Influence of thermal fluctuations on active diffusion at large Péclet numbers
Oliver T. Dyer, Robin C. Ball
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33 pages, 8 figures. The following article has been submitted to the journal: Physics of Fluids. If/after it is published, it will be found at https://aip.scitation.org/journal/phf
Wavelet Monte Carlo dynamics simulations are used to study the dynamics of passive particles in the presence of microswimmers, taking account of the often-omitted thermal motion alongside the hydrodynamic flows generated by the swimmers. Although the Péclet numbers considered are large, we find the thermal motion to have a significant effect on the dynamics of our passive particles, and can be included as a decorrelation factor in the velocity autocorrelation with a decay time proportional to the Péclet number. Similar decorrelation factors come from swimmer rotations, e.g.~run and tumble motion, and apply to both entrainment and far field loop contributions. These decorrelation factors lead to active diffusivity having a weak apparent power law close to $Pe^{0.2}$ for small tracer-like particles at Péclet numbers appropriate for E. coli swimmers at room temperature. Meanwhile, the reduced hydrodynamic response of large particles to nearby forces has a corresponding reduction in active diffusivity in that regime. Together, they lead to a non-monotonic dependence of active diffusivity on particle size that can shed light on similar behaviour observed in experiments by Patteson et al.
The dynamics of adhesion of a spherical micro-particle to a ligand-coated wall, in shear flow, is studied using a Langevin equation that accounts for thermal fluctuations, hydrodynamic interactions and adhesive interactions. Contrary to the conventional assumption that thermal fluctuations play a negligible role at high P$\acute{e}$clet numbers, we find that for particles with low surface densities of receptors, rotational diffusion caused by fluctuations about the flow and gradient directions aids in bond formation, leading to significantly greater adhesion on average, compared to simulations…
We derive and numerically solve a surface active nematodynamics model. We validate the numerical approach on a sphere and analyse the influence of hydrodynamics on the oscillatory motion of topological defects. For ellipsoidal surfaces the influence of geometric forces on these motion patterns is addressed by taking into account the effects of intrinsic as well as extrinsic curvature contributions. The numerical experiments demonstrate the stronger coupling with geometric properties if extrinsic curvature contributions are present and provide a possibility to tune flow and defect motion by sur…
Defect dynamics in a thin active nematic layer is studied by asymptotic matching of solutions in the defect core and the far field. The analysis is facilitated by the correspondence between the 2D nematic and complex scalar field models. Self-propulsion and topological interactions are identified as the primary drivers of the defect motion, surpassing the influence of both passive backflow and active flow induced by other defects.
Active matter studies are increasingly geared towards the high-density or glassy limit. This is mainly inspired by the remarkable resemblance between active glassy materials and conventional passive glassy matter. Interestingly, within this limit it has recently been shown that the relaxation dynamics of active quasi-hard spheres is non-monotonic and most enhanced by activity when the intrinsic active length scale (e.g., the persistence length) is equal to the cage length, i.e. the length scale of local particle caging. This optimal enhancement effect is claimed to result from the most efficie…
Micrometer scale colloidal particles that propel in a deterministic fashion in response to local environmental cues are useful analogs to self-propelling entities found in nature. Both natural and synthetic active colloidal systems are often near boundaries or are located in crowded environments. Herein, we describe experiments in which we measured the influence of hydrogen peroxide concentration and dispersed polyethylene glycol (PEG) on the clustering behavior of 5 micrometer catalytic active Janus particles at low concentration. We found the extent to which clustering occurred in ensembles …
Suspensions of self-motile, elongated particles are a topic of significant current interest, exemplifying a form of `active matter'. Examples include self-propelling bacteria, algae and sperm, and artificial swimmers. Ericksen's model of a transversely-isotropic fluid [J. L. Ericksen, Colloid Polym. Sci. 173(2):117-122 (1960)] treats suspensions of non-motile particles as a continuum with an evolving preferred direction; this model describes fibrous materials as diverse as extracellular matrix, textile tufts and plant cell walls. Director-dependent effects are incorporated through a modified s…
Dense assemblies of self-propelled particles undergo a nonequilibrium form of glassy dynamics. Physical intuition suggests that increasing departure from equilibrium due to active forces fluidifies a glassy system. We falsify this belief by devising a model of self-propelled particles where increasing departure from equilibrium can both enhance or depress glassy dynamics, depending on the chosen state point. We analyze a number of static and dynamic observables and suggest that the location of the nonequilibrium glass transition is primarily controlled by the evolution of two-point static dens…
We investigate the stochastic dynamics of one sedimenting active Brownian particle in three dimensions under the influence of gravity and passive fluctuations in the translational and rotational motion. We present an analytical solution of the Fokker--Planck equation for the stochastic process which allows us to describe the dynamics of the active Brownian particle in three dimensions. We address the time evolution of the monopole, the polarization, and the steady-state solution. We also perform Brownian dynamics simulations and study the effect of the activity of the particles on their collec…
Using a minimal model of active Brownian discs, we study the effect of a crucial parameter, namely the softness of the inter-particle repulsion, on motility-induced phase separation. We show that an increase in particle softness reduces the ability of the system to phase-separate and the system exhibit a delayed transition. After phase separation, the system state properties can be explained by a single relevant lengthscale, the effective inter-particle distance. We estimate this lengthscale analytically and use it to rescale the state properties at dense phase for systems with different inter…
Because active particles break time-reversal symmetry, an active fluid can sustain currents even without an external drive. We show that when a passive body is placed in a fluid of pairwise interacting active particles, it generates long-range currents, corresponding to density and pressure gradients. By using a multipole expansion and a far-field constitutive relation, we show that the leading-order behavior of all three corresponds to a source dipole. Then, when two bodies or more are placed in the active fluid, generic long-range interactions between the bodies occur. We find these to be qu…
In this paper we provide high precision estimates of the phase diagram of active Brownian particles. We extract coexisting densities from simulations of phase separated states in an elongated box (slab geometry) which minimizes finite-size effects and allows for precise determination of points on the binodal lines. Using this method, we study the influence of both shape and dimensionality on the two-phase region. Active spheres and dumbbells of active particles are compared to the known phase diagram of active Brownian disks. In the case of dimers, both correlated and uncorrelated propulsion o…
Self-propelled particles can undergo complex dynamics due to a range of bulk and surface interactions. When a particle is embedded in a host solid near its bulk melting temperature, the latter may melt at the surface of the former in a process known as interfacial premelting. The thickness of the melt film depends on the temperature, impurities, material properties and geometry. A temperature gradient is accompanied by a thermomolecular pressure gradient that drives the interfacial liquid from high to low temperatures and hence the particle from low to high temperatures, in a process called th…
We study unbiased translocation of a flexible polymer chain through a membrane pore under the influence of active noise and steric exclusion using Langevin dynamics simulations. The active noise is incorporated by introducing nonchiral and chiral active particles on one or both sides of the membrane. Translocation of the polymer into either side of the pore is assisted by an effective pulling due to particle activity and is hindered by an effective pushing due to steric repulsions between the polymer and active particles. As a result of the competition between these effective forces, we find a…
The influence of frequency and gravity on the orientation of active metallo-dielecric Janus particles translating under a uniform applied alternating-current electric field
Biological microswimmers often inhabit a porous or crowded environment such as soil. In order to understand how such a complex environment influences their spreading, we numerically study non-interacting active Brownian particles (ABPs) in a two-dimensional random Lorentz gas. Close to the percolation transition in the Lorentz gas, they perform the same subdiffusive motion as ballistic and diffusive particles. However, due to their persistent motion they reach their long-time dynamics faster than passive particles and also show superdiffusive motion at intermediate times. While above the criti…
We describe simulations of active Brownian particles carried out to explore how dynamics and clustering are influenced by particle shape. Our particles are composed of four disks, held together by springs, whose relative size can be varied. These compound objects can be tuned smoothly from having a concave to a convex surface. We show that even two of these composite particles can exhibit collective motion modifying the effective Peclet number. We then investigate how particle geometry can be used to explain the phase behaviour of many such particles.
We study the distribution of active, noninteracting particles over two bulk states separated by a ratchet potential. By solving the steady-state Smoluchowski equations in a flux-free setting, we show that the ratchet potential affects the distribution of particles over the bulks, and thus exerts an influence of infinitely long range. As we show, crucial for having such a long-range influence is an external potential that is nonlinear. We characterize how the difference in bulk densities depends on activity and on the ratchet potential, and we identify power law dependencies on system parameter…
Janus particles propel themselves by generating concentration gradients along their active surface. This induces a flow near the surface, known as the diffusio-osmotic slip, which propels the particle even in the absence of externally applied concentration gradients. In this work, we study the influence of viscoelasticity and shear-thinning (described by the second-order-fluid and Carreau model, respectively) on the diffusio-osmotic slip on an active surface. Using matched asymptotic expansions, we provide an analytical expression for the modification of slip induced by the non-Newtonian behav…
Tracking experiments in dense biological tissues reveal a diversity of sources f or local energy injection at the cell scale. The effect of cell motility has been largely studied, but much less is known abo ut the effect of the observed volume fluctuations of individual cells. We devise a simple microscopic model of `actively-deforming' particles where local fluctuations of the particle size constitute a unique source of motion. We demonstrate that collective motion can emerge under the sole influence of such active volume fluctuations. We interpret the onset of diffusive motion as a nonequili…
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…
An active swimmer can tow a passive cargo by binding it to form a self-propelling dimer. The orientation of the cargo relative to the axis of the active dimer's head is determined by the hydrodynamic interactions associated with the propulsion mechanism of the latter. We show how the tower-cargo angular configuration greatly influences the dimer's diffusivity and, therefore, the efficiency of the active swimmer as a micro-towing motor.
We consider an ideal gas of active Brownian particles that undergo self-propelled motion and both translational and rotational diffusion under the influence of gravity. We solve analytically the corresponding Smoluchowski equation in two space dimensions for steady states. The resulting one-body density is given as a series, where each term is a product of an orientation-dependent Mathieu function and a height-dependent exponential. A lower hard wall is implemented as a no-flux boundary condition. Numerical evaluation of the suitably truncated analytical solution shows the formation of two dif…
We recently argued that a self-propelled particle is formally equivalent to a system consisting of two subsystems coupled by a non-reciprocal interaction [Phys. Rev. E 100, 050603(R) (2019)]. Here we show that this non-reciprocal coupling allows to extract useful work from a single self-propelled particle maintained at constant temperature, by using an aligning interaction to influence correlations between the particle's position and self-propulsion.
We investigate the steady-state and dynamical properties of a reciprocal many-body system consisting of self-propelled active particles with local alignment interactions that exists within a fan-shaped neighborhood of each particle. We find that the nonreciprocity can emerge in this reciprocal system once the spontaneous symmetry breaking is present, and the effective description of the system assumes a non-Hermitian structure that directly originates from the emergent nonreciprocity. This emergent nonreciprocity can impose strong influences on the properties the system. In particular, it can …
We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modeled as a two state model; the particle moves with a constant propulsion strength but its orientation switches from one state to other as in a random telegraphic process. We study the influence of a finite resetting rate $r$ on the mean first passage time to a fixed target of a single free Active Brownian Particle and map this result using an effective diffusion process. As in the case of a passive Brownian particle, we can find an optimal …
We investigate the influence of external forces on the collective dynamics of interacting active Brownian particles in two as well as three spatial dimensions. Via explicit coarse graining, we derive predictive models that are applicable for space- and time-dependent external force fields. We study these models for the cases of gravity and harmonic traps. In particular, we derive a generalized barometric formula for interacting active Brownian particles under gravity that is valid for low to high concentrations and activities of the particles. Furthermore, we show that one can use an external …
