Analytical approach to sorting in periodic and random potentials

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.

Collective effects and pattern formation for directional locking of disks moving through obstacle arrays

We examine directional locking effects in an assembly of disks driven through a square array of obstacles as the angle of drive rotates from 0^{∘} to 90^{∘}. For increasing disk densities, the system exhibits a series of different dynamic patterns along certain locking directions, including one-dimensional or multiple-row chain phases and density-modulated phases. For nonlocking driving directions, the disks form disordered patterns or clusters. When the obstacles are small or far apart, a large number of locking phases appear; however, as the number of disks increases, the number of possible locking phases drops due to the increasing frequency of collisions between the disks and obstacles. For dense arrays or large obstacles, we find an increased clogging effect in which immobile and moving disks coexist.

Critical dispersion of advecting-diffusing tracers in periodic landscapes of hard-wall symmetric potentials

Large-scale, time-asymptotic dispersion properties of diffusing tracers dragged by a uniform drive through a two-dimensional periodic lattice of hard-wall symmetric potentials are investigated. Dispersion is quantified by a typically anisotropic effective diffusivity tensor D, whose eigenvalues and eigenvectors depend on the dimensionless bare diffusivity 1/Pe for each given lattice geometry. Attention is focused on critical lattice geometries yielding sustained macroscale dispersion D([perpendicular]) along the direction orthogonal to the uniform drive in the limit where Pe→∞. A simple one-dimensional model is proposed, which predicts the anomalous scaling D([perpendicular])~1/[A(1)+A(2)log(Pe)].

Sorting colloidal particles into multiple channels with optical forces: prismatic optical fractionation

Brownian particles drifting through a periodically structured force landscape can become entrained by the landscape's symmetries. What direction a particular particle takes can depend strongly on subtle variations in its physical properties. Consequently, a homogeneously structured force field can sort a mixture of particles into spatially separated fractions, much as an optical prism refracts light into its component wavelengths. When the force landscape is implemented with structured light fields, such continuous multichannel sorting may be termed prismatic optical fractionation. We describe experimental and numerical studies of colloidal spheres' transport through periodic arrays of optical tweezers, which reveal an important role for three-dimensional motion in determining a drifting particle's fate. These studies also demonstrate sorting on the basis of statistically locked-in transport, in which brownian fluctuations contribute to direction selection.

Controlling chaotic transport in two-dimensional periodic potentials

We uncover and characterize different chaotic transport scenarios in perfect two-dimensional periodic potentials by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect (i.e., with no directed transport by symmetry breaking of zero-mean forces). After identifying relevant symmetries of the equations of motion, analytical estimates in parameter space for the occurrence of different transport scenarios are provided and confirmed by numerical simulations. These scenarios are highly sensitive to variations of the system's asymmetry parameters, including the eccentricity of the two-dimensional periodic potential and the direction of dc and ac forces, which could be useful for particle sorting purposes in those cases where chaos is unavoidable.

Exploiting lattice potentials for sorting chiral particles

Several ways are demonstrated of how periodic potentials can be exploited for sorting molecules or other small objects which only differ by their chirality. With the help of a static bias force, the two chiral partners can be made to move along orthogonal directions. Time-periodic external forces even lead to motion into exactly opposite directions.

Multidimensional optical fractionation of colloidal particles with holographic verification

The trajectories of colloidal particles driven through a periodic potential energy landscape can become kinetically locked-in to directions dictated by the landscape's symmetries. When the landscape is realized with a structured light field, the path a given particle follows has been predicted to depend exquisitely sensitively on such properties as the particle's size and refractive index. We confirm these predictions by measuring the transport of colloidal silica spheres through arrays of holographic optical traps, using holographic video microscopy to track individual spheres' motions in three dimensions and simultaneously to measure each sphere's radius and refractive index with part-per-thousand resolution. These measurements demonstrate optical fractionation's ability to sort with part-per-thousand resolution on multiple characteristics simultaneously.

Diffusion coefficient in periodic and random potentials

Transport and diffusion of particles on modulated surfaces is a nonequilibrium problem which is receiving a great deal of attention due to its technological applications, but analytical calculations are scarce. In earlier work, we developed a perturbative approach to begin to provide an analytic platform for predictions about particle trajectories over such surfaces. In some temperature and forcing regimes, we successfully reproduced results for average particle velocities obtained from numerical simulations. In this paper, we extend the perturbation theory to the calculation of higher moments, in particular the diffusion tensor and the skewness. Numerical simulations are used to check the domain of validity of the perturbative approach.

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.

Directing Brownian motion on a periodic surface

We consider an overdamped Brownian particle, exposed to a two-dimensional, square lattice potential and a rectangular ac drive. Depending on the driving amplitude, the linear response to a weak dc force along a lattice symmetry axis consist in a mobility in basically any direction. In particular, motion exactly opposite to the applied dc force may arise. Upon changing the angle of the dc force relatively to the square lattice, the particle motion remains predominantly opposite to the dc force. The basic physical mechanism consists in a spontaneous symmetry breaking of the unbiased deterministic particle dynamics.

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.

Localized and delocalized motion of colloidal particles on a magnetic bubble lattice

We study the motion of paramagnetic colloidal particles placed above magnetic bubble domains of a uniaxial garnet film and driven through the lattice by external magnetic field modulation. An external tunable precessing field propels the particles either in localized orbits around the bubbles or in superdiffusive or ballistic motion through the bubble array. This motion results from the interplay between the driving rotating signal, the viscous drag force and the periodic magnetic energy landscape. We explain the transition in terms of the incommensurability between the transit frequency of the particle through a unit cell and the modulation frequency. Ballistic motion dynamically breaks the symmetry of the array and the phase locked particles follow one of the six crystal directions.

Colloidal transport through optical tweezer arrays

Viscously damped particles driven past an evenly spaced array of potential energy wells or barriers may become kinetically locked in to the array, or else may escape from the array. The transition between locked-in and free-running states has been predicted to depend sensitively on the ratio between the particles' size and the separation between wells. This prediction is confirmed by measurements on monodisperse colloidal spheres driven through arrays of holographic optical traps.

Cellular and Colloidal Separation Using Optical Forces

The separation or sorting of cellular and colloidal particles is currently a central topics of research. In this chapter, we give an overview of the range of optical methods for cell sorting. We begin with an overview of fluorescence and magnetically activated cell sorting. We progress to describing methods at the microfluidic scale level particularly those exploiting optical forces. We distinguish between what we term passive and active schemes for sorting. Optical forces pertinent to the sorting schemes are described, notably the gradient force and the optical radiation pressure (or scattering force). We discuss some of the most recent advances. This includes techniques without fluid flow where we have either stationary or moving light patterns to initiate separation. Further methods have shown how using an externally driven flow either counter-propagating against a light field (optical chromatography) or over a periodic light pattern (an optical potential energy landscape) may result in the selection of particles and cells based on physical attributes such as size and refractive index. We contrast these schemes with the field of dielectrophoresis where electric field gradients may separate cells and also briefly mention the upcoming area of light-induced dielectrophoresis which marries the reconfigurability of optical fields with the power of dielectrophoresis.