Inertial Particles Research Articles

Analysis and Discussion of Two-Way Coupling Effects in Particle-Laden Turbulent Channel Flow

This paper studies the turbulence modification caused by the presence of solid particles in fully developed channel flow by means of the point particle Direct Numerical Simulations (DNS) approach. Inertial particles much smaller than the smallest vortical flow structures are considered, maintaining a volume fraction of the order , where inter-particle collisions are rare and have nearly no influence on flow development. To avoid concurrent effects that could mask the analysis of fluid turbulence interaction, gravity is not included in the study, and particle-smooth wall collisions are modelled as ideal reflections. The alteration of fluid turbulence dynamics by the particles is illustrated and discussed, providing an overview of the fluid-particle interaction phenomena occurring at both microscopic and macroscopic flow levels. Finally, the relation of such phenomena with drag-reducing effects by particles is demonstrated.

Migration of non-Brownian particles localized inside sheared droplets

• Particles inside sheared droplets migrate along the vorticity direction. • The migration direction depends on the viscosity ratio. • The migration kinetics depends on Ca, interfacial tension and particle concentration. • VOF simulations provide velocity and shear rate distribution in a particle-free droplet. • Shear-induced migration plays a major role. The migration of non-Brownian particles inside a droplet subjected to shear flow is investigated. The viscosity ratio, particle concentration, particle to droplet size ratio and capillary number are systematically varied. It was observed that particles migrate in the vorticity direction either towards or away from the equatorial plane. The main factor determining the migration direction is the viscosity ratio. The particle concentration and applied capillary number have no influence on the equilibrium distribution and only affect the time necessary to reach this distribution. In order to identify the flow profile, both velocity and shear rate magnitudes to which the particles inside the droplet are subjected, are numerically simulated using the Volume-of-Fluid method in a particle-free droplet/matrix system. The numerical predictions of the flow are used to evaluate the presence of possible driving mechanisms for cross-streamline particle motion, such as particle inertia and shear rate gradients. Depending on the conditions, the simulations reveal significant differences in the streamline profiles and shear rate gradients within the droplet. The observed steady state particle distributions can partially be explained by shear-induced migration towards zones of low shear rates and/or low streamline curvature. However, in complex flows, such as inside a deformed droplet, different migration mechanisms can occur simultaneously. Hence, confinement inside the droplet and potential secondary flows may also play a role.

Giant oscillations of diffusion in ac-driven periodic systems.

We revisit the problem of diffusion in a driven system consisting of an inertial Brownian particle moving in a symmetric periodic potential and subjected to a symmetric time-periodic force. We reveal parameter domains in which diffusion is normal in the long time limit and exhibits intriguing giant damped quasiperiodic oscillations as a function of the external driving amplitude. As the mechanism behind this effect, we identify the corresponding oscillations of difference in the number of locked and running trajectories that carry the leading contribution to the diffusion coefficient. Our findings can be verified experimentally in a multitude of physical systems, including colloidal particles, Josephson junction, or cold atoms dwelling in optical lattices, to name only a few.

Kinematic simulations as a subgrid-scale model for particle motion: a priori LES of homogeneous isotropic turbulence

In this work we investigated the impact of filtering and subgrid-scale modeling on particle settling velocity and collision-related statistics in a turbulent flow. To reduce the complexity of this task we first studied the motion of inertial particles in the low-pass filtered homogeneous and isotropic turbulence, which was subsequently enriched with the subgrid-scale velocity components obtained from a frozen high-pass filtered velocity field. Particular emphasis has been put on the radial distribution function and the radial relative velocity of nearly touching particles both in the presence or absence of the gravitational settling. These statistics are the key input parameters to the kinematic collision kernel which is of crucial importance in determining the collision rate of inertial particles in a turbulent flow. Furthermore, kinematic simulations were selected as a means of enhancing the fluid velocity at particle locations. We analyzed a wide range of Stokes numbers, i.e. a measure of particle inertia, and, in contrast to scientific premises found in the literature, we observed no improvement of particle statistics when the low-pass filtered fluid velocity was enriched with both a synthetic or spectrally-filtered small-scale structures. We discuss the shortages of any frozen-velocity-based subgrid-scale model in predicting both single- and two-point particle statistics. We also indicate that in some cases, particularly concerning the collision rate of particles suspended in homogeneous and isotropic turbulence, subgrid-scale contribution in the particle equation of motion can be neglected.

Two-dimensional characterization of particle entrainment over a downstream obstacle

This study conducts a two-dimensional numerical investigation of the particle entrainment in the presence of a large downstream circular obstacle, and aims to deepen the understanding of the entrainment mechanism and propose a dimensionless number to describe the entrainment threshold. With the coupled lattice Boltzmann and discrete element method, direct numerical simulations are conducted for a wide range of obstacle-to-particle radius ratios ( 2 < R o / R p < 8 ) and Reynolds numbers ( 38 ≤ R e ≤ 160 ). The results show that the low-pressure separated vortex due to the obstacle is the fluid structure to entrain the particle by vortex stretching at low R o / R p ( 2 < R o / R p < 3 . 8 ). Based on this mechanism, a dimensionless number defined as the ratio of the vertical drag force to the particle gravity is proposed, which can be understood as a generalized Shields number including the additional effect of the obstacle radius, and it approaches the constant value of 2.5198 at the critical conditions of entrainment. In addition, we find that at high R o / R p ( 5 . 6 ≤ R o / R p ≤ 8 . 0 ), the particle is too far from the separated vortex to undergo sufficient vertical drag force, and thus its inertia should be small enough to ensure the entrainment. In this situation, the entrainment threshold is well described by the Stokes number, which approaches the constant value of 0.2134. At the moderate R o / R p ( 3 . 8 ≤ R o / R p ≤ 5 . 6 ) the drag force of separated vortex and the low particle inertia are both essential to realize the particle entrainment. • Particle entrainment over a downstream obstacle is investigated by LB-DEM. • Two kind of entrainment mechanisms are identified. • Two dimensionless numbers are proposed to describe critical entrainment condition.

Null and timelike geodesics in the Kerr-Newman black hole exterior

We study the null and time-like geodesics of the light and the neutral particles respectively in the exterior of Kerr-Newman black holes. The geodesic equations are known to be written as a set of first-order differential equations in Mino time from which the angular and radial potentials can be defined. We classify the roots for both potentials, and mainly focus on those of the radial potential with an emphasis on the effect from the charge of the black holes. We then obtain the solutions of the trajectories in terms of the elliptical integrals and the Jacobian elliptic functions for both null and time-like geodesics, which are manifestly real functions of the Mino time that the initial conditions can be explicitly specified. We also describe the details of how to reduce those solutions into the cases of the spherical orbits. The effect of the black hole's charge decreases the radii of the spherical motion of the light and the particle for both direct and retrograde motions. In particular, we focus on the light/particle boomerang of the spherical orbits due to the frame dragging from the back hole's spin with the effect from the charge of the black hole. To sustain the change of the azimuthal angle of the light rays, say for example $\Delta \phi=\pi$ during the whole trip, the presence of the black hole's charge decreases the radius of the orbit and consequently reduces the needed values of the black hole's spin. As for the particle boomerang, the particle's inertia renders smaller change of the angle $\Delta \phi$ as compared with the light boomerang. Moreover, the black hole's charge also results in the smaller angle change $\Delta \phi$ of the particle than that in the Kerr case. The implications of the obtained results to observations are discussed.

Collision efficiency of non-Brownian spheres in a simple shear flow – the role of non-continuum hydrodynamic interactions

We study the collisions in a gaseous medium of a dilute bidisperse suspension of non-Brownian spherical particles sedimenting along the flow axis of a simple shear flow. Continuum lubrication forces prevent particles from coming into contact in a finite time, thus collisions can occur only due to attractive interactions such as the van der Waals force. However, in a low-pressure medium, the lubrication forces are weaker than their continuum counterparts and allow particle pairs to collide, even without any attractive forces. The Knudsen number, defined as the ratio of the mean free path of the medium to the mean radius of the interacting spheres, captures the significance of non-continuum interactions. We use uniformly valid hydrodynamic mobility functions, reflecting non-continuum lubrication at small separations and full continuum hydrodynamic interactions at moderate to larger separations. Due to the nature of the pair trajectory topology, the collision efficiency vanishes at a critical Knudsen number when simple shear flow alone drives the dynamics. Thus we perform collision calculations where particles experience the combined effects of van der Waals attraction and non-continuum hydrodynamics; van der Waals interactions enable collisions below the critical Knudsen number. Next, we calculate the collision efficiency for coupled differential sedimentation and simple shear driven motion in the presence of van der Waals interaction and non-continuum hydrodynamics. Finally, we explore the role of small particle inertia on relative trajectories and collision efficiencies in a non-continuum gas subject to a simple shear flow, ignoring the van der Waals force and gravity.

Active Refrigerators Powered by Inertia.

We present the operational principle for a refrigerator that uses inertial effects in active Brownian particles to locally reduce their (kinetic) temperature by 2 orders of magnitude below the environmental temperature. This principle exploits the peculiar but so-far unknown shape of the phase diagram of inertial active Brownian particles to initiate motility-induced phase separation in the targeted cooling regime only. Remarkably, active refrigerators operate without requiring isolating walls opening the route toward using them to systematically absorb and trap, e.g., toxic substances from the environment.

Deposition velocity of inertial particles driven by wall-normal external force in turbulent channel flow

The effect of wall-normal external force and particle inertia on the deposition of particles in wall-bounded turbulence has been investigated by a point-particle Lagrange simulation. The preferential distribution of particles in the near-wall regions and the insufficient deceleration in the viscous sublayer jointly cause the enhancement of deposition velocity. The external forces strongly affect the clustering of particles in coherent flow structures. The increasing of the wall-normal force inhibits the clustering of particles, which further affects the deposition velocity.

Inversion of thermal properties of lunar soil from penetration heat of projectile using a 2D axisymmetric model and optimized PSO algorithm

The thermophysical parameters of lunar soil can be inferred from the temperature field during the invasion process of reconnaissance projectile. This paper adopts a two-dimensional axisymmetric model to reconstruct the projectile invasion process. An optimized particle swarm optimization method is then used to retrieve the thermophysical parameters of lunar soil. When the reconnaissance projectile penetrates the lunar interior, it rubs against the lunar soil and generates heat, which diffuses between the projectile body and the lunar soil. The sensors inside the reconnaissance projectile measure the temperature variation of the projectile body to inverse the thermophysical parameters. This paper carried out physical modeling of the penetration process of reconnaissance projectile. A two-dimensional axisymmetric simulation model is constructed for the physical process, and the adaptive inertial weight particle swarm algorithm is adopted. The inversion experiment of lunar soil thermophysical parameters based on the simulation model shows that the inversion error is less than 10%, which verifies the feasibility of this method.

Modeling of submicron particle transport based on VOF-LPT method

The submicron particle transport inside a single bubble rising in water is investigated by the VOF-LPT method. As an improvement of the previous particle transport assumption in numerical studies, a new interfacial penetration model is developed according to the observed particle behavior in experimental works. The new criterion, namely particle Weber number is derived based on the dimensional analysis of the kinetic energy equation. The developed model is calibrated and evaluated based on the experimental data and parametric studies including particle size, density and gas–liquid surface tension are performed. The results indicated that the consideration of the interfacial penetration model is reasonable due to the presence of particle interfacial behavior dominant by surface tension force. The application of particle Weber number as the criterion is found to agree well with the experimental observations from both quantitative and qualitative aspects. In the presence of large particle inertia, the particle may deviate from the gas streamline and impact the bubble surface on one side, while the particle presents enhanced penetration capacity through the gas–liquid interface on the other side. With the decreasing gas–liquid surface tension, a competitive mechanism between the weakened internal flow and the enhanced penetration capacity is found, which complexes the effect of surface tension on particle transport in a non-monotonic way. In general, the interfacial penetration model developed in this study is proven to be feasible to describe submicron particle transport inside the rising bubble.

Particle manipulation with acoustic waves based on Hertz-Mindlin mechanics

Ultrasound noncontact particle manipulation (vibrotransportation) is of interest for a number of industrial applications: delivery of solid agents for defect healing, noninvasive excretion of undesirable particles, micromachine technology, and sorting of particles. It is known that a particle on a substrate can be moved by a combined action of acoustic waves and friction. A traditional theory describing the effect considers a particle as a material point capable of moving only against the wave, i.e., in a direction opposite to the wave propagation direction. Here, we use another approach based on Hertz-Mindlin mechanics in which a particle represents a deformable body whereas a zone of its contact with the substrate has a certain structure including evolving regions of stick and slip. The friction dynamics of the Hertz-Mindlin system with a mass comprises different regimes, including a consistent motion in a desired direction (not only the one opposite to the direction of wave propagation but also the one oriented like the wave), which allows a more elaborate manipulation or positioning of the particles. The presented numerical tool treats the problem of a particle on a substrate being moved by Rayleigh waves. We demonstrate various regimes in which steady movement is observed or not, depending on excitation parameters and particle inertia.

How the presence of particles at the interface influences the droplet deformation in a simple shear flow?

A lattice Boltzmann method is presented to simulate a particle-laden droplet subject to a simple shear flow, where the effect of particle concentration, viscosity ratio of droplet to ambient fluid and particle inertia on droplet deformation and particle movement is explored. With the increase of particle concentration, droplet deformation increases because of reduced interfacial free energy caused by reduced fluid-fluid interface length. When a sufficient number of particles are added to interface, droplet deformation monotonically decreases with viscosity ratio, but first rises and then declines for clean interface. This difference is attributed to an increased apparent viscosity of the ambient fluid by added particles. The particle inertia enhances droplet deformation remarkably only when the Reynolds number is relatively high. In addition, particles are found to revolve around the deformed droplet along the interface with a period, which is determined solely by deformation parameter at the viscosity ratio of unity. • A LBM is developed to simulate the fluid-fluid-solid three-phase flows. • The particle's revolution period can be determined by the droplet deformation. • The deposition of particles at the interface can enhance the droplet deformation.

Dust-acoustic periodic travelling waves in a magnetized dusty plasma with trapped ions and nonthermal electrons in astrophysical situations: oblique excitations

Obliquely propagating three-dimensional dust-acoustic periodic travelling waves (DAPTWs) in a magnetized dusty plasma composed of negatively charged inertial dust particles, trapped ions, and nonthermal fast electrons have been undertaken. In the dusty plasma model at hand, the dynamic behaviors of DAPTWs are governed by a Schamel equation. The presence of dust acoustic solitary waves (DASWs) and DAPTWs is investigated via bifurcation analysis of the Hamiltonian system. In the nonlinear regime, the Sagdeev potential and phase portrait structures indicate the presence of small-amplitude DAPTW solutions. The influences of intrinsic physical parameters include the strength of the static magnetic field, the obliqueness of propagation, the thermal pressure of charged dust grains, the electron to dust density ratio, the trapping parameter of trapped ions, and the degree of nonthermality of fast electrons on the characteristics of DAPTWs are simulated numerically. In particular, the findings illustrate that the amplitude of DAPTWs is reduced as the numerical values of the trapping parameter are decreased. Interestingly, the theoretical simulations of numerical results can significantly highlight the physical nature of DAPTWs in astrophysical situations such as Earth’s magnetosphere, auroral region, and heliospheric environments.

Caustics in turbulent aerosols: an excitable system approach

Aerosol particles are inertial particles. They cannot follow the surrounding fluid in a region of high vorticity. These encounters render the particle velocity field ${{\boldsymbol {v}}}$ locally compressible. Caustics occur if the trace of the gradient matrix $\textsf{$\boldsymbol{\sigma}$}$ of the field ${{\boldsymbol {v}}}$ locally diverges. For three-dimensional isotropic and homogeneous turbulence, the dynamics of the gradient matrix can be expressed in terms of three geometric invariants. In the present paper we establish a parametrisation of this problem where the dynamics takes the form of an excitable stochastic dynamical system with a three-dimensional phase space. The deterministic part of the dynamics is solved analytically. We show that the deterministic system has a globally attractive stable fixed point. Small noise induces excursions from the fixed point that typically relax straight back towards the fixed point. Caustics emerge as non-trivial return to a global fixed point when noise excites a trajectory across a stability threshold. The relaxation to the global fixed point will then involve at least one, and it may involve two or even three divergences of $\boldsymbol {Tr}\,\textsf{$\boldsymbol{\sigma}$}$ . Based on a combination of analytical insights and numerical analysis, we determine the rate of occurrence, duration and relative observation probability of caustic events in turbulent aerosols. Our analysis reveals that each approach towards a divergence proceeds along a straight line in the phase space of the dynamical system, which can help identify caustics. Moreover, there are infinite ways in which caustics can arise, namely whenever $\boldsymbol {Tr}\,\textsf{$\boldsymbol{\sigma}$}$ tends to $-\infty$ , so that no two caustics look the same.

Scale-to-scale turbulence modification by small settling particles

Despite decades of investigations, there is still no consensus on whether inertial particles augment or dampen turbulence. Here, we perform the first experimental study in which the particle concentration is varied systematically across a broad range of volume fractions $\varPhi _{v}$ , from nominally one-way coupled to heavily two-way coupled regimes, keeping all other parameters constant. We utilize a zero-mean flow chamber where steady, homogeneous and approximately isotropic air turbulence is realized, with a Taylor-microscale Reynolds number $Re_{\lambda } = 150\unicode{x2013}300$ . We consider spherical solid particles of two sizes, both much smaller than the Kolmogorov length, and yielding Stokes numbers $St_{\eta } = 0.3$ and 2.6 based on the Kolmogorov time scale. By adjusting the turbulent intensity, the settling velocity parameter is kept constant for both cases, $Sv_{\eta } = V_{t}/u_{\eta }\approx 3$ (where $V_{t}$ is the still-air terminal velocity, and $u_{\eta }$ is the Kolmogorov velocity scale). Unlike previous studies focused on massively inertial particles, we find that the turbulent kinetic energy increases with particle loading, being more than doubled at $\varPhi _{v} =5\times 10^{-5}$ . This is attributed to the energy input associated with gravitational settling: the particles release their potential energy into the fluid and increase its dissipation rate, while the time scale associated with the inter-scale energy transfer is not strongly changed. Two-point statistics indicate that the energy-containing eddies become vertically elongated in the presence of falling particles, and that the latter redistribute the energy more homogeneously across the scales compared to unladen turbulence. This is rooted in an enhanced cascade, as shown by the nonlinear inter-scale energy transfer rate.

Vortex Flows with Particles and Droplets (A Review)

Single-phase vortices are a classic example of objects characterized by symmetry in the distribution of all main parameters. The presence of inertial particles (or droplets) in such objects, even with their initial uniform distribution in space, leads to symmetry breaking due to the inverse effect of the dispersed phase on the characteristics of carrier vortices. A review of calculation-theoretical and experimental works devoted to the study of the motion of particles (or droplets) in various concentrated vortex structures, as well as their inverse effect on vortex characteristics, is conducted. The main characteristics (inertia, concentration) as well as dimensionless parameters (Reynolds, Stokes, Froude, Tachikawa numbers) determining the interaction between the dispersed phase and vortices are described. The results of available studies are analyzed in order to establish the peculiarities of particle (or droplet) behavior and stability of different vortex structures, including natural ones. The works analyzed in the review cover a wide range of inertia of the dispersed phase (Stkf = 0.002 − 14.7) and vortex intensities (ReΓ = 200 − 5000).

Instability of a dusty vortex

We investigate the effect of inertial particles dispersed in a circular patch of finite radius on the stability of a two-dimensional Rankine vortex in semi-dilute dusty flows. Unlike the particle-free case where no unstable modes exist, we show that the feedback force from the particles triggers a novel instability. The mechanisms driving the instability are characterized using linear stability analysis for weakly inertial particles and further validated against Eulerian–Lagrangian simulations. We show that the particle-laden vortex is always unstable if the mass loading $M&gt;0$ . Surprisingly, even non-inertial particles destabilize the vortex by a mechanism analogous to the centrifugal Rayleigh–Taylor instability in radially stratified vortex with density jump. We identify a critical mass loading above which an eigenmode $m$ becomes unstable. This critical mass loading drops to zero as $m$ increases. When particles are inertial, modes that fall below the critical mass loading become unstable, whereas modes above it remain unstable but with lower growth rates compared with the non-inertial case. Comparison with Eulerian–Lagrangian simulations shows that growth rates computed from simulations match well the theoretical predictions. Past the linear stage, we observe the emergence of high-wavenumber modes that turn into spiralling arms of concentrated particles emanating out of the core, while regions of particle-free flow are sucked inward. The vorticity field displays a similar pattern which leads to the breakdown of the initial Rankine structure. This novel instability for a dusty vortex highlights how the feedback force from the disperse phase can induce the breakdown of an otherwise resilient vortical structure.

Detailed comparative analysis of environmental microparticle deposition characteristics between human and monkey nasal cavities using a surface mapping technique

Inhaled particulate matter is associated with nasal diseases such as allergic rhinitis, rhinosinusitis and neural disorders. Its health risks on humans are usually evaluated by measurements on monkeys as they share close phylogenetic relationship. However, the reliability of cross-species toxicological extrapolation is in doubt due to physiological and anatomical variations, which greatly undermine the reliability of these expensive human surrogate models. This study numerically investigated in-depth microparticle transport and deposition characteristics on human and monkey (Macaca fuscata) nasal cavities that were reconstructed from CT-images. Deposition characteristics of 1–30μm particles were investigated under resting and active breathing conditions. Similar trends were observed for total deposition efficiencies and a single correlation using Stokes Number was fitted for both species and both breathing conditions, which is convenient for monkey-human extrapolation. Regional deposition patterns were carefully compared using the surface mapping technique. Deposition patterns of low, medium and high inertial particles, classified based on their total deposition efficiencies, were further analyzed in the 3D view and the mapped 2D view, which allows locating particle depositions on specific nasal regions. According to the particle intensity contours and regional deposition profiles, the major differences were observed at the vestibule and the floor of the nasal cavity, where higher deposition intensities of medium and high inertial particles were shown in the monkey case than the human case. Comparisons of airflow streamlines indicated that the cross-species variations of microparticle deposition patterns are mainly contributed by two factors. First, the more oblique directions of monkey nostrils result in a sharper airflow turn in the vestibule region. Second, the monkey's relatively narrower nasal valves lead to higher impaction of medium and high inertial particles on the nasal cavity floor. The methods and findings in this study would contribute to an improved cross-species toxicological extrapolation between human and monkey nasal cavities.

Clustering in laboratory and numerical turbulent swirling flows

We study the three-dimensional clustering of velocity stagnation points, of nulls of the vorticity and of the Lagrangian acceleration, and of inertial particles in turbulent flows at fixed Reynolds numbers, but under different large-scale flow geometries. To this end, we combine direct numerical simulations of homogeneous and isotropic turbulence and of the Taylor–Green flow, with particle tracking velocimetry in a von Kármán experiment. While flows have different topologies (as nulls cluster differently), particles behave similarly in all cases, indicating that Taylor-scale neutrally buoyant particles cluster as inertial particles.