Dynamics Of Inertial Particles Research Articles

Dynamics of inertial particles on the ocean surface with unrestricted reserve buoyancy

Dynamics of inertial particles on the ocean surface with unrestricted reserve buoyancy

Turbulence Modulation By Large Heavy Particles In Wall-Bounded Turbulence

"Most studies on particle laden flows have focused either on small heavy particles or large neutrally buoyant particles. We present, for the first time (to the best of our knowledge), results in the regime of large and heavy particles, investigating the particle-turbulence dynamics over a parameter space covering a wide range of particle-volume fractions, Stokes and Froude numbers. We consider a flow in a pipe aligned with the gravitational vector, thus allowing for the investigation of the two-way coupling between particles and carrier phase turbulence, while excluding the effect of gravity on the wall-normal migration of particles. Time-resolved images of both tracers (10 micrometers particles) and the dispersed particles (700 micrometers in diameter) were taken in the streamwise-wall-normal pipe plane using a planar particle image velocimetry (PIV) system consisting of a high speed camera (Phantom VEO 440), and an Nd:YLF Laser as light source. Using Voronoi tessellations to analyze the inertial particle dynamics, we show a strong deviation from Poisson behaviour for cases with and without turbophoresis. From the time-resolved PIV measurements, we also show that the carrier phase turbulence is modulated even at particle concentrations as low as 0.3% indicating that particle-induced stresses due to distortion of fluid streamlines cannot be neglected. An increase or decrease in the peak streamwise velocity fluctuation in the particle laden flow was observed, depending on the Stokes number, while the radial velocity fluctuation was found either to be the same as in the single phase flow case or higher. Furthermore, pressure drop measurements indicate a linear increase in the skin friction coefficient with volume fraction of particles. This was true for all Stokes and Froude numbers considered. The growth rate (β) of the skin friction coefficient was however observed to be only a function of the Froude number. A power-law fit to the data shows that β scales inversely with the Froude number indicating that for Froude numbers less than 1, the influence of gravity cannot be neglected. "

On the dynamics of aligned inertial particles settling in a quiescent, stratified two-layer medium

On the dynamics of aligned inertial particles settling in a quiescent, stratified two-layer medium

Dynamics of inertial particles under velocity resetting

We investigate stochastic resetting in coupled systems involving two degrees of freedom, where only one variable is reset. The resetting variable, which we think of as hidden, indirectly affects the remaining observable variable via correlations. We derive the Fourier–Laplace transforms of the observable variable’s propagator and provide a recursive relation for all the moments, facilitating a comprehensive examination of the process. We apply this framework to inertial transport processes where we observe the particle position while the velocity is hidden and is being reset at a constant rate. We show that velocity resetting results in a linearly growing spatial mean squared displacement at later times, independently of reset-free dynamics, due to resetting-induced tempering of velocity correlations. General expressions for the effective diffusion and drift coefficients are derived as a function of the resetting rate. A non-trivial dependence on the rate may appear due to multiple timescales and crossovers in the reset-free dynamics. An extension that incorporates refractory periods after each reset is considered, where post-resetting pauses can lead to anomalous diffusive behavior. Our results are of relevance to a wide range of systems, such as inertial transport where the mechanical momentum is lost in collisions with the environment or the behavior of living organisms where stop-and-go locomotion with inertia is ubiquitous. Numerical simulations for underdamped Brownian motion and the random acceleration process confirm our findings.

Experimental study of the effect of particle–wall interactions on inertial particle dynamics in wall turbulence

Based on Voronoi analysis, the properties related to the near-wall motion of particles in a turbulent boundary layer were experimentally investigated via different release modes, with a friction Reynolds number $Re_\tau =3530$ . For high-inertia sand particles with Stokes number $St^+ \sim O(10^2\unicode{x2013}10^3)$ and a volume fraction $\varPhi _v \sim O(10^{-4})$ , particle image tracking velocimetry was used to determine the particle position and near-wall distribution properties. We established three particle release modes, including top-released, bottom overall-released and bottom partially released sand particles, under the same flow field conditions and calculated the differences in particle near-wall clustering and void properties. It was confirmed that wall effects (including collision and strike-splash) have a great influence on particle clustering and void behaviour near the wall. In the top-released sand particle and locally laid sand particle cases, particles bounced off the smooth walls and re-entered the carrier flow, causing significant clustering and sparsing of particles near the walls. In contrast, in the overall sand-laying case where the bottom wall was completely covered with sand particles, there is no apparent cluster or void phenomenon near the wall $(z/\delta <0.12)$ and the particles are randomly distributed, due to the combined effect of particle impact and splashing. In addition, the clustering and voids of particles become more pronounced with increasing wall-normal distance in the three release modes, and the particle distribution shows some self-similarity at each flow layer. The probability density function of the concentration of cluster particles decreases following a ‘ $-5/3$ ’ power law. However, due to the particle–wall interaction, the probability density function gradually deviates from the ‘ $-5/3$ ’ power law.

Effect of slip-induced fluid inertial torque on the angular dynamics of spheroids in a linear shear flow

The angular dynamics of tiny spheroidal particles in shear flows have been widely investigated, but most of the studies mainly focus on the effect of strong shear, while the combined effect of both shear and slip velocity at the center of the particle has been less considered. Actually, the fluid inertial torque induced by the slip velocity between particle and fluid plays a significant role in spheroid angular dynamics. However, it is difficult to investigate these dynamics theoretically until the analytical expression of the fluid inertial torque at a small Reynolds number was derived by Dabade et al. [J. Fluid Mech. 778, 133–188 (2015)]. In this study, the effect of the fluid inertial torque on the particle rotations is considered in a linear shear flow with a small streamwise slip velocity at the center of the particle. We find that as the fluid inertial torque dominates, the prolate spheroids tend to logroll while oblate ones have a tendency to tumble or align to a direction with a relative angle to the streamwise direction. These results are opposite to the earlier results in the absence of the fluid inertial torque. Different ultimate rotation modes of spheroids are dependent on the relative importance between the fluid inertial torque and the particle inertia, as well as the initial orientations. This reflects a non-trivial effect of fluid inertial torque on the angular dynamics of inertial spheroidal particles.

Clustering, rotation, and swirl of inertial particles in turbulent channel flow

Clustering dynamics of inertial particles in turbulent channel flow are studied via tessellation-based analysis of high-fidelity simulation data at Reτ≈230 with various values of mass loading (10%−100%) and the Stokes number (St+=[1−60]). We then characterise the solenoidal, rotational, and swirling motions of clusters by computing the probability density functions (PDFs) of the divergence, curl, and helicity of the particle velocity, as well as their dependence on wall-normal distance, using the methods of Oujia et al. (2020); Maurel–Oujia et al. (2023). Particle inertia gives heavier tails to the PDFs of divergence and curl, suggesting enhanced intermittency in the convergence/divergence of clusters, and in their rotational motions. The fluctuations of the divergence and curl are most intense in the buffer layer, due to the stronger fluctuations of fluid velocity there. Similarities are identified between the cluster dynamics in the logarithmic region and those in homogeneous isotropic turbulence, including the dependence of divergence, curl, and helicity on Stokes number. The effect of increasing mass loading on cluster dynamics is relatively small except in the viscous sublayer, where attenuation of clustering, rotation, and swirling motions are observed. The effect of increasing Stokes number on the viscous sublayer is different, resulting in more intense convergence/divergence and rotation of particle clusters, as the particles become more independent of the carrier fluid.

Effect of fluid inertial torque on the rotational and orientational dynamics of tiny spheroidal particles in turbulent channel flow

Rotation and orientation of non-spherical particles in a fluid flow depend on the hydrodynamic torque they experience. However, little is known about the effect of the fluid inertial torque on the dynamics of tiny inertial spheroids in turbulent channel flows, as only Jeffery torque has been considered in previous studies by point-particle direct numerical simulations. In this study, we investigate the rotation and orientation of tiny spheroids with both fluid inertial torque and Jeffery torque in a turbulent channel flow. By comparing with the case in the absence of fluid inertial torque, we find that the rotational and orientational dynamics of spheroids is significantly affected by the fluid inertial torque when the Stokes number, which is non-dimensionalized by fluid viscous time scale, is larger than the critical value $St_c\approx 2$ , indicating that the fluid inertial torque is non-negligible for most particle cases considered in earlier studies. In contrast to the earlier findings considering only Jeffery torque (Challabotla et al., J. Fluid Mech., vol. 776, 2015, p. R2), we find that prolate (oblate) spheroids with a large Stokes number tend to tumble (spin) in the streamwise–wall-normal plane in a thinner region near the wall due to the presence of the fluid inertial torque. Approaching the channel centre, the flow shear gradually vanishes, but the velocity difference between local fluid and particles is still pronounced and increasing as particle inertia grows. As a result, in the core region, fluid inertial torque is dominant and drives the particles to align with its broad side normal to the streamwise direction rather than a random orientation observed in earlier studies without fluid inertial torque. Meanwhile, the presence of fluid inertial torque enhances the tumbling rates of spheroids in the core region. In addition, the effect of fluid inertial force on the dynamics of spheroids is also examined in this study, but the results indicate the effect of fluid inertial force is weak. Our findings imply the importance of fluid inertial torque in modelling the dynamics of inertial non-spherical particles in turbulent channel flows.

Dynamics and dispersion of inertial particles in circular cylinder wake flows: A two-way coupled Eulerian–Lagrangian approach

In this paper, the motion of inertial particles in three-dimensional (3D) unsteady cylindrical wake flow is investigated by a two-way coupled Eulerian–Lagrangian approach. At different flow Reynolds numbers (Re), the corresponding striking dynamic property and dispersion mechanism of four particle classes have been studied, with inertia parameterized by means of Stokes number (Sk). It is found that inertial particles with lower Stokes number are expelled from vortex cores, and coherent voids encompass the local Kármán vortex cells. As Stokes number increases, a low velocity particle channel could be formed, which almost coincides with the results in the literature. Moreover, with the increase of Reynolds number, numerous irregular coherent voids are observed in the cylinder wake, and the high-speed particles follow the fluid flow closely when they are contained in the vortices. Although the centrifugal force of Kármán vortex cells significantly affects the dynamics of inertial particles, the fluid flow modulation is believed to be responsible for the distinctive particle dispersion patterns in the vortex streets. For particles with medium inertia, the two-way coupled modulation weakens the centrifugal effect of vortex structures on the particles. This trend declines with the increase of Reynolds number, and vanishes with light particles, while both two-way coupled modulation and the centrifugal effect of vortex structures are almost equally effective with heavy particles. The investigations contribute to a better understanding of the particle-laden flows in practical applications, which will benefit the optimized design of certain machinery and equipment for the industry.

Inertial and geometrical effects of self-propelled elliptical Brownian particles.

Active particles that self-propel by transforming energy into mechanical motion represent a growing area of research in mathematics, physics, and chemistry. Here we investigate the dynamics of nonspherical inertial active particles moving in a harmonic potential, introducing geometric parameters which take into account the role of eccentricity for nonspherical particles. A comparison between the overdamped and underdamped models for elliptical particles is performed. The model of overdamped active Brownian motion has been used to describe most of the basic aspects of micrometer-sized particles moving in a liquid ("microswimmers"). We consider active particles by extending the active Brownian motion model to incorporate translation and rotation inertia and account for the role of eccentricity. We show how the overdamped and the underdamped models behave in the same way for small values of activity (Brownian case) if eccentricity is equal to zero, but increasing eccentricity leads the two dynamics to substantially depart from each other-in particular, the action of a torque induced by external forces, induced a marked difference close to the walls of the domain if eccentricity is high. Effects induced by inertia include an inertial delay time of the self-propulsion direction from the particle velocity, and the differences between the overdamped and underdamped systems are particularly evident in the first and second moments of the particle velocities. Comparison with the experimental results of vibrated granular particles shows good agreement and corroborates the notion that self-propelling massive particles moving in gaseous media are dominated by inertial effects.

Imaging-based 3D particle tracking system for field characterization of particle dynamics in atmospheric flows

A particle tracking velocimetry apparatus is presented that is capable of measuring three-dimensional particle trajectories across large volumes, of the order of several meters, during natural snowfall events. Field experiments, aimed at understanding snow settling kinematics in atmospheric flows, were conducted during the 2021/2022 winter season using this apparatus, from which we show preliminary results. An overview of the methodology, wherein we use a UAV-based calibration method, is provided, and analysis is conducted of a select dataset to demonstrate the capabilities of the system for studying inertial particle dynamics in atmospheric flows. A modular camera array is used, designed specifically for handling the challenges of field deployment during snowfall. This imaging system is calibrated using synchronized imaging of a UAV-carried target to enable measurements centered 10 m above the ground within approximately a 4 m $$\times$$ 4 m $$\times$$ 6 m volume. Using the measured Lagrangian particle tracks, we present data concerning 3D trajectory curvature and acceleration statistics, as well as clustering behavior using Voronoï analysis. The limitations, as well as potential future developments, of such a system are discussed in the context of applications with other inertial particles.

Bouncing dynamics of inertial self-propelled particles reveals directional asymmetry.

This study aims to examine experimental conditions in which active particles are forced by their surroundings to move forward and backward in a continuous oscillatory manner. The experimental design is based on using a vibrating self-propelled toyrobot called hexbug, which is placed inside a narrow channel closed on one end by a rigid moving wall. Using the end-wall velocity as a controlling factor, the main forward mode of the hexbug movement can be turned to mostly rearward mode. We investigate the bouncing hexbug motion on both experimental and theoretical grounds. The Brownian model of active particles with inertia is employed in the theoretical framework. The model itself uses a pulsed Langevin equationin order to simulate abrupt changes in velocity that mimic hexbug propulsion in the moments when its legs make contact with the base plate. Significant directional asymmetry is caused by the legs bending backward. We demonstrate that the simulation successfully reproduces the experimental characteristics of hexbug motion after regressing the spatial and temporal statistical characteristics, especially when directional asymmetry is under consideration.

Clustering of inertial particles in turbulent flow through a porous unit cell

Direct numerical simulation is used to investigate effects of turbulent flow in the confined geometry of a face-centred cubic porous unit cell on the transport, clustering and deposition of fine particles at different Stokes numbers ( $St = 0.01, 0.1, 0.5, 1, 2$ ) and at a pore Reynolds number of 500. Particles are advanced using one-way coupling and the collision of particles with pore walls is modelled as perfectly elastic with specular reflection. Tools for studying inertial particle dynamics and clustering developed for homogeneous flows are adapted to take into account the embedded, curved geometry of the pore walls. The pattern and dynamics of clustering are investigated using the volume change of Voronoi tesselation in time to analyse the divergence and convergence of the particles. Similar to the case of homogeneous, isotropic turbulence, the cluster formation is present at large volumes, while cluster destruction is prominent at small volumes and these effects are amplified with the Stokes number. However, unlike homogeneous, isotropic turbulence, the formation of a large number of very small volumes was observed at all Stokes numbers and attributed to the collision of particles with the pore wall. Multiscale wavelet analysis of the particle number density indicates that the peak of the energy density spectrum, representative of enhanced particle clustering, shifts towards larger scales with an increase in the Stokes number. Scale-dependent skewness and flatness quantify the intermittent void and cluster distribution, with cluster formation observed at small scales for all Stokes numbers, and void regions at large scales for large Stokes numbers.

On analysis and stochastic modeling of the particle kinetic energy equation in particle-laden isotropic turbulent flows

We analyze three-dimensional particle-laden, isotropic turbulence to develop an understanding of inertial particle dynamics from a kinetic energy perspective. Data trends implying inhomogeneous sampling of the flow by particles are identified and used to support a proposed particle behavior: particles appear to accumulate in regions of low flow kinetic energy over time because they lose kinetic energy and slow down in such regions, ultimately causing them to spend more time there. To elucidate this behavior, we derive a particle kinetic energy equation from the particle momentum equation, which incorporates inertial effects through the Schiller–Naumann drag correlation. Upon extracting fundamental physics from this equation, hypotheses regarding the role of the Stokes number in the temporal change of particle kinetic energy and the previously proposed particle behavior are evaluated using simulation data considering three Stokes numbers. Finally, a Fokker–Planck equation is used to derive the steady-state probability density function of the particle kinetic energy. The model fits the simulation data well and provides a tool for further investigation into understanding preferential concentration, as well as a reduced order model for predicting particle kinetic energy in turbulent flows.

On the Dynamics of Inertial Particles in an Intensive Atmospheric Vortex

On the Dynamics of Inertial Particles in an Intensive Atmospheric Vortex

Inertial forces in the Maxey–Riley equation in nonuniform flows

Here, inertial forces on particles in nonuniform ambient flows, previously missing from the Maxey---Riley formulation of inertial particle dynamics, are identified. These forces involve both local and convective fluid inertia and depend on the curvature of the ambient flow. These new terms provide quantitative corrections and qualitative additions to the Maxey---Riley equation and are relevant when the particle size is appreciable relative to the characteristic length scale of the ambient flow.

Surfing and crawling macroscopic active particles under strong confinement: Inertial dynamics

This work studies the dynamics of inertial active particles under strong confinement and observe that he probability density of position peaks at a finite distance away from the confining wall, and that individual particles exhibit several dynamical states and transitions between them can be controlled by the level of self-propulsion.

Nonlinear dynamics of inertial particles in the ocean: from drifters and floats to marine debris and Sargassum

Buoyant, finite-size or inertial particle motion is fundamentally unlike neutrally buoyant, infinitesimally small or Lagrangian particle motion. The de-jure fluid mechanics framework for the description of inertial particle dynamics is provided by the Maxey-Riley equation. Derived from first principles - a result of over a century of research since the pioneering work by Sir George Stokes - the Maxey-Riley equation is a Newton-type-law with several forces including (mainly) flow, added mass, shear-induced lift, and drag forces. In this paper we present an overview of recent efforts to port the Maxey-Riley framework to oceanography. These involved: 1) including the Coriolis force, which was found to explain behavior of submerged floats near mesoscale eddies; 2) accounting for the combined effects of ocean current and wind drag on inertial particles floating at the air-sea interface, which helped understand the formation of great garbage patches and the role of anticyclonic eddies as plastic debris traps; and 3) incorporating elastic forces, which are needed to simulate the drift of pelagic Sargassum. Insight on the nonlinear dynamics of inertial particles in every case was possible to be achieved by investigating long-time asymptotic behavior in the various Maxey-Riley equation forms, which represent singular perturbation problems involving slow and fast variables.

Clustering of Marine‐Debris‐ and Sargassum‐Like Drifters Explained by Inertial Particle Dynamics

AbstractDrifters designed to mimic floating marine debris and small patches of pelagic Sargassum were satellite tracked in four regions across the North Atlantic. Though subjected to the same initial conditions at each site, the tracks of different drifters quickly diverged after deployment. We explain the clustering of drifter types using a recent Maxey‐Riley theory for surface ocean inertial particle dynamics applied on multidata‐based mesoscale ocean currents and winds from reanalysis. Simulated trajectories of objects at the air‐sea interface are significantly improved when represented as inertial (accounting for buoyancy and size), rather than as perfectly Lagrangian (fluid following) particles. Separation distances between simulated and observed trajectories were substantially smaller for debris‐like drifters than for Sargassum‐like drifters, suggesting that additional consideration of its physical properties relative to fluid velocities may be useful. Our findings can be applied to model variability in movements and distribution of diverse objects floating at the ocean surface.

Inertial effects on trapped active matter.

In this work, the dynamics of inertial (mass and moment of inertia) active Brownian particles trapped in a harmonic well is studied. This scenario has seen success when characterizing soft passive and active overdamped matter. Motivated by the variety of applications of this system, we analytically find the effect of translational and rotational inertia on the mean-square displacement (MSD), mean-square speed (MSS), swim, Reynolds, and total pressures of a system of inertial active Brownian particles subject to a weak and a strong harmonic trap. Following a Langevin formalism, we explicitly find that as inertia grows, the systems' MSD and total pressure are enhanced, but its MSS and swim pressure decrease. The use of Langevin dynamics simulations enables us to observe that as inertia grows, inertial active matter under a strong trap no longer "condensates" at the "border" of the trap, but it rather tends to uniformly spread in space. Our analytical results are also numerically validated.