Particles In Three-dimensional Space Research Articles

Numerical investigation of induction of chaotic micromixing via vibration switching

Enhanced mixing in microfluidic systems is necessary in many applications such as chemical processing, biological assays, and diagnosis. We are developing a microfluidic system to efficiently mix minute reagents (down to several microliters) using vibration-induced flow (VIF), in which a net flow is generated around a micropillar by applying periodic vibration. In this study, we numerically investigate the enhancement in chaotic mixing using the VIF technique and periodic switching of vibrations. By extending our previous numerical simulation model, we investigate the flow field and trajectories of fluid particles in three-dimensional space. We demonstrate that chaotic advection characteristics can be observed by periodically switching the vibrational direction of a substrate using simple cylindrical pillars. In addition, using an appropriate interval for switching the vibration axes yields better mixing performance. The extent of chaotic advection is evaluated quantitatively using the Lyapunov exponent considering various vibration parameters, such as the vibration amplitude, separation distance between each pillar and pillar shape. The flow field induced by a large-amplitude and sharp-edged wall pillar provides excellent mixing results. Thus, VIF is successfully applied to obtain an efficient mixing strategy with the aid of the chaotic theory.

The World in the Wave Function

<i>The World in the Wave Function</i>

Digital holographic visualization of microparticles retained by an optical spatial trap

We propose a convenient method for generating optical traps based on a spatially structured beam. The proposed method of optical trap shaping utilizes interference of few Gaussian beams which waists, inclination angles and beam number are chosen for controllable trapping of micron-sized particles in three-dimensional space. In addition to implementing non-contact trapping, optical visualization in all planes was performed with digital holographic microscopy. This method contributes to the accurate localization of the studied specimens inside the cuvette over whole volume.

Optical trapping of the low index of refraction particles by focused vortex beams and two face-to-face focused beams

Using the extended Huygens–Fresnel principle and Rayleigh scattering theory, optical trapping of the low index of refraction particles using a focused Gaussian Schell-model (GSM) non-vortex beam, a focused GSM vortex beam, and two face-to-face focused GSM vortex beams have been studied. The results demonstrate that the focused GSM non-vortex beam cannot capture the low index of refraction particles, however, the focused GSM vortex beam can be a two-dimensional trap of particles in the z-axis, and the transverse gradient force Fgrad,x and the trapping equilibrium region increase as the topological charge m increases. As the focal length f or the refractive index of particles np decreases, the radiation forces increase and the trapping ability also enhances. To trap the low index particles in three-dimensional space, we adopt that the two face-to-face focused GSM vortex beams can be used to construct an optical potential well. The transverse gradient force of two face-to-face focused GSM vortex beams is twice that of a single GSM vortex beam. The limit of the radius for the low index of refraction particles that were stably captured has also been determined. The obtained results provide valuable information for trapping and manipulating the low index of refraction particles using GSM vortex beams, which may be applied in micromanipulation, biotechnology, nanotechnology and so on.

Scattering of neutrons on $${\upalpha }$$-particles in three-dimensional space

This letter demonstrates that there are some mistakes in the article of Roshan et al (Pramana – J. Phys. 90(3): 30, 2018) in dealing with the scattering of neutrons on $${\upalpha }$$ -particles in three-dimensional space. In fact, there is no one-to-one correspondence between the incident neutron energy and the scattering angle of the $${\upalpha }$$ -particle even if they have definite velocities before scattering. Instead, the situation is complex, and all the scattered $${\upalpha }$$ -particles will emit in a cone, which is called the velocity cone. At each scattering angle, which is smaller than the apex angle of the velocity cone, there are two groups of $${\upalpha }$$ -particles with different kinetic energies.

Focus shaping and optical manipulation using highly focused second-order full Poincaré beam.

Generation of vectorial optical fields with arbitrary polarization distribution is of great interest in plenty of applications. In this work, we propose and experimentally demonstrate the generation of a second-order full Poincaré (FP) beam and its application in two-dimensional (2D) flattop beam shaping with spatially variant polarization under a high numerical aperture focusing condition. In addition, the force mechanism of the focal field with 2D flattop beam profile is numerically studied, demonstrating the feasibility to trap a dielectric Rayleigh particle in three-dimensional space. The results show that the additional degree of freedom provided by the FP beam allows one to control the spatial structure of polarization, to engineer the focusing field, and to tailor the optical force exerted on a dielectric Rayleigh particle. The findings reported in the work may find useful applications in laser micromachining, optical trapping, and optical assembly.

Enhancing size based size separation through vertical focus microfluidics using secondary flow in a ridged microchannel

High throughput size based separation and sorting of bioparticles and cells is critical to a variety of biomedical processing steps for medical diagnostics and pharmaceutical purification. Improving microfluidic size-based particle/cell sorting is a challenge to better address the need for generating more homogeneous subpopulations for study and use. We propose a novel advance to microfluidic sorting devices that uses three-dimensional focusing of the sample to optimally position particles to amplify the size-dependent differences in trajectories caused by differential secondary flows. The result is an increase in the purity of small particles by 35- fold and large particles by 8-fold in comparison to unfocused flow. Our simulated and experimental data reveal for the first time that positioning particles in three-dimensional space can be used to better leverage the differential lateral movement of particles with different sizes as they flow in microchannel with transverse secondary flows. The focusing approach may also be useful to improve positioning of particles with inertial channels with multiple equilibrium positions. This technique performs continuous-flow, high throughput size based sorting of millions of particles and cells in a minute without any pre and post-processing. We have also demonstrated improved enrichment and recovery of white blood cells from human blood.

Diffusion of active chiral particles.

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the direction v[over ̂] at time t, and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution, which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean-squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around a uniformly distributed random axis, evidence is found of the so-called effect "anomalous, yet Brownian, diffusion," for which particles follow a non-Gaussian distribution for the positions yet the mean-squared displacement is a linear function of time.

Fluid mechanics calculations in physics of droplets I: Theoretical hydrodynamic formalism for the formation and condensation of spherical drops

It is proposed here a hydrodynamic formalism in order to obtain an approximate numerical solution to the Navier–Stokes equations. This formalism consists in the interpolation of the properties of the system of particles. The Smoothed Particle Hydrodynamics formalism (SPH) is employed when the system exhibits big deformation and large velocities because it is mesh-free in nature. In this study, it is simulated for the first time the condensation and formation of a spherical van der Waals drop by means of particles in three-dimensional space with the SPH formalism. When the drop is formed, starting from a gas box, the distribution of density implies that there are zones where the mass of gas is converted to a liquid state, but out of the droplet radius, some particles remain in the gas form.

Macroscopic three-dimensional particle location using stereoscopic imaging and astigmatic aberrations.

This Letter presents a stereoscopic imaging concept for measuring the locations of particles in three-dimensional space. The method is derived from astigmatism particle tracking velocimetry (APTV), a powerful technique that is capable of determining 3D particle locations with a single camera. APTV locates particle xy coordinates with high accuracy, while the particle z coordinate has a larger location uncertainty. This is not a problem for 3D2C (i.e., three dimensions, two velocity components) measurements, but for highly three-dimensional flows, it is desirable to measure three velocity components with similar accuracy. The stereoscopic APTV approach discussed in this report has this capability. The technique employs APTV for giving an initial estimate of the particle locations. With this information, corresponding particle images on both sensors of the stereoscopic imaging system are matched. Particle locations are then determined by mapping the two particle image sensor locations to physical space. The measurement error of stereo APTV, determined by acquiring images of 1-μm DEHS particles in a 40 mm×40 mm×20 mm measurement volume in air at Δxyz→0 between two frames, is less than 0.012mm for xy and 0.025mm for z. This error analysis proves the excellent suitability of stereo APTV for the measurement of three-dimensional flows in macroscopic domains.

Set Voronoi diagrams of 3D assemblies of aspherical particles

Several approaches to quantitative local structure characterization for particulate assemblies, such as structural glasses or jammed packings, use the partition of space provided by the Voronoi diagram. The conventional construction for spherical mono-disperse particles, by which the Voronoi cell of a particle is that of its centre point, cannot be applied to configurations of aspherical or polydisperse particles. Here, we discuss the construction of a Set Voronoi diagram for configurations of aspherical particles in three-dimensional space. The Set Voronoi cell of a given particle is composed of all points in space that are closer to the surface (as opposed to the centre) of the given particle than to the surface of any other; this definition reduces to the conventional Voronoi diagram for the case of mono-disperse spheres. An algorithm for the computation of the Set Voronoi diagram for convex particles is described, as a special case of a Voronoi-based medial axis algorithm, based on a triangulation of the particles’ bounding surfaces. This algorithm is further improved by a pre-processing step based on morphological erosion, which improves the quality of the approximation and circumvents the problems associated with small degrees of particle–particle overlap that may be caused by experimental noise or soft potentials. As an application, preliminary data for the volume distribution of disordered packings of mono-disperse oblate ellipsoids, obtained from tomographic imaging, is computed.

Trajectory of Charged Particle in Combined Electric and Magnetic Fields Using Interactive Spreadsheets

The objective of this article is to graphically illustrate to the students the physical phenomenon of motion of charged particle under the action of simultaneous electric and magnetic fields by simulating particle motion on a computer. Differential equations of motions are solved analytically and path of particle in three-dimensional space are obtained using interactive spreadsheet. Spreadsheets can be setup to solve numerical solutions of complex systems. This will make the concept, which so far is left to the abstract imagination come alive for the student, and initiate a deeper understanding of particle motion.

Large Core−Shell Poly(methyl methacrylate) Colloidal Clusters: Synthesis, Characterization, and Tracking

We present a multistep procedure yielding large (diameter > 2 μm) monodisperse, fluorescently labeled core-shell poly(methyl methacrylate) (PMMA) latex particles via dispersion polymerization. The particles' physical properties were controlled by adjusting two reaction parameters, the initiator and chain transfer agent concentrations, which influence the molecular weight of the PMMA. Under certain conditions, particles with the requisite properties for fabricating colloidal clusters were synthesized. The resulting clusters represent a new type of nonspherical colloid that can be dispersed in a density- and refractive index-matching solvent, making them ideal for quantitative studies using confocal microscopy. To demonstrate the utility of our clusters, we measured the translational and rotational diffusion coefficients of a tetrahedral cluster by tracking the motion of its constituent particles in three-dimensional space. More broadly, our findings provide new insights concerning PMMA dispersion polymerization in apolar media.

Manifoldization of [formula omitted]-shapes in [formula omitted] time

The β -shape and the β -complex are recently announced geometric constructs which facilitate efficient reasoning about the proximity among spherical particles in three-dimensional space. They have proven to be very useful for the structural analysis of bio-molecules such as proteins. Being non-manifold, however, the topology traversal on the boundary of the β -shape is inconvenient for reasoning about the surface structure of a sphere set. In this paper, we present an algorithm to transform a β -shape from being non-manifold to manifold without altering any of the geometric characteristics of the model. After locating the simplexes where the non-manifoldness is defined on the β -shape, the algorithm augments the β -complex which corresponds to the β -shape so that all the non-manifoldness is resolved on such simplexes. The algorithm runs in O ( n ) time, without any floating-point operation, in the worst case for protein models where n is the number of spherical atoms. We also provide some experimental results obtained from real protein models available from the Protein Data Bank.

Spatial Phase-Shifting Digital Holography for Three-Dimensional Particle Tracking Velocimetry

This paper presents a holographic technique for three-dimensional particle tracking. The complex amplitude on an image sensor is measured with two pairs of spatially phase-shifted digital holograms captured in a short time interval using a phase-shifting technique. Pairs of digital holograms are used to track small tracer particles in three-dimensional space and the phase-adjusted complex amplitude is employed in numerical image reconstruction to accurately detect the particles. The performance of the method is evaluated by numerical simulation. In order to demonstrate the feasibility of the method for real flow measurement, it is applied to the velocity measurement of tracer particles in a small water channel along which a high voltage is applied. The resulting components of the velocity vector in three-dimensional space are compared to those obtained using a conventional single-shot phase-shifting technique.

Self-Assembly of Polyhedral Hybrid Colloidal Particles

ABSTRACTWe have developed a new method to produce hybrid particles with polyhedral shapes in very high yield (liter quantities at up to 70% purity) using a combination of emulsion polymerization and inorganic surface chemistry. The procedure has been generalized to create complex geometries, including hybrid line segments, triangles, tetrahedra, octahedra, and more. The optical properties of these particles are tailored for studying their dynamics and self-assembly. For example, we produce systems that consist of index-matched spheres allowing us to define the position of each elementary particle in three-dimensional space. We present some preliminary studies on the self-assembly of these complex shaped systems based on electron and optical microscopy.

Integral equation procedure based on tailored orthogonal functions for theXYspin fluid in an external magnetic field

The classical XY model describes particles in three-dimensional space that carry magnetic moments or spins whose motion is restricted to rotations in a plane. Introduction of an external magnetic field lying in the same plane then generates a system that is anisotropic in the azimuthal angle phi . We use numerical simulations and integral equation techniques to study this system, producing in the latter case a formalism that is identical to that of the simpler isotropic version having no external field. The basis for this simplification is a generalization Em(phi) of the ordinary exponential basis set eimphi that restores orthogonality in the presence of the external field. We display results of sample calculations obtained with two integral equation closures, reference hypernetted-chain and soft mean-spherical approximation, both coupled to the Lovett-Mou-Buff-Wertheim relation, along with results from the numerical simulations for comparison. Construction of the Em(phi) is described in an Appendix.

Using the fractional interaction law to model the impact dynamics of multiparticle collisions in arbitrary form

Using the molecular dynamics method, we examine a discrete deterministic model for the motion of spherical particles in three-dimensional space. The model takes into account multiparticle collisions in arbitrary forms. Using fractional calculus we proposed an expression for the repulsive force, which is the so-called fractional interaction law. We then illustrate and discuss how to control (correlate) the energy dissipation and the collisional time for an individual particle within multiparticle collisions. We included in the multiparticle collisions the friction mechanism needed for the transition from coupled torsion-sliding friction through rolling friction to static friction. Analyzing simple simulations we found that binary collisions dominate in the strong repulsive state. However, weak repulsion is observed to be much stronger within multiparticle collisions. The presented numerical results can be used to realistically model the impact dynamics of an individual particle in a group of colliding particles.

Turbulent scales of dilute particle-laden flows in microgravity

The work described in this paper attempts to characterize the effects of inertia, isolated from gravity, on the dispersion of solid particles in a turbulent air flow. The experiment consisted of releasing particles of various sizes in an enclosed box of fan-generated, near-homogeneous, isotropic, and stationary turbulent airflow and examining the particle behavior in a microgravity environment. The turbulence box was characterized in ground-based experiments using laser Doppler velocimetry techniques. Microgravity was established by free floating the experiment apparatus during the parabolic trajectory of NASA’s KC-135 reduced-gravity aircraft. The microgravity generally lasted about 20 s, with about 50 parabolas per flight and one flight per day over a testing period of four days. To cover a broad range of flow regimes of interest, particles with Stokes numbers St of about 1–100 were released in the turbulence box. The three-dimensional measurements of particle motion were made with a particle-tracking algorithm using a three-camera stereo imaging system. Digital photogrammetric techniques were used to determine the particle locations from the calibrated camera images. The epipolar geometry constraint identified matching particles from the three different camera views and a direct spatial intersection scheme determined the coordinates of particles in three-dimensional space. Since particle loadings were light, velocity and acceleration constraints allowed particles in a sequence of frames to be matched, resulting in particle tracks and dispersion measurements. The goal was to compare the dispersion of different Stokes number particles in zero gravity and thereby decouple the effects of gravity from inertia on the dispersion. Results show that higher inertia particles disperse less in isotropic, nondecaying turbulent flows under zero gravity, in agreement with current models. Measurements show that particles with St≈1 dispersed about ten times more than the St≈100 particles.

The K Value Distribution of Liquid Phase Sintered Microstructures

A complex geometry of a powder compact in the three-dimensional multiple particle arrangement was generated by a Monte Carlo method, and the K value (a constant links the two-dimensional connectivity to the three-dimensional coordination number) distributions of liquid phase sintered systems, parameters linked the two-dimensional connectivity to the three-dimensional coordination number, were solved by the numerical computation. With this probability model, irregular packing of particles in three-dimensional space could be formulated with the variations of the particle size distribution. Unlike previous analytical models in which the grain boundary energy was set to a constant value, a relationship between the grain boundary energy and the misorientation angle between neighboring grains could be incorporated into this model in a probability manner. Simulation results indicate that the mean K value in the initial stage of liquid phase sintering increases with an increasing volume fraction of liquid phase, an increasing ratio of the mean base particle size to the mean additive particle size, and a decreasing standard deviation of the particle size distribution. The findings of the simulation are favorably compared with previous experimental observations on W-Ni-Fe alloys.