Nonadditivity of fluctuation-induced forces in fluidized granular media

Tunable depletion force in active and crowded environments

We adopt two-dimensional Langevin dynamics simulations to study the effective interactions between two passive colloids in a bath crowded with active particles. We mainly pay attention to the significant effects of active particle size, crowding-activity coupling, and chirality. First, a transition of depletion force from repulsion to attraction is revealed by varying particle size. Moreover, larger active crowders with sufficient activity can generate strong attractive force, which is in contrast to the cage effect in passive media. It is interesting that the attraction induced by large active crowders follows a linear scaling with the persistence length of active particles. Second, the effective force also experiences a transition from repulsion to attraction as volume fraction increases, as a consequence of the competition between the two contrastive factors of activity and crowding. As bath volume fraction is relatively small, activity generates a dominant repulsion force, while as the bath becomes concentrated, crowding-induced attraction becomes overwhelming. Lastly, in a chiral bath, we observe a very surprising oscillation phenomenon of active depletion force, showing an evident quasiperiodic variation with increasing chirality. Aggregation of active particles in the vicinity of the colloids is carefully examined, which serves as a reasonable picture for our observations. Our findings provide an inspiring strategy for the tunable active depletion force by crowding, activity, and chirality.

Asymmetric and long range interactions in shaken granular media

We use a computational model to investigate the emergence of interaction forces between pairs of intruders in a horizontally vibrated granular fluid. The time evolution of a pair of particles shows a maximum of the likelihood to find the pair at contact in the direction of shaking. This relative interaction is further studied by fixing the intruders in the simulation box where we identify effective mechanical forces and torques between particles and quantify an emergent long range attractive force as a function of the shaking relative angle, the amplitude, and the packing density of grains. We determine the local density and kinetic energy profiles of granular particles along the axis of the dimer to find no gradients in the density fields and additive gradients in the kinetic energies.

Nonequilibrium forces following quenches in active and thermal matter

Nonequilibrium systems with conserved quantities like density or momentum are known to exhibit long-ranged correlations. This, in turn, leads to long-ranged fluctuation-induced (Casimir) forces, predicted to arise in a variety of nonequilibrium settings. Here, we study such forces, which arise transiently between parallel plates or compact inclusions in a gas of particles, following a change ("quench") in temperature or activity of the medium. Analytical calculations, as well as numerical simulations of passive or active Brownian particles, indicate two distinct forces: (i) The immediate effect of the quench is adsorption or desorption of particles of the medium to the immersed objects, which in turn initiates a front of relaxing (mean) density. This leads to time-dependent density-induced forces. (ii) A long-term effect of the quench is that density fluctuations are modified, manifested as transient (long-ranged) (pair-)correlations that relax diffusively to their (short-ranged) steady-state limit. As a result, transient fluctuation-induced forces emerge. We discuss the properties of fluctuation-induced and density-induced forces as regards universality, relaxation as a function of time, and scaling with distance between objects. Their distinct signatures allow us to distinguish the two types of forces in simulation data. Our simulations also show that a quench of the effective temperature of an active medium gives rise to qualitatively similar effects to a temperature quench in a passive medium. Based on this insight, we propose several scenarios for the experimental observation of the forces described here.

Casimir effect between pinned particles in two-dimensional jammed systems

The Casimir effect arises when long-ranged fluctuations are geometrically confined between two surfaces, leading to a macroscopic force. Traditionally, these forces have been observed in quantum systems and near critical points in classical systems. Here we show the existence of Casimir-like forces between two pinned particles immersed in two-dimensional systems near the jamming transition. We observe two components to the total force: a short-ranged, depletion force and a long-ranged, repulsive Casimir-like force. The Casimir-like force dominates as the jamming transition is approached, and when the pinned particles are much larger than the ambient jammed particles. We show that this repulsive force arises due to a clustering of particles with strong contact forces around the perimeter of the pinned particles. As the separation between the pinned particles decreases, a region of high-pressure develops between them, leading to a net repulsive force.

Transient Casimir Forces from Quenches in Thermal and Active Matter

We compute fluctuation-induced (Casimir) forces for classical systems after a temperature quench. Using a generic coarse-grained model for fluctuations of a conserved density, we find that transient forces arise even if the initial and final states are force free. In setups reminiscent of Casimir (planar walls) and van der Waals (small inclusions) interactions, we find comparable exact universal expressions for the force. Dynamical details only scale the time axis of transient force curves. We propose that such quenches can be achieved, for instance, in experiments on active matter, employing tunable activity or interaction protocols.

Persistent-random-walk approach to anomalous transport of self-propelled particles

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's displacement. It is shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short-time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.

Granular segregation driven by particle interactions

We report the results of an experimental study of particle-particle interactions in a horizontally shaken granular layer that undergoes a second order phase transition from a binary gas to a segregation liquid as the packing fraction C is increased. By focusing on the behavior of individual particles, the effect of C is studied on (1) the process of cluster formation, (2) cluster dynamics, and (3) cluster destruction. The outcomes indicate that the segregation is driven by two mechanisms: attraction between particles with the same properties and random motion with a characteristic length that is inversely proportional to C. All clusters investigated are found to be transient and the probability distribution functions of the separation times display a power law tail, indicating that the splitting probability decreases with time.

Three-body critical Casimir forces

Within mean-field theory we calculate universal scaling functions associated with critical Casimir forces for a system consisting of three parallel cylindrical colloids immersed in a near-critical binary liquid mixture. For several geometrical arrangements and boundary conditions at the surfaces of the colloids we study the force between two colloidal particles in the direction normal to their axes, analyzing the influence of the presence of a third particle on that force. Upon changing temperature or the relative positions of the particles we observe interesting features such as a change of sign of this force caused by the presence of the third particle. We determine the three-body component of the forces acting on one of the colloids by subtracting the pairwise forces from the total force. The three-body contribution to the total critical Casimir force turns out to be more pronounced for small surface-to-surface distances between the colloids as well as for temperatures close to criticality. Moreover, we compare our results with similar ones for other physical systems such as three atoms interacting via van der Waals forces.

Anomalous diffusion of self-propelled particles in directed random environments

We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of individual random walkers, which enables us to identify the contributions of key parameters: the motor processivity, and the anisotropy and heterogeneity of the underlying network. We prove the existence of different dynamical regimes of anomalous motion, and that the crossover times between these regimes as well as the asymptotic diffusion coefficient can be increased by several orders of magnitude within biologically relevant control parameter ranges. In terms of motion in continuous space, the interplay between stepping strategy and persistency of the walker is established as a source of anomalous diffusion at short and intermediate time scales.

Flow-mediated coupling on projectiles falling within a superlight granular medium

Interesting collective motion emerges when several heavy intruder disks fall in a loose packed, quasi-two-dimensional granular bed of extremely light grains [F. Pacheco-Vázquez and J. C. Ruiz-Suárez, Nat. Commun. 1, 123 (2010)]. In particular, when two disks impact side by side, they initially repel and then they attract each other until they finally stop. Here we perform experiments and discrete-element soft-particle simulations to determine the range of action and the origin of these attractive and repulsive flow-mediated forces. We find that (1) the drag force on the disks fluctuate with a characteristic length linked to force chains that build up and break; (2) the repulsive force is present when the separation of the intruder disks is less than 6 times the size of the grains of the granular bed, which is the size of an aperture that allows a continuous discharge flow from a container; (3) the attractive force has a range of action between 5 and 6 times the size of the intruder disks; and (4) attraction exists only when intruders move faster than 1 m/s. These results suggest that repulsion originates from jamming of grains between intruders, and it supports the idea that attraction could be due to a "granular pressure" drop in the region between intruders caused by a high flow velocity of grains: a Bernoulli-like effect. However, our results do not rule out other mechanisms of interaction, like fluctuation-induced forces.

Long-range interactions in randomly driven granular fluids

We study the long-range spatial correlations in the nonequilibrium steady state of a randomly driven granular fluid with the emphasis on obtaining the explicit form of the static structure factors. The presence of immobile particles immersed in such a fluidized bed of fine particles leads to the confinement of the fluctuation spectrum of the hydrodynamic fields, which results in effective long-range interactions between the intruders. The analytical predictions are in agreement with the results of discrete element method simulations. By changing the shape and orientation of the intruders, we address how the effective force is affected by small changes in the boundary conditions.