Passive Particles Research Articles

Tracking Point Vortices and Circulations via Advected Passive Particles: An Estimation Approach

We present a novel method for estimating the circulations and positions of point vortices in a two-dimensional (2D) environment using trajectory data of passive particles in the presence of Gaussian noise. The method comprises two algorithms: the first one calculates the vortex circulations, while the second one reconstructs the vortex trajectories. This reconstruction is done thanks to a hierarchy of optimization problems, involving the integration of systems of differential equations, over time sub-intervals all with the same amplitude defined by the autocorrelation function for the advected passive particles’ trajectories. Our findings indicate that accurately tracking the position of vortices and determining their circulations is achievable, even when passive particle trajectories are affected by noise.

An experiment generates a specified mean strained rate turbulent flow: Dynamics of particles

This study aimed to simulate straining turbulent flow empirically, having direct similarities with vast naturally occurring flows and engineering applications. The flow was generated in 100<Reλ<500 and seeded with passive and inertial particles. Lagrangian particle tracking and particle image velocimetry were employed to extract the dynamics of particle statistics and flow features, respectively. The studies for axisymmetric straining turbulent flow reported that the strain rate, flow geometry, and gravity affect particle statistics. To practically investigate mentioned effects in the literature, we present the behavior of both passive and inertial particles from the novel experiment conducted on initially homogeneous turbulence undergoing a sudden axisymmetric expansion. We represent the result with two different mean strains and Reynolds–Taylor microscales. However, this study, in contrast to the previous studies, considers the fields of inertial particles in the presence of gravity. The result discloses that the novel designed and conducted experiments simulated the flow satisfactorily. Then, the particle behavior in such flow showed the effectiveness of the flow distortion on particle dynamics such as velocity root mean square and Reynolds stress. Straining turbulence flow is subject to many industrial applications and physics studies, such as stagnation points, external flow around an airfoil, internal flow in changeable cross section pipe, expansion in the engine mixing chamber, and leading edge erosion. This study's conclusion could apply constructively to these areas.

Determination of the swimming mechanism of Au@TiO2 active matter and implications on active-passive interactions.

Non-equilibrium dynamic assembly attracts considerable attention due to the possibility of forming diverse structures that can potentially lead to functional materials. Despite significant progress in understanding and modelling, the complexity of the system implies that different phases of the assembly formation are governed by different interactions. It is clear that both, hydrodynamic and chemical interactions stem from the activity of the particle, but correlation to specific chemical species remains not yet understood. Here, we investigate the origin of the main driving forces for light-driven Au@TiO2 micromotors and look at the implication this causes for the interactions between active and passive particles. We develop precision experimental measurements of the photochemical reaction rate, which are correlated with the observed speed of Au@TiO2 micromotors. The comparison with two distinct models allows the conclusion that the dominant propulsion mechanism of the active particles is self-electrophoresis based on the self-generated H+ gradient. We verify this assumption by adding salt and confirm the dependence of the expected swimming behaviour on salt concentration and investigate the consequences for raft formation in COMSOL simulations.

Transfer of passive particles in the velocity field of vortex tripole moving on a plane

Purpose of this article is to study the transport of passive particles in the velocity field of a vortex tripole with a change in the parameter that determines the speed of the configuration movement. A structure consisting of a central vortex and satellite vortices rotating around it with the opposite vorticity is understood as a tripole. We employ a system of three point vortices, the most simple mathematical representation of a vortex tripole, which may be expressed as a system of nonlinear ordinary differential equations with a parameter. Consideration is limited to a particular case of a tripole with zero total vorticity. The influence of the speed values of vortex configuration movement on the processes of passive particle transport has been studied. Methods. The study was carried out numerically using algorithms based on the dynamical systems approaches including the construction of the Poincare map and the analysis of the dynamics of marker particles. Were carried out long ´ times calculations, corresponding to hundreds and thousands of turns around the tripole center. Integrators of high orders of accuracy were used to solve the Cauchy problems, which made it possible to adequacy of the calculation result control. Results. We found that transferring passive particles is fundamentally different depending on the speed of the tripole. A vast zone of chaotic dynamics forms in the neighborhood of the vortices when the velocity is low. This zone slowly shifts along with the tripole. There are subregions of active and slow mixing inside the chaos region. The possible stages of particle dynamics are: transfer from the region to the right of the tripole to the area to the left, vigorous mixing near the vortices, and slowly drifting to the region to the left of the tripole. At a high speed of vortex configuration in the entire chaotic region, the particles are strongly mixed. The vortex tripole removes particles from the vicinity of its initial position over long distances and practically does not capture new particles along its path. In intermediate situations, both processes can be realized at varying degrees. Conclusion. Non-trivial scenarios for the transport of passive particles by a vortex tripole, which can also occur in real vortex configurations of fluids, have been discovered and described.

Adaptive particle patterning in the presence of active synthetic nanomotors.

For the maintenance of a biological system, spatial organization of material condensates within the cell through the dissipation of energy is crucial. Besides directed transport via microtubules, material arrangement can be achieved via motor protein facilitated adaptive active diffusiophoresis. For example, the distribution of membrane proteins during the cell division of Escherichia coli is affected by the MinD system. Synthetic active motors exhibit the ability to simulate natural motors. Here we propose an active Au-Zn nanomotor driven by water and discovered an interesting adaptive interaction mode of the diffusiophoretic Au-Zn nanomotors with passive condensate particles in different environments. It is found that the attraction/repulsion between the nanomotor and passive particles is adaptive, while an interesting hollow pattern is formed with a negatively charged substrate and a cluster pattern is favored with a positively charged substrate.

Life cycle of cosmic-ray electrons in the intracluster medium

We simulate the evolution of relativistic eletrons injected into the medium of a small galaxy cluster by a central radio galaxy, studying how the initial jet power affects the dispersal and the emission properties of radio plasma. By coupling passive tracer particles to adaptive-mesh cosmological magnetohydrodynamic (MHD) simulations, we study how cosmic-ray electrons are dispersed as a function of the input jet power. We also investigate how the latter affects the thermal and non-thermal properties of the intracluster medium, with differences discernible up to about one Gyr after the start of the jet. We evolved the energy spectra of cosmic-ray electrons, subject to energy losses that are dominated by synchrotron and inverse Compton emission as well as energy gains via re-acceleration by shock waves and turbulence. We find that in the absence of major mergers, the amount of re-acceleration experienced by cosmic-ray electrons is not enough to produce long-lived detectable radio emissions. However, for all simulations, the role of re-acceleration processes is crucial to maintaining a significant and volume-filling reservoir of fossil electrons (γ ∼ 103) for at least one Gyr after the first injection by jets. This is important in attempting to establish plausible explanations of recent discoveries of cluster-wide emission and other radio phenomena in galaxy clusters.

Island hopping of active colloids.

Individual self-propelled colloidal particles, like active Brownian particles (ABP) or run-and-tumble (RT) swimmers, exhibit characteristic and well-known motion patterns. However, their interaction with obstacles remains an open and important problem. We here investigate the two-dimensional motion of silica-gold Janus particles (JP) suspended in a bath of smaller silica passive particles. Actuated by AC electric fields, the JP cruise through passive colloids organized in 'islands' due to attractive electrohydrodynamic (EHD) flows. A typical island contains dozens of particles. The JP travels straight in obstacle-free regions and reorients abruptly upon collision with an island. As an underlying mechanism, we propose that the scattering events are caused by the interplay of EHD flows, self-propulsion and local torques. The combination of directed motion and sudden reorientations leads to active trajectories resembling the RT behavior of biological microswimmers.

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.

Spontaneous symmetry-breaking of the active cluster drives the directed movement and self-sustained oscillation of symmetric rod-like passive particles.

Active particles without detailed balance can rectify their random motions to drive the directed movement or rotation of asymmetric passive obstacles. However, whether they can drive the directed movement of symmetric passive obstacles is still unclear. Here, we show that a rod-like passive particle which is fixed to move along the x-axis in an active bath can keep long-lived directed movement at nearly constant speed due to the spontaneous symmetry breaking of the neighboring active particle cluster. If the passive particle is further confined by a harmonic potential, it may undergo self-sustained periodic oscillation for an appropriate length of the passive particle and self-propelled velocity of active particles. The restoring force from the harmonic potential will trigger the velocity jump-off and thus lead to self-sustained periodic oscillation. Remarkably, the relationship between the velocity of the passive particle and the external force shows that the effective viscosity of the active bath may become negative in some regime. Finally, we develop a minimum 1D theoretical model to further probe the mechanism underlying the directed movement and self-sustained oscillation of the passive particle. Our findings reveal the effect of the moving boundary on the active bath and demonstrate a novel method to extract practical mechanical work from the active bath to propel microdevices.

How to capture active Marangoni surfers.

Surfers at the air-water interface form a large subset of the domain of active matter systems. They range from the water strider in the biological world to soluto-capillary effect driven artificial boats. In this work, we propose a general protocol to capture soluto-capillary effect driven interfacial surfers. By locally modifying the air-water interface using the perturbation from a micro-air-pump, these boats are reliably captured in the region of influence (ROI) of the perturbation. The surfers begin to explore the available space freely again once the perturbation is switched off. This method is successfully generalized to a couple of distinct surface-active chemicals used as fuel for the boats. Control experiments involving passive particles validate the results as being significantly better than purely mechanical "herding" of the particles. A possible mechanism behind the observed "trapping" is proposed.

Backscattering enhancement, vanishing extinction, and morphological effects of active scatterers

Using analytical Lorenz–Mie scattering formalism and numerical methods, we analyze the response of active particles to electromagnetic waves. The particles are composed of homogeneous, non-magnetic, and dielectrically isotropic medium. Spherical scatterers and sharp and rounded cubes are treated. The absorption cross section of active particles is negative, thus showing gain in their electromagnetic response. Since the scattering cross section is always positive, their extinction can be either positive, negative, or zero. We construct a five-class categorization of active and passive dielectric particles. We point out the enhanced backscattering phenomenon that active scatterers display and also discuss extinction paradox and optical theorem. Finally, using COMSOL Multiphysics and an in-house method-of-moments code, the effects of the non-sphericity of active scatterers on their electromagnetic response are illustrated.

Pattern formation and flocking for particles near the jamming transition on resource gradient substrates.

We numerically examine a bidisperse system of active and passive particles coupled to a resource substrate. The active particles deplete the resource at a fixed rate and move toward regions with higher resources, while all of the particles interact sterically with each other. We show that at high densities, this system exhibits a rich variety of pattern-forming phases along with directed motion or flocking as a function of the relative rates of resource absorption and consumption as well as the active to passive particle ratio. These include partial phase separation into rivers of active particles flowing through passive clusters, strongly phase separated states where the active particles induce crystallization of the passive particles, mixed jammed states, and fluctuating mixed fluid phases. For higher resource recovery rates, we demonstrate that the active particles can undergo motility-induced phase separation, while at high densities, there can be a coherent flock containing only active particles or a solid mixture of active and passive particles. The directed flocking motion typically shows a transient in which the flow switches among different directions before settling into one direction, and there is a critical density below which flocking does not occur. We map out the different phases as function of system density, resource absorption and recovery rates, and the ratio of active to passive particles.

Persistence of an active asymmetric rigid Brownian particle in two dimensions.

We have studied the persistence probability p(t) of an active Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the probability of a stochastic variable that has not changed its signin a given fixed time interval. We have investigated two cases: (1) diffusion of a free active particle and (2) that of a harmonically trapped particle. In our earlier work, by Ghosh et al. [J. Chem. Phys. 152, 174901 (2020)], we had shown that p(t) can be used to determine the translational and rotational diffusion constant of an asymmetrically shaped particle. The method has the advantage that the measurement of the rotational motion of the anisotropic particle is not required. In this paper, we extend the study to an active anisotropic particle and show how the persistence probability of an anisotropic particle is modified in the presence of a propulsion velocity. Furthermore, we validate our analytical expression against the measured persistence probability from the numerical simulations of single particle Langevin dynamics and test whether the method proposed in our earlier work can help distinguish between active and passive anisotropic particles.

The dynamics of single-to-multi layer transition in bacterial swarms

Wet self-propelled rods at high densities can exhibit a state of mesoscale turbulence: a disordered lattice of vortices with chaotic dynamics and a characteristic length scale. Such a state is commonly studied by a two-dimensional continuum model. However, less is known about the dynamic behaviour of self-propelled rods in three- or quasi-two- dimensions, which can be found in biological systems, for example, during the formation of bacterial aggregates and biofilms. In this study, we characterised the formation of multi-layered islands in a monolayer of swarming cells using the rod-shaped bacteria B. subtilis as a model system. We focused on how bacteria form multiple layers and how the presence of stress affects the multiple layer formation. Following our previous study where we reported that the initiation of the multilayer formation can be accounted by the framework of motility-induced phase separation (MIPS), this study analysed how this phase separation is impacted by the presence of stress, specifically under the exposure to a gradient of antibiotic. The analyses show that in the presence of an antibiotic gradient, the multi-layer formation happens by a nucleation and growth of well-defined multilayered clusters instead of by the uncontrolled emergence of the multilayer, resembling the traditional thermodynamic processes of binodal and spinodal decomposition respectively. Finally, the multilayer gives place to waves of bacteria that can travel towards high concentrations of antibiotics and that resemble travelling waves predicted by simulations of mixtures of passive and active particles.

Liquid-hexatic-solid phases in active and passive Brownian particles determined by stochastic birth and death events.

We study the effects of stochastic birth and death processes on the structural phases of systems of active and passive Brownian particles subject to volume exclusion. The total number of particles in the system is a fluctuating quantity, determined by the birth and death parameters and on the activity of the particles. As the birth and death parameters are varied, we find liquid, hexatic, and solid phases. For passive particles, these phases are found to be spatially homogeneous. For active particles, motility-induced phase separation (coexisting hexatic and liquid phases) occurs for large activity and sufficiently small birth rates. We also observe a reentrant transition to the hexatic phase when the birth rate is increased. This results from a balance of an increasing number of particles filling the system, and a larger number of defects resulting from the birth and death dynamics.

Nonequilibrium dynamical structure factor of a dilute suspension of active particles in a viscoelastic fluid.

In this work we investigate the dynamics of the number-density fluctuations of a dilute suspension of active particles in a linear viscoelastic fluid. We propose a model for the frequency-dependent diffusion coefficient of the active particles which captures the effect of rotational diffusion on the persistence of their self-propelled motion and the viscoelasticity of the medium. Using fluctuating hydrodynamics, the linearized equationsfor the active suspension are derived, from which we calculate its dynamic structure factor and the corresponding intermediate scattering function. For a Maxwell-type rheological model, we find an intricate dependence of these functions on the parameters that characterize the viscoelasticity of the solvent and the activity of the particles, which can significantly deviate from those of an inert suspension of passive particles and of an active suspension in a Newtonian solvent. In particular, in some regions of the parameter space we uncover the emergence of oscillations in the intermediate scattering function at certain wave numbers which represent the hallmark of the nonequilibrium particle activity in the dynamical structure of the suspension and also encode the viscoelastic properties of the medium.

Phase separation during sedimentation of dilute bacterial suspensions

Numerous natural systems depend on the sedimentation of passive particles in the presence of swimming microorganisms. Here, we investigate the dynamics of the sedimentation of spherical colloids at various E. coli concentrations within the dilute regime. Results show the appearance of two sedimentation fronts: a spherical particle front and the bacteria front. We find that the bacteria front behave diffusive at short times, whereas at long times it decays linearly. The sedimentation speed of passive particles decays at a constant speed and decreases as bacteria concentration (ϕb) is increased. As ϕb is increased further, the sedimentation speed becomes independent of ϕb. The timescales of the bacteria front are associated with the particle settling speeds. Remarkably, all experiments collapse onto a single master line by using the bacteria front timescale. A phenomenological model is proposed that captures the sedimentation of passive particles in active fluids.

Force-induced wrapping phase transition in activated cellular uptake

Intracellular pathogens, including all viruses and many bacteria, enter a host cell through either passive endocytosis or active self-propulsion. Though the cellular uptake of passive particles via endocytic process has been studied extensively, little work has been done on the active entry of self-propelled pathogens, such as Listeria monocytogenes. Here, we present a theoretical model to investigate the adhesive wrapping of a self-propelled particle by a plasma membrane, and find a type of first-order wrapping transition from a small partial wrapping state to a large partial wrapping state triggered by the active force. The phase diagram displays more complex behaviors compared with the passive wrapping mediated merely by adhesion. We also find that a tubular protrusion can be formed if the active force exceeds a force barrier. These results may provide a useful guidance to the study of activity-driven cellular entry of active particles into cells.

Derivation and analysis of a phase field crystal model for a mixture of active and passive particles

We discuss an active phase field crystal (PFC) model that describes a mixture of active and passive particles. First, a microscopic derivation from dynamical density functional theory is presented that includes a systematic treatment of the relevant orientational degrees of freedom. Of particular interest is the construction of the nonlinear and coupling terms. This allows for interesting insights into the microscopic justification of phenomenological constructions used in PFC models for active particles and mixtures, the approximations required for obtaining them, and possible generalizations. Second, the derived model is investigated using linear stability analysis and nonlinear methods. It is found that the model allows for a rich nonlinear behavior with states ranging from steady periodic and localized states to various time-periodic states. The latter include standing, traveling, and modulated waves corresponding to spatially periodic and localized traveling, wiggling, and alternating peak patterns and their combinations.

Formation and heating of chromospheric fibrils in a radiation-MHD simulation

Aims. We examine the movements of mass elements within dense fibrils using passive tracer particles (corks) in order to understand the creation and destruction processes of fibrils. Methods. Simulated fibrils were selected at times when they were visible in a Hα image proxy. The corks were selected within fibril Hα formation regions. From this set, we selected a cork and constructed the field line passing through it. Other fibrilar corks close to this field line were also selected and pathlines were constructed, revealing the locations of the mass elements forwards and backwards in time. Finally, we analysed the forces acting on these mass elements. Results. The main process of fibrilar loading in the simulation is different to the mass loading scenario in which waves steepen into shocks and push material upwards along the field lines from locations near their footpoints. The twisted, low-lying field lines were destabilised and then they untwisted, lifting the material trapped above their apexes via the Lorentz force. Subsequently, the majority of the mass drained down the field lines towards one or both footpoints under the influence of gravity. Material with large horizontal velocities could also be elevated in rising field lines, creating somewhat parabolic motions, but the material was not generally moving upward along a stationary magnetic field line during loading. Conclusions. The processes observed in the simulation are additional scenarios that are plausible. The criteria for observing such events are described in this work. We note that it is desirable for our simulations to also be able to form more densely packed fibrils from material fed from the base of field footpoints. The experimental parameters required to achieve this are also discussed in this paper.