Self-propulsion Velocity Research Articles

Extinction and coexistence in a binary mixture of proliferating motile disks.

A binary mixture of two-different-size proliferating motile disks is studied. As growth is space limited, we focus on the conditions such that there is a coexistence of both large and small disks, or dominance of the larger disks. The study involves systematically varying some system parameters, such as diffusivities, growth rates, and self-propulsion velocities. In particular, we demonstrate that diffusing faster confers a competitive advantage, so that larger disks can in the long time coexist or even dominate the smaller ones. In the case of self-propelled disks, a coexistence regime is induced by the activity where the two types of disks show the same spatial distribution: both particles are phase separated or both are homogeneously distributed in the whole system.

Ordering kinetics in the active Ising model.

We undertake a numerical study of the ordering kinetics in the two-dimensional (2D) active Ising model (AIM), a discrete flocking model with a conserved density field coupled to a nonconserved magnetization field. We find that for a quench into the liquid-gas coexistence region and in the ordered liquid region, the characteristic length scale of both the density and magnetization domains follows the Lifshitz-Cahn-Allen growth law, R(t)∼t^{1/2}, consistent with the growth law of passive systems with scalar order parameter and nonconserved dynamics. The system morphology is analyzed with the two-point correlation function and its Fourier transform, the structure factor, which conforms to the well-known Porod's law, a manifestation of the coarsening of compact domains with smooth boundaries. We also find the domain growth exponent unaffected by different noise strengths and self-propulsion velocities of the active particles. However, transverse diffusion is found to play the most significant role in the growth kinetics of the AIM. We extract the same growth exponent by solving the hydrodynamic equationsof the AIM.

Motility-induced phase separation of soft active Brownian particles

Motility-induced phase separation (MIPS) is the hallmark of non-equilibrium phase transition in active matter. Here, by means of Brownian dynamics simulations, we determine the phase behavior and the critical point for phase separation induced by motility of a two-dimensional system of soft active Brownian particles, whose interaction is modeled by the generalized purely repulsive Weeks–Chandler–Andersen potential. We refer to this model as soft active Brownian particles. We determine and analyze the influence of particle softness on the MIPS and show that the liquid–gas coexistence region is wider, the softer the interparticle interactions becomes. Moreover, the critical value of the self-propulsion velocity at which diluted and dense phases start to coexist also increases; as a consequence, the softer the particle interaction is, the bigger self-propulsion velocities are needed in order to observe a MIPS.

Active search for a reactive target in thermal environments.

We study a stochastic process where an active particle, modeled by a one-dimensional run-and-tumble particle, searches for a target with a finite absorption strength in thermal environments. Solving the Fokker-Planck equation for a uniform initial distribution, we analytically calculate the mean searching time (MST), the time for the active particle to be finally absorbed, and show that there exists an optimal self-propulsion velocity of the active particle at which MST is minimized. As the diffusion constant increases, the optimal velocity changes from a finite value to zero, which implies that a purely diffusive Brownian motion outperforms an active motion in terms of searching time. Depending on the absorption strength of the target, the transition of the optimal velocity becomes either continuous or discontinuous, which can be understood based on the Landau approach. In addition, we obtain the phase diagram indicating the passive-efficient and the active-efficient regions. Finally, the initial condition dependence of MST is presented in limiting cases.

Particle-wall alignment interaction and active Brownian diffusion through narrow channels.

We numerically examine the impacts of particle-wall alignment interactions on active species diffusion through a structureless narrow two-dimensional channel. We consider particle-wall interaction to depend on the self-propulsion velocity direction whereby some specific particle's alignments with respect to the boundary walls are stabilized more. Further, the alignment interaction is meaningful as long as particles are close to the confining boundaries. Unbiased diffusion of active particles for various possible stable velocity alignments against the walls has been examined. We show that for the most stable configuration leading to the self-propulsion velocity direction perpendicular to the wall, diffusivity becomes inversely proportional to the square of the alignment interaction torque. On the other hand, when the self-propulsion velocity direction making an acute angle to the channel walls is the most stable configuration, diffusion exponentially grows with strengthening alignment interaction. Hence, particle-wall interaction plays a pivotal role in the transport control of active particles through narrow channels. Moreover, the impacts of the alignment interactions on diffusion largely depend on the particle's self-propulsion properties and its chirality. Our simulation results can potentially be used to understand unbiased diffusion of artificial or living micro/nano-objects (such as virus, bacteria, Janus particles, etc.) though narrow confined structures.

Nanoswimmers in a ratchet potential: Effects of a transverse rocking force

We study the dynamics of a chemical nanoswimmer in a ratchet potential, which is periodically rocked in the transverse direction. As a result of the mechanochemical coupling, the self-propulsion velocity becomes force-dependent and particle trajectories are rectified in the direction of the ratchet modulation. The magnitude and direction of the nanoswimmer mean velocity depend upon both the rocking amplitude and the frequency. Remarkably, for frequencies larger than the inverse correlation time of the rotational diffusion, the velocity exhibits oscillatory behaviour as a function of the amplitude and the frequency with multiple reversals of the sign. These findings suggest that mechanochemical coupling can be utilized for controlling the motion of chemically active particles at the nanoscale.

Self-propulsion performance predictions of AUV based on response surface methodology

The self-propulsion performance of an autonomous underwater vehicle (AUV) is predicted based on computational fluid dynamics (CFD) and response surface methodology (RSM). The innovations are that a data-driven predictive framework is proposed and a model of coupled rotation speed, self-propulsion velocity and power is developed. In the present study, the discretized propeller method and multiple reference frames (MRF) model are adopted. The design of experiment (DOE) and numerical simulations are executed with inlet velocity and propeller rotation speed as inputs and drag, thrust and torque as outputs. Using the simulation results as sample data, the prediction accuracy of multiple models is compared. The polynomial model is applied to fit the response points, describing the relationship between inputs and outputs. The goodness of fit and predictive ability is assessed using the adjusted coefficient of determination (Radj2), root mean square error (RMSE) and relative error (RE). Finally, the predicted results are further validated by experiments, and all relative errors are below 6%. A linear function of self-propulsion velocity versus rotation speed and a specific cubic function of propeller input power versus self-propulsion velocity is obtained. The prediction method and achievements are beneficial for the navigation, control and safety of AUVs.

Stationary states of an active Brownian particle in a harmonic trap.

We study the stationary states of an overdamped active Brownian particle (ABP) in a harmonic trap in two dimensions via mathematical calculations and numerical simulations. In addition to translational diffusion, the ABP self-propels with a certain velocity, whose magnitude is constant, but its direction is subject to Brownian rotation. In the limit where translational diffusion is negligible, the stationary distribution of the particle's position shows a transition between two different shapes, one with maximum and the other with minimum density at the center, as the trap stiffness is increased. We show that this nonintuitive behavior is captured by the relevant Fokker-Planck equation, which, under minimal assumptions, predicts a continuous phase transition-like change between the two different shapes. As the translational diffusion coefficient is increased, both these distributions converge into the equilibrium, Boltzmann form. Our simulations support the analytical predictions and also show that the probability distribution of the orientation angle of the self-propulsion velocity undergoes a transition from unimodal to bimodal forms in this limit. We also extend our simulations to a three-dimensional trap and find similar behavior.

Most probable path of active Ornstein-Uhlenbeck particles.

Using the path integral representation of the nonequilibrium dynamics, we compute the most probable path between arbitrary starting and final points that is followed by an active particle driven by persistent noise. We focus our attention on the case of active particles immersed in harmonic potentials, where the trajectory can be computed analytically. Once we consider the extended Markovian dynamics where the self-propulsive drive evolves according to an Ornstein-Uhlenbeck process, we can compute the trajectory analytically with arbitrary conditions on position and self-propulsion velocity. We test the analytical predictions against numerical simulations and we compare the analytical results with those obtained within approximated equilibriumlike dynamics.

Collective behavior of passive and active circle swimming particle mixtures.

We present a numerical study on a binary mixture of passive and circle swimming, self-propelling particles which interact via the Lennard-Jones (LJ) potential in two dimensions. Using Brownian Dynamics (BD) simulations, we present state diagrams using the control parameters such as attraction strength, angular velocity, self-propulsion velocity and composition. In a symmetric mixture, the system undergoes a transition from a mixed gel to a rotating passive cluster state and finally to a homogeneous fluid state as translational activity increases. The formation of the rotating cluster of passive particles surrounded by active and passive monomers is attributed to the combined effect of composition, activity and strength of attraction of the active particles. Different phases are characterized using radial distribution functions, bond order parameters, cluster fraction and probability distribution of local volume fractions. The present study addresses comprehensively the intricate role of activity, angular velocity, inter-particle interaction and compositional variation on the phase behavior. The predictions presented in the study can be experimentally realized in synthetic colloidal swimmers and motile bacterial suspensions.

Dynamics of a spherical self-propelled tracer in a polymeric medium: interplay of self-propulsion, stickiness, and crowding.

We employ computer simulations to study the dynamics of a self-propelled spherical tracer particle in a viscoelastic medium, made of a long polymer chain. Here, the interplay between viscoelasticity, stickiness, and activity (self-propulsion) brings additional complexity to the tracer dynamics. Our simulations show that on increasing the stickiness of the tracer particle to the polymer beads, the dynamics of the tracer particle slows down as it gets stuck to the polymer chain and moves along with it. But with increasing self-propulsion velocity, the dynamics gets enhanced. In the case of increasing stickiness as well as activity, the non-Gaussian parameter (NGP) exhibits non-monotonic behavior, which also shows up in the re-scaled self part of the van-Hove function. Non-Gaussianity results owing to the enhanced binding events and the sticky motion of the tracer along with the chain with increasing stickiness. On the other hand, with increasing activity, initially non-Gaussianity increases as the tracer moves through the heterogeneous polymeric environment but for higher activity, the tracer escapes resulting in a negative NGP. For higher values of stickiness, the trapping time distributions of the passive tracer particle broaden and have long tails. On the other hand, for a given stickiness with increasing self-propulsion force, the trapping time distributions become narrower and have short tails. We believe that our current simulation study will be helpful in elucidating the complex motion of activity-driven probes in viscoelastic media.

Dynamics of self-propelled tracer particles inside a polymer network.

The transport of tracer particles through mesh-like environments such as biological hydrogels and polymer matrices is ubiquitous in nature. These tracers can be passive, such as colloids, or active (self-propelled), for example, synthetic nanomotors or bacteria. Computer simulations in principle could be extremely useful in exploring the mechanism of the active transport of tracer particles through mesh-like environments. Therefore, we construct a polymer network on a diamond lattice and use computer simulations to investigate the dynamics of spherical self-propelled particles inside the network. Our main objective is to elucidate the effect of the self-propulsion on the tracer particle dynamics as a function of the tracer size and the stiffness of the polymer network. We compute the time-averaged mean-squared displacement (MSD) and the van-Hove correlations of the tracer. On the one hand, in the case of a bigger sticky particle, the caging caused by the network particles wins over the escape assisted by the self-propulsion. This results an intermediate-time subdiffusion. On the other hand, smaller tracers or tracers with high self-propulsion velocities can easily escape from the cages and show intermediate-time superdiffusion. The stiffer the network, the slower the dynamics of the tracer, and bigger tracers exhibit longer lived intermediate time superdiffusion, since the persistence time scales as ∼σ3, where σ is the diameter of the tracer. At the intermediate time, non-Gaussianity is more pronounced for active tracers. At the long time, the dynamics of the tracer, if passive or weakly active, becomes Gaussian and diffusive, but remains flat for tracers with high self-propulsion, accounting for their seemingly unrestricted motion inside the network.

Microscopic field theory for structure formation in systems of self-propelled particles with generic torques.

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 perform a linear stability analysis of the homogeneous solution of the field equations and find both long-wavelength and short-wavelength instabilities. The former signals the emergence of a macroscopic structure, which we associate with motility-induced phase separation, while the second one signals the growth of a finite structure with a characteristic size. Intrinsic torques hinder phase separation, pushing the onset of the long-wavelength instability to higher activities. Furthermore, they generate finite-sized structures with a characteristic size proportional to both the self-propulsion velocity and the inverse of the self-rotation frequency. Our results show that a general mechanism might explain why chirality tends to suppress motility-induced phase separation but instead promotes the formation of non-equilibrium patterns.

Estimating the velocity of chemically-driven Janus colloids considering the anisotropic concentration field.

The application of the active colloids is strongly related to their self-propulsion velocity, which is controlled by the generated anisotropic concentration field. We investigated the effect of this anisotropy on velocity induced by numerical treatments and size of Janus colloids. The far-field approximation is effective in estimating the velocity, even though it neglects the shape effect on the anisotropy of the concentration field. If the surface mobility contrast between the active and the inert part is moderate, the spherical approximation is feasible for sphere-like Janus colloids. Legendre expansion of the concentration field causes artificial anisotropy. Raising the order of the expansion can suppress this effect, but also distorts the concentration field at the top of active part. Thus, the order of the expansion should be chosen carefully depending on the goal of the study. Based on the verified Legendre expansion method and ionic-diffusiophoresis model, we show that due to the size-effect on both the concentration field and the surface mobility, increasing size of colloids can lower the self-propulsion velocity. Our finding is consistent with previous experimental observations without fitting parameter, shedding new light on the self-propulsion mechanism of chemically-driven active colloids. We further show a velocity reversal at high overall ζ potential induced by increasing size, providing a new way for controlling the dynamics of acitve colloids.

Accurate Solutions to Non-Linear PDEs Underlying a Propulsion of Catalytic Microswimmers

Catalytic swimmers self-propel in electrolyte solutions thanks to an inhomogeneous ion release from their surface. Here, we consider the experimentally relevant limit of thin electrostatic diffuse layers, where the method of matched asymptotic expansions can be employed. While the analytical solution for ion concentration and electric potential in the inner region is known, the electrostatic problem in the outer region was previously solved but only for a linear case. Additionally, only main geometries such as a sphere or cylinder have been favoured. Here, we derive a non-linear outer solution for the electric field and concentrations for swimmers of any shape with given ion surface fluxes that then allow us to find the velocity of particle self-propulsion. The power of our formalism is to include the complicated effects of the anisotropy and inhomogeneity of surface ion fluxes under relevant boundary conditions. This is demonstrated by exact solutions for electric potential profiles in some particular cases with the consequent calculations of self-propulsion velocities.

Nonsinusoidal motion effect on a self-propelled heaving foil

In order to explore the mechanism of bionic propulsion and bionic robots, to make up for the limitations of traditional propulsion with a uniform incoming flow, numerical methods are used to couple fluid dynamics and flapping foil motions, and a flapping-fluid coupling self-propulsion calculation model is established in this paper. K is used as the waveform adjustment parameter to change the waveform from triangle wave to sine wave and square wave. The self-propulsion performances of non-sinusoidal heave motion under two frequency-heaving amplitude combinations are numerically simulated to study the influence of different motion waveforms on self-propulsion velocity, efficiency and flow field structure in still water. The results show that the non-sinusoidal waveform has a great influence on the self-propulsion. With the increase of K, the closer to the square wave, the more violent the speed oscillation, the faster the starting acceleration, the greater the forward displacement and the average speed, as K decreases, self-propulsion efficiency and energy utilization continue to increase. The results of this study have certain guiding significance for the design of bionic underwater vehicles.

The parental active model: A unifying stochastic description of self-propulsion.

We propose a new overarching model for self-propelled particles that flexibly generates a full family of "descendants." The general dynamics introduced in this paper, which we denote as the "parental" active model (PAM), unifies two special cases commonly used to describe active matter, namely, active Brownian particles (ABPs) and active Ornstein-Uhlenbeck particles (AOUPs). We thereby document the existence of a deep and close stochastic relationship between them, resulting in the subtle balance between fluctuations in the magnitude and direction of the self-propulsion velocity. Besides illustrating the relation between these two common models, the PAM can generate additional offsprings, interpolating between ABP and AOUP dynamics, that could provide more suitable models for a large class of living and inanimate active matter systems, possessing characteristic distributions of their self-propulsion velocity. Our general model is evaluated in the presence of a harmonic external confinement. For this reference example, we present a two-state phase diagram that sheds light on the transition in the shape of the positional density distribution from a unimodal Gaussian for AOUPs to a Mexican-hat-like profile for ABPs.

Simulating wet active polymers by multiparticle collision dynamics.

The conformational and dynamical properties of active Brownian polymers embedded in a fluid depend on the nature of the driving mechanism, e.g., self-propulsion or external actuation of the monomers. Implementations of self-propelled and actuated active Brownian polymers in a multiparticle collision (MPC) dynamics fluid are presented, which capture the distinct differences between the two driving mechanisms. The active force-free nature of self-propelled monomers requires adaptations of the MPC simulation scheme, with its streaming and collision steps, where the monomer self-propulsion velocity has to be omitted in the collision step. Comparison of MPC simulation results for active polymers in dilute solution with results of Brownian dynamics simulations accounting for hydrodynamics via the Rotne-Prager-Yamakawa tensor confirm the suitability of the implementation. The polymer conformational and dynamical properties are analyzed by the static and dynamic structure factor, and the scaling behavior of the latter with respect to the wave number and time dependence are discussed. The dynamic structure factor displays various activity-induced temporal regimes, depending on the considered wave number, which reflect the persistent diffusive motion of the whole polymer at small wave numbers, and the activity-enhanced internal dynamics at large wave numbers. The obtained simulation results are compared with theoretical predictions.

Time scale of directional change of active Brownian particles

For active Brownian particles (ABPs), the time scale τR=DR−1 has been widely used, with DR the rotational diffusion coefficient. Since the only independent non-dimensional number is Pe=v0DT−1/2DR−1/2 with v0 the self-propulsion velocity and DT the translational diffusion coefficient, any time scale of the ABP statistics should be the order of PeατR. In the present contribution, we show that by introducing the concept of relative angle Θ along with its expectation Φ(τ), a novel time scale with α=−1 can be observed, which indicates that the phenomenon of directional change is sensitive to Pe. This time scale corresponds to the transition time from the active overdamped particles (i.e., DT=0) to the PBPs under a background uniform velocity (i.e., DR=0). The direction change of both particle types can be estimated by using simplified analytical models. Comparisons with Navier-Stokes turbulence and football players indicate that the statistical similarity between ABPs and the latter is high.

Flow around topological defects in active nematic films.

We study the active flow around isolated defects and the self-propulsion velocity of defects in an active nematic film with both viscous dissipation (with viscosity ) and frictional damping with a substrate. The interplay between these two dissipation mechanisms is controlled by the hydrodynamic dissipation length that screens the flows. For an isolated defect, in the absence of screening from other defects, the size of the shear vorticity around the defect is controlled by the system size . In the presence of friction that leads to a finite value of , the vorticity field decays to zero on the lengthscales larger than . We show that the self-propulsion velocity of defects grows with in small systems where , while in the infinite system limit or when , it approaches a constant value determined by .