Periodic Array Of Obstacles Research Articles

Vortex Lattices in Active Nematics with Periodic Obstacle Arrays.

We numerically model a two-dimensional active nematic confined by a periodic array of fixed obstacles. Even in the passive nematic, the appearance of topological defects is unavoidable due to planar anchoring by the obstacle surfaces. We show that a vortex lattice state emerges as activity is increased, and that this lattice may be tuned from "ferromagnetic" to "antiferromagnetic" by varying the gap size between obstacles. We map the rich variety of states exhibited by the system as a function of distance between obstacles and activity, including a pinned defect state, motile defects, the vortex lattice, and active turbulence. We demonstrate that the flows in the active turbulent phase can be tuned by the presence of obstacles, and explore the effects of a frustrated lattice geometry on the vortex lattice phase.

Active motion of tangentially driven polymers in periodic array of obstacles

One key question about transport of active polymers within crowded environments is how spatial order of obstacles influences their conformation and dynamics when compared to disordered media. To this end, we computationally investigate the active transport of tangentially driven polymers with varying degrees of flexibility and activity in two-dimensional square lattices of obstacles. Tight periodic confinement induces notable conformational changes and distinct modes of transport for flexible and stiff active filaments. It leads to caging of low activity flexible polymers inside the inter-obstacle pores while promoting more elongated conformations and enhanced diffusion for stiff polymers at low to moderate activity levels. The migration of flexible active polymers occurs via hopping events, where they unfold to move from one cage to another, similar to their transport in disordered media. However, in ordered media, polymers are more compact and their long-time dynamics is significantly slower. In contrast, stiff chains travel mainly in straight paths within periodic inter-obstacle channels while occasionally changing their direction of motion. This mode of transport is unique to periodic environment and leads to more extended conformation and substantially enhanced long-time dynamics of stiff filaments with low to moderate activity levels compared to disordered media. At high active forces, polymers overcome confinement effects and move through inter-obstacle pores just as swiftly as in open spaces, regardless of the spatial arrangement of obstacles. We explain the center of mass dynamics of semiflexible polymers in terms of active force and obstacle packing fraction by developing an approximate analytical theory.

Pattern formation and transport for externally driven active matter on periodic substrates (a)

We investigate the transport of interacting active run-and-tumble particles moving under an external drift force through a periodic array of obstacles for increasing drive amplitudes. For high activity where the system forms a motility-induced phase-separated state, there are several distinct dynamic phases including a low drive pinned cluster phase, an intermediate uniform fluid, and a higher drive stripe crystal state. The transitions between the phases are correlated with signatures in the transport curves, differential mobility, and power spectra of the velocity fluctuations. In contrast, in the low activity regime the transport curves and power spectra undergo little change as a function of drive. We argue that in the high activity limit, the behavior is similar to that of driven solids on periodic substrates, while in the low activity limit the system behaves like a driven fluid.

Effect of process parameters on separation efficiency in a deterministic lateral displacement device

Deterministic lateral displacement (DLD) is a hydrodynamic method known for its high-resolution sorting of particles. It achieves this through a periodic array of obstacles and laminar flow that passively directs particles along in two different directions depending on the particles’ diameter. Many prior publications have been dedicated to the structural and geometrical development of DLD arrays to improve separation performance; however, a successful separation requires much more than a well-designed array. This paper shows how separation performance is affected by process parameters. For this purpose, the design and fabrication of a DLD device are described. Then three experiments show how process parameters affect the performance of the device. The first experiment uses dye solutions to visualize the formation of a hydrodynamically focused sample stream. The second experiment shows that the particle separation performance (of 7- & 15-µm particles) is affected by the way output fluids are collected. Finally, the third experiment looks at the particle separation efficiency as the input flow rates and the ratio of buffer to sample are changed. The results show that the proper range for buffer and sample flow rate in this device is 1–10 and 0.1–1 (µl/min), respectively. The buffer to sample flow rate ratio of 10 gives the highest separation efficiency, but at a lower sample throughput. The optimized values are specific for our device but demonstrate processes that we believe are universal for DLD separations.

Reversible to irreversible transitions for cyclically driven particles on periodic obstacle arrays.

We examine the collective dynamics of disks moving through a square array of obstacles under cyclic square wave driving. Below a critical density, we find that the system organizes into a reversible state in which the disks return to the same positions at the end of every drive cycle. Above this density, the dynamics are irreversible and the disks do not return to the same positions after each cycle. The critical density depends strongly on the angle θ between the driving direction and a symmetry axis of the obstacle array, with the highest critical densities appearing at commensurate angles such as θ = 0° and θ = 45° and the lowest critical densities falling at θ = arctan(0.618), the inverse of the golden ratio, where the flow is the most degenerate. As the density increases, the number of cycles required to reach a reversible state grows as a power law with an exponent near ν = 1.36, similar to what is found in periodically driven colloidal and superconducting vortex systems.

Effective Toughness of Heterogeneous Materials with Rate-Dependent Fracture Energy.

We investigate the dynamic fracture of heterogeneous materials experimentally by measuring displacement fields as a rupture propagates through a periodic array of obstacles of controlled fracture energy. Our measurements demonstrate the applicability of the classical equation of motion of cracks at a discontinuity of fracture energy: the crack speed jumps at the entrance and exit of an obstacle, as predicted by the crack-tip energy balance within the brittle fracture framework. The speed jump amplitude is governed by the fracture energy contrast and by the combination of the rate dependency of the fracture energy and the inertia of the medium, which allows the crack to cross a fracture energy discontinuity at a constant energy release rate. This discontinuous dynamics and the rate dependence cause higher effective toughness, which governs the coarse-grained behavior of these cracks.

Directional locking effects for active matter particles coupled to a periodic substrate.

Directional locking occurs when a particle moving over a periodic substrate becomes constrained to travel along certain substrate symmetry directions. Such locking effects arise for colloids and superconducting vortices moving over ordered substrates when the direction of the external drive is varied. Here we study the directional locking of run-and-tumble active matter particles interacting with a periodic array of obstacles. In the absence of an external biasing force, we find that the active particle motion locks to various symmetry directions of the substrate when the run time between tumbles is large. The number of possible locking directions depends on the array density and on the relative sizes of the particles and the obstacles. For a square array of large obstacles, the active particle only locks to the x, y, and 45^{∘} directions, while for smaller obstacles, the number of locking angles increases. Each locking angle satisfies θ=arctan(p/q), where p and q are integers, and the angle of motion can be measured using the ratio of the velocities or the velocity distributions in the x and y directions. When a biasing driving force is applied, the directional locking behavior is affected by the ratio of the self-propulsion force to the biasing force. For large biasing, the behavior resembles that found for directional locking in passive systems. For large obstacles under biased driving, a trapping behavior occurs that is nonmonotonic as a function of increasing run length or increasing self-propulsion force, and the trapping diminishes when the run length is sufficiently large.

Diffusion of Anisotropic Colloids in Periodic Arrays of Obstacles

Colloidal suspensions in confined geometries exhibit rich diffusion dynamics governed by particle shapes and particle-confinement interactions. Here, we propose a colloidal system, consisting of ellipsoids in periodic array of obstacles, to investigate the confined diffusion of anisotropic colloids. From the obstacle density-dependent diffusion, we discover a decoupling of translational and rotational diffusion in which only rotational motion is localized while translational motion remains diffusive. Moreover, by evaluating the probability distributions of displacements, we found Brownian but non-Gaussian diffusion behaviors with increasing the obstacle densities, which originates from the shape anisotropy of the colloid and the multiplicity of the local configurations of the ellipsoids with respect to the obstacle. Our results suggest that the shape anisotropy and spatial confinements play a vital role in the diffusion dynamics. It is important for understanding the transportations of anisotropic objects in complex environments.

Organizing bacterial vortex lattices by periodic obstacle arrays

Recent experiments have shown that the complex spatio-temporal vortex structures emerging in active fluids are susceptible to weak geometrical constraints. This observation poses the fundamental question of how boundary effects stabilize a highly ordered pattern from seemingly turbulent motion. Here we show, by a combination of continuum theory and experiments on a bacterial suspension, how artificial obstacles guide the flow profile and reorganize topological defects, which enables the design of bacterial vortex lattices with tunable properties. To this end, the continuum model is extended by appropriate boundary conditions. Beyond the stabilization of square and hexagonal lattices, we also provide a striking example of a chiral, antiferromagnetic lattice exhibiting a net rotational flow, which is induced by arranging the obstacles in a Kagome-like array.

Diffusion-controlled, Size-based Separation of Narrowedly Distributed Suspensions in Pressure-driven Flows Through Microfluidic Bumper Arrays

Microfluidic bumper arrays (also referred to as Deterministic Lateral Displacement devices, DLD) have been proposed in the last fifteen years as a simple and effective mean to implement the label-free, size-based separation of a suspension of micrometric-sized particles. The separation resolution in these devices resolution is significantly higher than that associated with more traditional separation techniques such as, e.g., SEC columns. In DLD devices, the suspended particles are dragged by a pressure-driven flow through a periodic array of obstacles, typically hosted in a channel with rectangular cross-section. Experiments have proven that if a focused current entraining a suspension of particles of different size is continuously introduced upstream the obstacle array, size-sorted populations of particles can be collected at different locations of the device outlet. This is because, as a consequence of the fluid drag and of the hydrodynamics-mediated collisions with the obstacles, particles of different size follow on the average differentmigration pathts, which are at an angle with respect to the average direction of the carrier flow. Based on the DLD separation mechanism, prototypes have been constructed and used for sorting and isolating suspensions of clinical and biological interest, ranging from the size of red blood and circulating tumor cells, down the nanometric scale of exosomes. Recently, a novel chromatographic use of DLD devices has been proposed, where the suspension is separated in time and space coordinates by exploiting the dependence on particle mobility on particle size. By investigating particle transport in a idealized setting (associated with point-sized obstacles), it has been argued that the separation-enhancing effect due to mobility should allow, in principle, to effectively separate particles suspensions characterized by a narrow size distribution to very high degrees of resolution. In this contribution, the possibility of reproducing the same phenomenon in a classical pressure-driven flow in the presence of finite-sized obstacles is explored. Specifically, it is shown that (ideal) conditions similar to the type of particle motion predicted for point-size obstacles can be obtained even in the presence of obstacles of finite dimension, provided that the obstacle shape near the collision point is accurately tuned to obtain a diffusion-controlled behavior of particle dynamics.

Enhanced dynamics of active Brownian particles in periodic obstacle arrays and corrugated channels.

We study the motion of an active Brownian particle (ABP) using the overdamped Langevin dynamics on a two-dimensional substrate with periodic array of obstacles and in a quasi-one-dimensional corrugated channel comprised of periodically arrayed obstacles. The periodic arrangement of the obstacles enhances the persistent motion of the ABP in comparison to its motion in the free space. Persistent motion increases with the activity of the ABP. We note that the periodic arrangement induces directionality in ABP motion at late time, and it increases with the size of the obstacles. We also note that the ABP exhibits a super-diffusive dynamics in the corrugated channel. The transport property is independent of the shape of the channel; rather it depends on the packing fraction of the obstacles in the system. However, the ABP shows the usual diffusive dynamics in the quasi-one-dimensional channel with flat boundary.

One-Way Particle Transport Using Oscillatory Flow in Asymmetric Traps.

One challenge of integrating of passive, microparticles manipulation techniques into multifunctional microfluidic devices is coupling the continuous-flow format of most systems with the often batch-type operation of particle separation systems. Here, a passive fluidic technique-one-way particle transport-that can conduct microparticle operations in a closed fluidic circuit is presented. Exploiting pass/capture interactions between microparticles and asymmetric traps, this technique accomplishes a net displacement of particles in an oscillatory flow field. One-way particle transport is achieved through four kinds of trap-particle interactions: mechanical capture of the particle, asymmetric interactions between the trap and the particle, physical collision of the particle with an obstacle, and lateral shift of the particle into a particle-trapping stream. The critical dimensions for those four conditions are found by numerically solving analytical mass balance equations formulated using the characteristics of the flow field in periodic obstacle arrays. Visual observation of experimental trap-particle dynamics in low Reynolds number flow (<0.01) confirms the validity of the theoretical predictions. This technique can transport hundreds of microparticles across trap rows in only a few fluid oscillations (<500 ms per oscillation) and separate particles by their size differences.

Clogging and jamming transitions in periodic obstacle arrays.

We numerically examine clogging transitions for bidisperse disks flowing through a two-dimensional periodic obstacle array. We show that clogging is a probabilistic event that occurs through a transition from a homogeneous flowing state to a heterogeneous or phase-separated jammed state where the disks form dense connected clusters. The probability for clogging to occur during a fixed time increases with increasing particle packing and obstacle number. For driving at different angles with respect to the symmetry direction of the obstacle array, we show that certain directions have a higher clogging susceptibility. It is also possible to have a size-specific clogging transition in which one disk size becomes completely immobile while the other disk size continues to flow.

Space-time transport schemes and homogenization. I: general theory of Markovian and non-Markovian processes

Motivated by the phenomenology of random particle motion in localized repulsive potentials or in periodic arrays of obstacles at low diffusivities, the article introduces several classes of abstract transport schemes deriving from two basic prototypes, referred to as space-time and non-Markovian spin-driven diffusion. The homogenization theory of these transport processes is developed and a closed-form expression for the effective velocity vector and the effective dispersion tensor obtained. Some applications are also presented.

Vibrations of a thin elastic plate floating atop a heavy density-stratified fluid

An analytic solution is derived for the wave field induced by a normal incidence of a surface flexural-gravitational wave of a small amplitude upon a finite number of narrow infinitely long parallel straight-line obstacles in a plate floating on a surface of a two-layered incompressible and ideal fluid. A case of a periodic array of obstacles in the floating plate is also considered.

Simulation study of rare cell trajectories and capture rate in periodic obstacle arrays

Microfluidic devices that contain periodic obstacle arrays are frequently used for capture of rare cells such as circulating tumour cells (CTC). Detailed computational analysis can give valuable insights into understanding of fluidic processes inside such devices. Using our previously developed Object-in-fluid framework, we investigate characteristics of a single CTC in a suspension of red blood cells.In this work, we describe a new model for evaluation of cell capture probability that includes the surface area of the cell-obstacle contact. We analyze individual trajectories of CTCs and their distribution between the obstacles during the transport through the device.We vary two parameters – hematocrit and column radius of the cylindrical obstacles. While the hematocrit has a slight influence on the CTC trajectories and the cell capture rate computed by the newly developed model, the effect of column radius is much more pronounced. We observe that increase in column radius increases the capture rate quadratically. And secondly, with the exception of the very small column radius, increase in hematocrit slightly decreases the capture rate linearly.

Object-In-Fluid Framework in Modeling of Blood Flow in Microfluidic Channels

We present a fully three-dimensional computational model of red blood cells and their flow in a fluid. This model includes all components necessary to capture important physical and biological aspects of the cell flow. It comprises descriptions of elasticity of the cell membrane, cell-cell interactions, two-way cell-fluid interaction, and adhesion of cell to surfaces. Using this model, we analyze different processes involving flow of cells. We present the results of ongoing research concerning the development of model for cell adhesion, the analysis of microfluidic devices with periodic obstacle arrays, the optimization of microfluidic connectors and biological process of red blood cells formation from reticulocytes.

Collision rates for rare cell capture in periodic obstacle arrays strongly depend on density of cell suspension

Recently, computational modelling has been successfully used for determination of collision rates for rare cell capture in periodic obstacle arrays. The models were based on particle advection simulations where the cells were advected according to velocity field computed from two dimensional Navier–Stokes equations. This approach may be used under the assumption of very dilute cell suspensions where no mutual cell collisions occur. We use the object-in-fluid framework to demonstrate that even with low cell-to-fluid ratio, the optimal geometry of the obstacle array significantly changes. We show computational simulations for ratios of 3.5, 6.9 and 10.4% determining the optimal geometry of the periodic obstacle arrays. It was already previously demonstrated that cells in periodic obstacle arrays follow trajectories in two modes: the colliding mode and the zig–zag mode. The colliding mode maximizes the cell-obstacle collision frequency. Our simulations reveal that for dilute suspensions and for suspensions with cell-to-fluid ratio 3.5%, there is a range of column shifts for which the cells follow colliding trajectories. However we showed, that for 6.9 and 10.4%, the cells never follow colliding trajectories.

Particle suspension concentration with sparse obstacle arrays in a flow channel

We report on an efficient method to concentrate suspensions in a flow channel comprising sparse periodic arrays of obstacles. The obstacle spacings are a few times larger than the diameter of the particles. We perform up-scaled experiments, in which all particles flow along a few obstacle lines rotated with respect to the main flow direction. We found that for a diluted suspension a single line is sufficient to displace all particles into a concentrated stream. With visual high speed camera images particle–particle interactions were observed at increasing concentrations. Although one obstacle line was no longer enough to retain all particles, few additional obstacle lines facilitated good separation. This provides the insight that while the angle of the lines determines the primary separation, the number of lines is coupled to the maximum particle volume fraction that can be separated. With CFD simulations we showed that the flow resistance in these sparse arrays is very low and that the flow distribution across the outlets is easily controlled by the outlet tubing. These conclusions show the potential of sparse obstacle arrays for effective concentration of suspensions.

High throughput particle separation with a mirrored deterministic ratchet design

Deterministic ratchets, also called lateral displacement arrays, consist of periodic arrays of obstacles, spaced such that suspended particles having a minimum size are displaced. They have potential for suspension separation and fractionation. We report on the development of designs with obstacle arrays mirrored along the center plane providing more efficient displacement compared to non-mirrored designs. Depending on the application (e.g. concentration or cleaning) the design can be oriented to the center or to the sides. Highest recovery of incoming particles was found 88% in the center orientation, while the strongest depletions were achieved with the side orientation. Halving the length of the array did not always yield similar separation to the conventional design, especially at higher concentrations. This implies that particle displacement was not pure deterministic, but influenced by stochastic particle–particle interactions. Fractionation experiments demonstrated high recoveries of large particles, which were not much influenced by presence of small particles.