The role of the spatial structure of a turbulent flow in enhancing particle collision rates in suspensions is an open question. We show and quantify, as a function of particle inertia, the correlation between the multiscale structures of turbulence and particle collisions: Straining zones contribute predominantly to rapid head-on collisions compared to vortical regions. We also discover the importance of vortex-strain worm-rolls, which goes beyond ideas of preferential concentration and may explain the rapid growth of aggregates in natural processes, such as the initiation of rain in warm clouds.
Collisions between particles suspended in a fluid play an important role in many physical processes. As an example, collisions of microscopic water droplets in clouds are a necessary step in the production of macroscopic raindrops. Collisions of dust grains are also conjectured to be important for planet formation in the gas surrounding young stars, and also to play a role in the dynamics of sand storms. In these processes, collisions are favoured by fast turbulent motions. Here we review recent advances in the understanding of collisional aggregation due to turbulence. We discuss the role of …
In the present work the generation of zonal flows in collisionless trapped electron mode (TEM) turbulence is studied analytically. A reduced model for TEM turbulence is utilized based on an advanced fluid model for reactive drift waves. An analytical expression for the zonal flow growth rate is derived and compared with the linear TEM growth, and its scaling with plasma parameters is examined for typical tokamak parameter values.
To understand the earliest stages of planet formation, it is crucial to be able to predict the rate and the outcome of dust grains collisions, be it sticking and growth, bouncing, or fragmentation. The outcome of such collisions depends on the collision speed, so we need a solid understanding of the rate and velocity distribution of turbulence-induced dust grain collisions. The rate of the collisions depends both on the speed of the collisions and the degree of clustering experienced by the dust grains, which is a known outcome of turbulence. We evolve the motion of dust grains in simulated tu…
Length scales are determined that govern the behavior at small separations of the correlations of fluid-particle acceleration, viscous force, and pressure gradient. The length scales and an associated universal constant are quantified on the basis of published data. The length scale governing pressure spectra at high wave numbers is discussed. Fluid-particle acceleration correlation is governed by two length scales; one arises from the pressure gradient, the other from the viscous force.
Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulence arises from one such solution branch.
Hydrodynamic flow in both classical and quantum fluids can be either laminar or turbulent. To describe the latter, vortices in turbulent flow are modelled with stable vortex filaments. While this is an idealization in classical fluids, vortices are real topologically stable quantized objects in superfluids. Thus superfluid turbulence is thought to hold the key to new understanding on turbulence in general. The fermion superfluid 3He offers further possibilities owing to a large variation in its hydrodynamic characteristics over the experimentally accessible temperatures. While studying the hyd…
We discuss the probability distribution of relative speed $ΔV$ of inertial particles suspended in a highly turbulent gas when the Stokes numbers, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise to the distribution $P(ΔV) \sim \exp(-C |ΔV|^{4/3})$ (for some constant $C$). Our conclusions are supported by numerical simulations and the analytical solution of a model equation of motion. The results determine the rate of collisions between suspended particles. They are relevant to the hypothesised mechanism for formation of planets by aggregation of dust part…
The use of simplified models of turbulent flows provides an appealing possibility to study the collision rate of turbulent suspensions, especially in conditions relevant to astrophysics, which require large time scale separations. To check the validity of such approaches, we used a direct numerical simulation (DNS) velocity field, which satisfies the Navier-Stokes equations (although it neglects the effect of the suspended particles on the flow field), and a kinematic simulation (KS) velocity field, which is a random field designed so that its statistics are in accord with the Kolmogorov theor…
Turbulence facilitates collisions between particles suspended in a turbulent flow. Two effects have been proposed which can enhance the collision rate at high turbulence intensities: 'preferential concentration' (a clustering phenomenon) and the 'sling effect' (arising from the formation of caustic folds in the phase-space of the suspended particles). We have determined numerically the collision rate of small heavy particles as a function of their size and densities. The dependence on particle densities reveals that the enhancement by turbulence of the collision rate of particles with signific…
Planetesimals in gaseous protoplanetary disks may grow by collecting dust particles. Hydrodynamical studies show that small particles generally avoid collisions with the planetesimals because they are entrained by the flow around them. This occurs when $St$, the Stokes number, defined as the ratio of the dust stopping time to the planetesimal crossing time, becomes much smaller than unity. However, these studies have been limited to the laminar case, whereas these disks are believed to be turbulent. We want to estimate the influence of gas turbulence on the dust-planetesimal collision rate and…
We carry out direct numerical simulation combined with adhesive discrete element calculations to investigate collision-induced breakage of agglomerates in homogeneous isotropic turbulence. Based on extensive simulation runs, an adhesion parameter Adn is constructed to quantify the possibility of occurrence of sticking, rebound, and breakage events. The collision-induced breakage rate is then formulated based on the Smoluchowski equation and a breakage fraction. The breakage fraction, defined as the fraction of collisions that result in breakage, is then analytically estimated by a convolution …
The eddy viscosity for a turbulent compressible fluid with a relativistic equation of state is derived. Compressibility allows for sound modes, but the eddy viscosity in the shear mode is found to be the same as for incompressible fluids. For two space dimensions (which is the relevant case for the dynamics of relativistic heavy-ion collisions) the eddy viscosity in the shear mode is negative, reducing the effective viscosity below its microscopic value. This could explain the tiny viscosity found at RHIC. Implications for the experimentally accessible elliptic flow coefficient at the LHC are …
We study the collision rates and velocities for point-particles of different sizes in turbulent flows. We construct fits for the collision rates at specified velocities (effectively a collisional velocity probability distribution) for particle stopping time ratios up to four; already by that point the collisional partners are very poorly correlated and so the results should be robust for even larger stopping time ratios. Significantly, we find that while particles of very different masses have approximately Maxwellian collisional statistics, as the mass ratio shrinks the distribution changes d…
We study theoretically and numerically spatial distribution and collision rate of droplets that sediment in homogeneous isotropic Navier-Stokes turbulence. It is assumed that typical turbulent accelerations of fluid particles are much smaller than gravity. This was shown to imply that the particles interact weakly with individual vortices and, as a result, form a smooth flow in most of the space. In weakly intermittent turbulence with moderate Reynolds number, rare regions where the flow breaks down can be neglected in the calculation of space averaged rate of droplet collisions. However, incr…
In this paper we numerically investigate the influence of dissipation during particle collisions in an homogeneous turbulent velocity field by coupling a discrete element method to a Lattice-Boltzmann simulation with spectral forcing. We show that even at moderate particle volume fractions the influence of dissipative collisions is important. We also investigate the transition from a regime where the turbulent velocity field significantly influences the spatial distribution of particles to a regime where the distribution is mainly influenced by particle collisions.
We use theory and Direct Numerical Simulations (DNS) to explore the average vertical velocities and spatial distributions of inertial particles settling in a wall-bounded turbulent flow. The theory is based on the exact phase-space equation for the Probability Density Function describing particle positions and velocities. This allowed us to identify the distinct physical mechanisms governing the particle transport. We then examined the asymptotic behavior of the particle motion near the wall, revealing the fundamental differences to the near wall behavior that is produced when incorporating gr…
This paper studies the turbulent kinetic energy ($k_\perp$) in 2D isothermal electrostatic interchange-dominated ExB drift turbulence in the scrape-off layer and its relation to particle transport. An evolution equation for the former is analytically derived from the underlying turbulence equations. Evaluating this equation shows that the dominant source for the turbulent kinetic energy is due to interchange drive, while the parallel current loss to the sheath constitutes the main sink. Perpendicular transport of the turbulent kinetic energy seems to play a minor role in the balance equation. …
Kinetic closure of turbulence: collision-side modeling beyond the filtered Boltzmann equation
Department of Computer Science, University of Geneva（日内瓦大学计算机科学系）；HEPIA, University of Applied Sciences and Arts of Western Switzerland（瑞士西部应用科学与艺术大学 HEPIA）
Ionization occurs in the upper atmospheres of hot Jupiters and in the interiors of Gas Giant Planets, leading to magnetohydrodynamic (MHD) effects which couple the momentum and the magnetic field, thereby significantly altering the dynamics. In regions of moderate temperatures the gas is only partially ionized, which also leads to interactions with neutral molecules. To explore the turbulent dynamics of these regions we utilize Partially-Ionized MHD (PIMHD), a two-fluid model -- one neutral and one ionized -- coupled by a collision term proportional to the difference in velocities. Motivated b…
We use Direct Numerical Simulations (DNS) to investigate the dynamics of settling, bidisperse particles in isotropic turbulence. In agreement with previous studies, we find that without gravity (i.e. $Fr=\infty$, where $Fr$ is the Froude number), bidispersity leads to an enhancement of the relative velocities, and a suppression of their spatial clustering. For $Fr<1$, the relative velocities in the direction of gravity are enhanced by the differential settling velocities of the bidisperse particles, as expected. However, we also find that gravity can strongly enhance the relative velocities in…
A message of any sort can be regarded as a source of information. Claude. E. Shannon showed in the last century that information ("what we don't already know") is equivalent to the entropy as defined in statistical mechanics. A string of experimental observations is like a succession of words; they both convey information and can be characterized by their entropy. For the fluid flow measurements and simulations to be discussed here (pipe and soap film flow, GOY model), the entropy depends on controllable parameters such as the Reynolds number. The information theory approach is applicable to m…
Correlated collisions and history filtering: unraveling and reproducing the statistics of coalescing particles in turbulence from the ghost-particle framework
We propose a one-way coupled model that tracks individual primary particles in a conceptually simple cellular flow setup to predict flocculation in turbulence. This computationally efficient model accounts for Stokes drag, lubrication, cohesive and direct contact forces on the primary spherical particles and allows for a systematic simulation campaign that yields the transient mean floc size as a function of the governing dimensionless parameters. The simulations reproduce the growth of the cohesive flocs with time, and the emergence of a log-normal equilibrium distribution governed by the bal…
Recent work suggests unstable recurrent solutions of the equations governing fluid flow can play an important role in structuring the dynamics of turbulence. Here we present a method for detecting intervals of time where turbulence "shadows" (spatially and temporally mimics) recurrent solutions. We find that shadowing occurs frequently and repeatedly in both numerical and experimental observations of counter-rotating Taylor-Couette flow, despite the relatively small number of known recurrent solutions in this system. Our results set the stage for experimentally-grounded dynamical descriptions …
