular but the whole dynamics of the body changes. We calculate the mean first passage time, by varying the strength of the chemical gradient and the adaptation time, to determine the success rate of chemotaxis.

Current reversals of active particles in time-oscillating potentials

Rectification of interacting active particles is numerically investigated in a two-dimensional time-oscillating potential. It is found that the oscillation of the potential and the self-propulsion of active particles are two different types of nonequilibrium driving, which can induce net currents with opposite directions. For a given asymmetry of the potential, the direction of the transport is determined by the competition of the self-propulsion and the oscillation of the potential. There exists an optimal oscillating angular frequency (or self-propulsion speed) at which the average velocity takes its maximal positive or negative value. Remarkably, when the oscillation of the potential competes with the self-propulsion, the average velocity can change direction several times due to the change in the oscillating frequency. Especially, particles with different self-propulsion velocities will move in opposite directions and can be separated. Our results provide a novel and convenient method for controlling and manipulating the transport (or separation) of active particles.

Pseudochemotaxis in inhomogeneous active Brownian systems

We study dynamical properties of confined, self-propelled Brownian particles in an inhomogeneous activity profile. Using Brownian dynamics simulations, we calculate the probability to reach a fixed target and the mean first passage time to the target of an active particle. We show that both these quantities are strongly influenced by the inhomogeneous activity. When the activity is distributed such that high-activity zone is located between the target and the starting location, the target finding probability is increased and the passage time is decreased in comparison to a uniformly active system. Moreover, for a continuously distributed profile, the activity gradient results in a drift of active particle up the gradient bearing resemblance to chemotaxis. Integrating out the orientational degrees of freedom, we derive an approximate Fokker-Planck equation and show that the theoretical predictions are in very good agreement with the Brownian dynamics simulations.

Spontaneous membrane formation and self-encapsulation of active rods in an inhomogeneous motility field

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, semipermeable 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 models confined on a two-dimensional planar or spherical surface with a stepwise constant motility field, but the phenomenon should be observable in any geometry with sufficiently large spatial inhomogeneity. We also discuss possibilities to verify our predictions of active-membrane formation in experiments of self-propelled colloidal rods and vibrated granular matter.

Activated barrier crossing dynamics of a Janus particle carrying cargo

We numerically study the escape kinetics of a self-propelled Janus particle, carrying a cargo, from a meta-stable state.

Surface fouling as a mechanism for chemotaxis in isotropic catalytic swimmers

We present microscopic models for surface fouling of an isotropic spherical catalytic microswimmer at and away from equilibrium and show how a foulant gradient can induce chemotactic behavior. Our simulations establish that the presence of foulant manifests itself in two ways: as a braking effect on propulsive particle motion, and as a drift term which probes the foulant concentration gradient. Our results suggest that, while foulant gradients are unlikely to be directly useful for chemotactically directed particles, they nevertheless exert a non-negligible influence on particle motion under a wide range of conditions.

Transport of underdamped active particles in ratchet potentials

We study the rectified transport of underdamped active noninteracting particles in an asymmetric periodic potential. It is found that the ratchet effect of active noninteracting particles occurs in a single direction (along the easy direction of the substrate asymmetry) in the overdamped limit. However, when the inertia is considered, it is possible to observe reversals of the ratchet effect, where the motion is along the hard direction of the substrate asymmetry. By changing the friction coefficient or the self-propulsion force, the average velocity can change its direction several times. Therefore, by suitably tailoring the parameters, underdamped active particles with different self-propulsion forces can move in different directions and can be separated.

Effects of hydrodynamic interactions on rectified transport of self-propelled particles

Directed transport of self-propelled particles is numerically investigated in a three-dimensional asymmetric potential. Beside the steric repulsive forces, hydrodynamic interactions between particles have been taken into account in an approximate way. From numerical simulations, we find that hydrodynamic interactions can strongly affect the rectified transport of self-propelled particles. Hydrodynamic interactions enhance the performance of the rectified transport when particles can easily pass across the barrier of the potential, and reduce the rectified transport when particles are mainly trapped in the potential well.

Self-Polarizing Microswimmers in Active Density Waves

An artificial microswimmer drifts in response to spatio-temporal modulations of an activating suspension medium. We consider two competing mechanisms capable of influencing its tactic response: angular fluctuations, which help it explore its surroundings and thus diffuse faster toward more active regions, and self-polarization, a mechanism inherent to self-propulsion, which tends to orient the swimmer's velocity parallel or antiparallel to the local activation gradients. We investigate, both numerically and analytically, the combined action of such two mechanisms. By determining their relative magnitude, we characterize the selective transport of artificial microswimmers in inhomogeneous activating media.

Phototaxis of synthetic microswimmers in optical landscapes

Many microorganisms, with phytoplankton and zooplankton as prominent examples, display phototactic behaviour, that is, the ability to perform directed motion within a light gradient. Here we experimentally demonstrate that sensing of light gradients can also be achieved in a system of synthetic photo-activated microparticles being exposed to an inhomogeneous laser field. We observe a strong orientational response of the particles because of diffusiophoretic torques, which in combination with an intensity-dependent particle motility eventually leads to phototaxis. Since the aligning torques saturate at high gradients, a strongly rectified particle motion is found even in periodic asymmetric intensity landscapes. Our results are in excellent agreement with numerical simulations of a minimal model and should similarly apply to other particle propulsion mechanisms. Because light fields can be easily adjusted in space and time, this also allows to extend our approach to dynamical environments.

Chemotaxis of artificial microswimmers in active density waves

Living microorganisms are capable of a tactic response to external stimuli by swimming toward or away from the stimulus source; they do so by adapting their tactic signal transduction pathways to the environment. Their self-motility thus allows them to swim against a traveling tactic wave, whereas a simple fore-rear asymmetry argument would suggest the opposite. Their biomimetic counterpart, the artificial microswimmers, also propel themselves by harvesting kinetic energy from an active medium, but, in contrast, lack the adaptive capacity. Here we investigate the transport of artificial swimmers subject to traveling active waves and show, by means of analytical and numerical methods, that self-propelled particles can actually diffuse in either direction with respect to the wave, depending on its speed and waveform. Moreover, chiral swimmers, which move along spiraling trajectories, may diffuse preferably in a direction perpendicular to the active wave. Such a variety of tactic responses is explained by the modulation of the swimmer's diffusion inside traveling active pulses.

Ratchet transport powered by chiral active particles

We numerically investigate the ratchet transport of mixtures of active and passive particles in a transversal asymmetric channel. A big passive particle is immersed in a ‘sea’ of active particles. Due to the chirality of active particles, the longitudinal directed transport is induced by the transversal asymmetry. For the active particles, the chirality completely determines the direction of the ratchet transport, the counterclockwise and clockwise particles move to the opposite directions and can be separated. However, for the passive particle, the transport behavior becomes complicated, the direction is determined by competitions among the chirality, the self-propulsion speed, and the packing fraction. Interestingly, within certain parameters, the passive particle moves to the left, while active particles move to the right. In addition, there exist optimal parameters (the chirality, the height of the barrier, the self-propulsion speed and the packing fraction) at which the rectified efficiency takes its maximal value. Our findings could be used for the experimental pursuit of the ratchet transport powered by chiral active particles.