Nonlinear dynamics, rectification, and phase locking for particles on symmetrical two-dimensional periodic substrates with dc and circular ac drives

Particle dispersion through porous media with heterogeneous attractions

Porous media used in many practical applications contain natural spatial variations in composition and surface charge that lead to heterogeneous physicochemical attractions between the media and transported particles. We performed Stokesian dynamics (SD) simulations to examine the effects of heterogeneous attractions on quiescent diffusion and hydrodynamic dispersion of particles within geometrically ordered arrays of nanoposts. We find that transport under quiescent conditions occurs by two mechanisms, diffusion through the void space and intermittent hopping between the attractive wells of different nanoposts. As the attraction heterogeneity increases, the latter mechanism becomes dominant, resulting in an increase in the particle trajectory tortuosity, deviations from Gaussian behavior in the particle displacement distributions, and a decrease in the long-time particle diffusivity. Similarly, under flow conditions corresponding to low Péclet number (Pe), increased attraction heterogeneity leads to transient localization near the nanoposts, resulting in a broadening of the particle distribution and enhanced longitudinal dispersion in the direction of flow. At high Pe where advection strongly dominates, however, the longitudinal dispersion coefficient is insensitive to attraction heterogeneity and exhibits Taylor-Aris dispersion behavior. Our findings provide insight into how heterogeneous interactions may influence particle transport in complex 3-D porous media.

Nanoparticle dispersion in porous media: Effects of attractive particle-media interactions

We investigate the effects of physicochemical attractions on the transport of finite-sized particles in three-dimensional ordered nanopost arrays using Stokesian dynamics simulations. We find that weak particle-nanopost attractions negligibly affect diffusion due to the dominance of Brownian fluctuations. Strong attractions, however, significantly hinder particle diffusion due to localization of particles around the nanoposts. Conversely, under flow, attractions significantly enhance longitudinal dispersion at low to moderate Péclet number (Pe). At high Pe, by contrast, advection becomes dominant and attractions weakly enhance dispersion. Moreover, attractions frustrate directional locking at moderate flow rates, and shift the onset of this behavior to higher Pe.

Separation of suspended particles in microfluidic systems by directional locking in periodic fields

We investigate the transport and separation of overdamped particles under the action of a uniform external force in a two-dimensional periodic energy landscape. Exact results are obtained for the deterministic transport in a square lattice of parabolic, repulsive centers that correspond to a piecewise-continuous linear-force model. The trajectories are periodic and commensurate with the obstacle lattice and exhibit phase-locking behavior in that the particle moves at the same average migration angle for a range of orientation of the external force. The migration angle as a function of the orientation of the external force has a Devil's staircase structure. The first transition in the migration angle was analyzed in terms of a Poincare map, showing that it corresponds to a tangent bifurcation. Numerical results show that the limiting behavior for impenetrable obstacles is equivalent to the high Peclet number limit in the case of transport of particles in a periodic pattern of solid obstacles. Finally, we show how separation occurs in these systems depending on the properties of the particles.

Light at work: the use of optical forces for particle manipulation, sorting, and analysis

We review the combinations of optical micro-manipulation with other techniques and their classical and emerging applications to non-contact optical separation and sorting of micro- and nanoparticle suspensions, compositional and structural analysis of specimens, and quantification of force interactions at the microscopic scale. The review aims at inspiring researchers, especially those working outside the optical micro-manipulation field, to find new and interesting applications of these methods.

Phase synchronization in tilted inertial ratchets as chaotic rotators

The phenomenon of phase synchronization for a particle in a periodic ratchet potential is studied. We consider the deterministic dynamics in the underdamped case where the inertia plays an important role since the dynamics can become chaotic. The ratchet potential is tilted due to a constant external force and is rocking by an external periodic forcing. This potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of the external periodic forcing; this oscillator then acquires an intrinsic frequency that can be locked with the frequency of the external driving. We introduced an instantaneous linear phase, using a set of discrete time markers, and the associated average frequency, and show that this frequency can be synchronized with the frequency of the driving. We calculate Arnold tongues in a two-dimensional parameter space and discuss their implications for the chaotic transport in ratchets. We show that the local maxima in the current correspond to the borders of these Arnold tongues; in this way we established a link between optimal transport in ratchets and phase synchronization.

Ratchet effect and nonlinear transport for particles on random substrates with crossed ac drives

We show in simulations that overdamped interacting particles in two dimensions with a randomly disordered substrate can exhibit novel nonequilibrium transport phenomena including a transverse ratchet effect, where a combined dc drive and circular ac drive produce a drift velocity in the direction transverse to the applied dc drive. The random disorder does not break any global symmetry; however, in two dimensions, symmetry breaking occurs due to the chirality of the circular drive. In addition to inducing the transverse ratchet effect, increasing the ac amplitude also strongly affects the longitudinal velocity response and can produce what we term an overshoot effect where the longitudinal dc velocity is higher in the presence of the ac drive than it would be for a dc drive alone. We also find a dynamical reordering transition upon increasing the ac amplitude. In the absence of a dc drive, it is possible to obtain a ratchet effect when the combined ac drives produce particle orbits that break a reflection symmetry. In this case, as the ac amplitude increases, current reversals can occur. These effects may be observable for vortices in type-II superconductors as well as for colloids interacting with random substrates.

One-dimensional optical thermal ratchets

The ability to rectify Brownian forces with spatially extended time-varying light fields creates new opportunities for studying the statistical properties of thermal ratchet models and to exploit these models' interesting and useful properties for practical applications. This paper describes experimental studies of one-dimensional thermal ratchets implemented with the holographic optical trapping technique applied to fluid-borne colloidal spheres. These studies demonstrate the complementary roles of global spatiotemporal symmetry and local dynamics in establishing the direction of ratchet-induced motion and also highlight avenues for future advances in higher-dimensional systems.

Elastically coupled two-dimensional Brownian motors

Many workers have theoretically and numerically studied Brownian motors (ratchet models) as models for molecular motors for many years. Their studies have been mainly concerned about one-dimensional motion of a particle or coupled particles experiencing spatially asymmetric interaction force. In this paper, we introduce a coupled flashing ratchet model, that is, elastically coupled Brownian particles with their own easily advancing directions under the on-and-off (or occasional) influence of two-dimensional interaction force asymmetric in the easily advancing direction of each particle. The dynamics of the model is investigated by computer simulation and characteristic motion of the particles in the two-dimensional space is observed. Our model is also studied as that for molecular motors in muscle contraction and the simulation results are compared with those of in vitro biological experiments in motility assays of the molecular motors. We succeed in reproducing the experimental results qualitatively with our model.