We measure acceleration statistics of neutrally buoyant spherical particles with diameter 0.4 < d/eta <27 in intense turbulence (400< R_lambda <815). High speed cameras image polystyrene tracer particles in a flow between counter-rotating disks. The measurements of acceleration variance, <a^2>, clearly resolve the transition from the tracer like behavior of small particles to the much smaller accelerations of large particles. For d>5 eta, <a^2> decreases with diameter as d^{-2/3} in agreement with inertial range scaling arguments. A model relating <a^2> to the pressure structure functions matches the transition from small to large particle behavior if the particles respond to pressure differences over (1.7 +- 0.3) d. A model relating <a^2> to the fluid acceleration averaged over the particle diameter predicts the transition with no free parameters, but does not show clean inertial range scaling in the size range studied. Consistent with earlier work, we find that the scaled acceleration probability density function shows very little dependence on particle size.
Turbulence modulation by inertial-range-size, neutrally-buoyant particles is investigated experimentally in a von Kármán flow. Increasing the particle volume fraction $Φ_\mathrm{v}$, maintaining constant impellers Reynolds number attenuates the fluid turbulence. The inertial-range energy transfer rate decreases as $\proptoΦ_\mathrm{v}^{2/3}$, suggesting that only particles located on a surface affect the flow. Small-scale turbulent properties, such as structure functions or acceleration distribution, are unchanged. Finally, measurements hint at the existence of a transition between two differe…
We investigate the sedimentation properties of quasi-neutrally buoyant inertial particles carried by incompressible zero-mean fluid flows. We obtain generic formulae for the terminal velocity in generic space-and-time periodic (or steady) flows, along with further information for flows endowed with some degree of spatial symmetry such as odd parity in the vertical direction. These expressions consist in space-time integrals of auxiliary quantities which satisfy partial differential equations of the advection--diffusion--reaction type, that can be solved at least numerically since our scheme im…
The dynamics of neutrally buoyant particles transported by a turbulent flow is investigated for spherical particles with radii of the order of the Kolmogorov dissipative scale or larger. The pseudo-penalisation spectral method that has been proposed by Pasquetti et al. (2008) is adapted to integrate numerically the simultaneous dynamics of the particle and of the fluid. Such a method gives a unique handle on the limit of validity of point-particle approximations, which are generally used in applicative situations. Analytical predictions based on such models are compared to result of very well …
We analyze the evolution of the distribution, both in the phase space and in the physical space, of inertial particles released by a spatially-localized (punctual) source and advected by an incompressible flow. The difference in mass density between fluid and particles is assumed as small, and represents the basic parameter for a regular perturbative expansion. By means of analytical techniques such as Hermitianization, we derive a chain of equations of the advection--diffusion--reaction type, easily solvable at least numerically. Our procedure provides results also for finite particle inertia…
We investigate the preferential concentration of particles which are neutrally buoyant but with a diameter significantly larger than the dissipation scale of the carrier flow. Such particles are known not to behave as flow tracers (Qureshi et al., Phys. Re. Lett. 2007) but whether they do cluster or not remains an open question. For this purpose, we take advantage of a new turbulence generating apparatus, the Lagrangian Exploration Module which produces homogeneous and isotropic turbulence in a closed water flow. The flow is seeded with neutrally buoyant particles with diameter 700\mum, corres…
Two motions of oscillation and vacillating breathing (swing) of a red blood cell have been observed in bounded Poiseuille flows (Phys. Rev. E 85, 16307 (2012)). To understand such motions, we have studied the oscillating motion of a neutrally buoyant rigid particle of the same shape in Poiseuille flow in a narrow channel and obtained that the crucial point is to have the particle interacting with Poiseuille flow with its mass center moving up and down in the channel central region. Since the mass center of the cell migrates toward the channel central region, its oscillating motion of the incli…
At finite Reynolds numbers particles migrate across flow streamlines to their equilibrium positions in microchannels. Such a migration is attributed to an inertial lift force, and it is well-known that the equilibrium location of neutrally-buoyant particles is determined only by their size and the Reynolds number. Here we demonstrate that the decoration of a bottom wall of the channel by superhydrophobic grooves provides additional possibilities for manipulation of neutrally-buoyant particles. It is shown that the effective anisotropic hydrodynamic slip of such a bottom wall can be readily use…
We use the bailout embeddings of three-dimensional volume-preserving maps to study qualitatively the dy- namics of small spherical neutrally buoyant impurities suspended in a time-periodic incompressible fluid flow. The accumulation of impurities in tubular vortical structures, the detachment of particles from fluid trajectories near hyperbolic invariant lines, and the formation of nontrivial three-dimensional structures in the distribution of particles are predicted.
Inertial particles in stably stratified flows play a fundamental role in geophysics, from the dynamics of nutrients in the ocean to the dispersion of pollutants in the atmosphere. We consider the Maxey-Riley equation for small neutrally buoyant inertial particles in the Boussinesq approximation, and discuss its limits of validity. We show that particles behave as forced damped oscillators, with different regimes depending on the particles Stokes number and the fluid Brunt-Väisälä frequency. Using direct numerical simulations we study the particles dynamics and we show that small neutrally buoy…
For low-Reynolds number shear-flows of neutrally-buoyant suspensions, the shear stress is often modeled using an effective viscosity that depends only on the solid fraction. As the Reynolds number ($Re$) is increased and inertia becomes important, the effective viscosity also depends on the Reynolds number itself. The current experiments measure the torque for flows of neutrally-buoyant particles in a coaxial-cylinder rheometer for solid fractions, $ϕ$, from 10\% to 50\% and Reynolds numbers based on particle diameter from 2 to 1,000. For experiments for Reynolds of O(10) and solid fractions l…
We investigate the large-scale transport properties of quasi-neutrally-buoyant inertial particles carried by incompressible zero-mean periodic or steady ergodic flows. We show how to compute large-scale indicators such as the inertial-particle terminal velocity and eddy diffusivity from first principles in a perturbative expansion around the limit of added-mass factor close to unity. Physically, this limit corresponds to the case where the mass density of the particles is constant and close in value to the mass density of the fluid which is also constant. Our approach differs from the usual ov…
We show that, even in the most favorable case, the motion of a small spherical tracer suspended in a fluid of the same density may differ from the corresponding motion of an ideal passive particle. We demonstrate furthermore how its dynamics may be applied to target trajectories in Hamiltonian systems.
In this article we discuss the generalization of a Lagrange multiplier based fictitious domain (DLM/FD) method to simulating the motion of neutrally buoyant particles of non-symmetric shape in non-Newtonian shear thinning fluids. Numerical solutions of steady Poiseuille flow of non-Newtonian shear thinning fluids are compared with the exact solutions in a two-dimensional channel. Concerning a self-propelled swimmer formed by two disks, the effect of shear thinning makes the swimmer moving faster and decreases the critical Reynolds number (for the moving direction changing to the opposite one) …
In this paper, we investigate the motion of a neutrally buoyant cylinder of circular or elliptic shape in two dimensional shear flow of a Newtonian fluid by direct numerical simulation. The numerical results are validated by comparisons with existing theoretical, experimental and numerical results, including a power law of the normalized angular speed versus the particle Reynolds number. The centerline between two walls is an expected equilibrium position of the cylinder mass center in shear flow. When placing the particle away from the centerline initially, it migrates toward another equilibr…
Hydrodynamic forces acting on a neutrally-buoyant spherical particle immersed in a wall-bounded axisymmetric stagnation point flow (Hiemenz-Homann flow) are predicted, based on a suitable form of the reciprocal theorem. An approximate algebraic form of the undisturbed velocity field is set up, mimicking the gradual transition of the actual carrying flow throughout the boundary layer, from a pure linear straining flow in the bulk to a parabolic flow at the wall. The particle Reynolds number is assumed to be small and predictions based on the creeping-flow assumption are first derived. Then, ine…
We numerically analyse the rotation of a neutrally buoyant spheroid in a shear flow at small shear Reynolds number. Using direct numerical stability analysis of the coupled nonlinear particle-flow problem we compute the linear stability of the log-rolling orbit at small shear Reynolds number, ${\rm Re}_a$. As ${\rm Re}_a \to 0$ and as the box size of the system tends to infinity we find good agreement between the numerical results and earlier analytical predictions valid to linear order in ${\rm Re}_a$ for the case of an unbounded shear. The numerical stability analysis indicates that there ar…
Dense particle suspensions are widely encountered in many applications and in environmental flows. While many previous studies investigate their rheological properties in laminar flows, little is known on the behaviour of these suspensions in the turbulent/inertial regime. The present study aims to fill this gap by investigating the turbulent flow of a Newtonian fluid laden with solid neutrally-buoyant spheres at relatively high volume fractions in a plane channel. Direct Numerical Simulation are performed in the range of volume fractions Phi=0-0.2 with an Immersed Boundary Method used to acco…
We study the turbulent square duct flow of dense suspensions of neutrally-buoyant spherical particles. Direct numerical simulations (DNS) are performed in the range of volume fractions $ϕ=0-0.2$, using the immersed boundary method (IBM) to account for the dispersed phase. Based on the hydraulic diameter a Reynolds number of $5600$ is considered. We report flow features and particle statistics specific to this geometry, and compare the results to the case of two-dimensional channel flows. In particular, we observe that for $ϕ=0.05$ and $0.1$, particles preferentially accumulate on the corner bi…
The aim of this Letter is to characterize the flow regimes of suspensions of finite-size rigid particles in a viscous fluid at finite inertia. We explore the system behavior as function of the particle volume fraction and the Reynolds number (the ratio of flow and particle inertia to viscous forces). Unlike single phase flows where a clear distinction exists between the laminar and the turbulent states, three different regimes can be identified in the presence of a particulate phase, with smooth transitions between them. At low volume fractions, the flow becomes turbulent when increasing the R…
Direct numerical simulations of turbulent suspension flows are carried out with the Force-Coupling Method in plane Couette and pressure-driven channel configurations. Dilute to moderately concentrated suspensions of neutrally buoyant finite-size (L_y /d = 20) spherical particles are considered when the Reynolds number is slightly above the laminar-turbulent transition. Tests performed with synthetic streaks, in both turbulent channel and Couette flows, show clearly that particles trigger the instability in channel flow whereas the plane Couette flow becomes laminar. Moreover, we have shown tha…
Direct numerical simulations are used to investigate the individual dynamics of large spherical particles suspended in a developed homogeneous turbulent flow. A definition of the direction of the particle motion relative to the surrounding flow is introduced and used to construct the mean fluid velocity profile around the particle. This leads to an estimate of the particle slipping velocity and its associated Reynolds number. The flow modifications due to the particle are then studied. The particle is responsible for a shadowing effect that occurs in the wake up to distances of the order of it…
In this paper, we investigate the motion of a neutrally buoyant cylinder of an elliptic shape freely moving in two dimensional shear flow by direct numerical simulation. An elliptic shape cylinder in shear flow, when initially being placed at the middle between two walls, either keeps rotating or has a stationary inclination angle depending on the particle Reynolds number $Re=G_r r_a^2/ν$, where $G_r$ is the shear rate, $r_a$ is the semi-long axis of the elliptic cylinder and $ν$ is the kinetic viscosity of the fluid. The critical particle Reynolds number $Re_{cr}$ for the transition from a ro…
We study the cross-stream inertial migration of a torque-free neutrally buoyant spheroid, of an arbitrary aspect ratio $κ$, in wall-bounded plane Poiseuille flow for small particle Reynolds numbers\,($Re_p\ll1$) and confinement ratios\,($λ\ll1$), with the channel Reynolds number, $Re_c = Re_p/λ^2$, assumed to be arbitrary; here, $λ=L/H$ where $L$ is the semi-major axis of the spheroid and $H$ denotes the separation between the channel walls. In the Stokes limit\,($Re_p =0)$ and for $λ\ll 1$, a spheroid rotates along any of an infinite number of Jeffery orbits parameterized by an orbit constant…
A new scale-dependent dynamic subgrid-scale (SGS) model based on Kolmogorov's scaling hypothesis is presented. This SGS model is utilized in large-eddy simulation of a well-known case study on shear-driven neutral atmospheric boundary layer flows. The results are compared comprehensively with an alternate scale-dependent dynamic SGS model based on the popular Smagorinsky closure. Our results show that, in the context of this particular problem, the scale-dependent dynamic modeling approach is extremely useful, and reproduces several establised results (e.g., the surface layer similarity theory…
We discuss possible definitions for a stochastic slip velocity that describes the relative motion between large particles and a turbulent flow. This definition is necessary because the slip velocity used in the standard drag model fails when particle size falls within the inertial subrange of ambient turbulence. We propose two definitions, selected in part due to their simplicity: they do not require filtration of the fluid phase velocity field, nor do they require the construction of conditional averages on particle locations. A key benefit of this simplicity is that the stochastic slip veloc…
The microstructure and rheological properties of suspensions of neutrally buoyant hard spherical particles in Newtonian fluid under conditions of finite inertia are studied using the lattice-Boltzmann method (LBM), which is based on a discrete Boltzmann model for the fluid and Newtonian dynamics for the particles. The suspensions are subjected to simple-shear flow and the properties are studied as a function of Reynolds number and volume fraction, $ϕ$. The inertia is characterized by the particle-scale shear flow Reynolds number $Re = \frac{ρ\dotγa^{2}}μ$, where $a$ is the particle radius, $\d…
KEY WORDS suspensions, inertial focusing, particle-laden flows, high Reynolds numbers SHORT SUMMARY The inertial migration of particles in square channel flows at the micro-scale has been deeply investigated in the last two decades. The well-known four equilibrium positions are located near the center of each channel face at moderate Reynolds numbers [1]. More recently, Miura et al. [2] revealed experimentally the presence of eight equilibrium positions in millimetric square channels for Reynolds numbers higher than 250. The aim of the present work is to extend these results obtained at millim…
The influence of the underlying flow topology on the shape and size of sub-Kolmogorov droplets dispersed in a turbulent flow is of considerable interest in many industrial and scientific applications. In this work we study the deformation and orientation statistics of sub-Kolmogorov droplets dispersed into a turbulent Taylor-Couette flow. Along with Direct Numerical Simulations (DNS) of the carrier phase and Lagrangian tracking of the dispersed droplets, we solve a phenomenological equation proposed by Maffettone and Minale (\emph{J. Fluid Mech.} 78, 227-241 (1998)) to track the shape evolutio…
Finite size effects can lead neutrally buoyant particles to exhibit different dynamics than tracer particles, and can alter their transport properties in fluid flows. Here we investigate the effect of the particle's shape on their dispersion in 2-dimensional complex flows. Combining numerical simulations with laboratory experiments, we show that particles with isotropic and anisotropic shapes exhibit different Lagrangian coherent structures, resulting in distinct dispersion phenomena within a given flow field. Experiments with rod shaped particles show a focusing effect in the vicinity of vort…
We investigate experimentally the spatial distributions of heavy and neutrally buoyant particles of finite size in a fully turbulent flow. As their Stokes number (i.e. ratio of the particle viscous relaxation time to a typical flow time scale) is close to 1, one may expect both classes of particles to aggregate in specific flow regions. This is not observed. Using a Voronoi analysis we show that neutrally buoyant particles sample turbulence homogeneously, whereas heavy particles do cluster. One implication for the understanding and modeling of particle laden flows, is that the Stokes number ca…
Small droplets in turbulent flows can undergo highly variable deformations and orientational dynamics. For neutrally buoyant droplets smaller than the Kolmogorov scale, the dominant effects from the surrounding turbulent flow arise through Lagrangian time histories of the velocity gradient tensor. Here we study the evolution of representative droplets using a model that includes rotation and stretching effects from the surrounding fluid, and restoration effects from surface tension including a constant droplet volume constraint, while assuming that the droplets maintain an ellipsoidal shape. T…
In the Stokesian limit, the streamline topology around a single neutrally buoyant sphere is identical to the topology of pair-sphere pathlines, both in an ambient simple shear flow. In both cases there are fore-aft symmetric open and closed trajectories spatially demarcated by an axisymmetric separatrix surface. This topology has crucial implications for both scalar transport from a single sphere, and for the rheology of a dilute suspension of spheres. We show that the topology of the fluid pathlines around a neutrally buoyant freely rotating spheroid, in simple shear flow, is profoundly diffe…
We analyse the angular dynamics of a neutrally buoyant nearly spherical particle immersed in a steady general linear flow. The hydrodynamic torque acting on the particle is obtained by means of a reciprocal theorem, regular perturbation theory exploiting the small eccentricity of the nearly spherical particle, and assuming that inertial effects are small, but finite.
The motion of a large, neutrally buoyant, particle, freely advected by a turbulent flow is determined experimentally. We demonstrate that both the translational and angular accelerations exhibit very wide probability distributions, a manifestation of intermittency. The orientation of the angular velocity with respect to the trajectory, as well as the translational acceleration conditioned on the spinning velocity provide evidence of a lift force acting on the particle.
We investigate experimentally the influence of suspended particles on the transition to turbulence. The particles are monodisperse and neutrally-buoyant with the liquid. The role of the particles on the transition depends both upon the pipe to particle diameter ratios and the concentration. For large pipe-to-particle diameter ratios the transition is delayed while it is lowered for small ratios. A scaling is proposed to collapse the departure from the critical Reynolds number for pure fluid as a function of concentration into a single master curve.
We propose a scaling law for the onset of turbulence in pipe flow of neutrally buoyant suspensions. This scaling law, based on a large set of experimental data, relates the amplitude of the particle-induced perturbations ($ε$) to the critical suspension Reynolds number, $Re_{s,c}$. Here $ε$ is a function of the particle-to-pipe diameter ratio and the volume fraction of the suspended particles, $ε= (d/D)^{1/2} ϕ^{1/6}$. $Re_{s,c}$ is found to scale as $ε^{-1}$. Furthermore, the perturbation amplitude allows a distinction between classical, intermediate and particle-induced transition.
We compute the angular dynamics of a neutrally buoyant nearly spherical particle immersed in an unsteady fluid. We assume that the particle is small, that its translational slip velocity is negligible, and that unsteady and convective inertia are small perturbations. We derive an approximation for the torque on the particle that determines the first inertial corrections to Jeffery's equation. These corrections arise as a consequence of local vortex stretching, and can be substantial in turbulence where local vortex stretching is strong and closely linked to the irreversibility of turbulence.
We study the translational and rotational dynamics of neutrally-buoyant finite-size spheroids in hydrodynamic turbulence by means of fully resolved numerical simulations. We examine axisymmetric shapes, from oblate to prolate, and the particle volume dependences. We show that the accelerations and rotations experienced by non-spherical inertial-scale particles result from volume filtered fluid forces and torques, similar to spherical particles. However, the particle orientations carry signatures of preferential alignments with the surrounding flow structures, which is reflected in distinct axi…
We measure the rotational statistics of neutrally buoyant rods with lengths $2.8 < l/η<72.9 $ in turbulence. For particles with length in the inertial range, we derive a scaling relationship for the mean square rotation rate, $< \dot{p}_i \dot{p}_i > \propto l^{-4/3}$ and show that measurements approach this scaling. Deviations from the proposed scaling are explained as the effect of dissipation range scales. The correlation time of the Lagrangian autocorrelation of rod rotation rate scales as the turn over time of eddies of the size of the rod. Measuring rotational dynamics of single long rod…
The statistics of the deformation and breakup of neutrally buoyant sub-Kolmogorov ellipsoidal drops is investigated via Lagrangian simulations of homogeneous isotropic turbulence. The mean lifetime of a drop is also studied as a function of the initial drop size and the capillary number. A vector model of drop previously introduced by Olbricht, Rallison and Leal [J. Non-Newtonian Fluid Mech. $\mathbf{10}$, 291 (1982)] is used to predict the behaviour of the above quantities analytically.
We have developed novel instrumentation for making Lagrangian measurements of temperature in diverse fluid flows. A small neutrally buoyant capsule is equipped with on-board electronics which measure temperature and transmit the data via a wireless radio frequency link to a desktop computer. The device has 80 dB dynamic range, resolving milli-Kelvin changes in temperature with up to 100 ms sampling time. The capabilities of these "smart particles" are demonstrated in turbulent thermal convection in water. We measure temperature variations as the particle is advected by the convective motion, a…
We investigate the statistics of orientation of small, neutrally buoyant, spherical tracers whose center of mass is displaced from the geometrical center. If appropriate-sized particles are considered, a linear relation can be derived between the horizontal components of the orientation vector and the same components of acceleration. Direct numerical simulations are carried out, showing that such relation can be used to reconstruct the statistics of acceleration fluctuations up to the order of the gravitational acceleration. Based on such results, we suggest a novel method for the local experi…
The macroscopic behavior of dense suspensions of neutrally-buoyant spheres in turbulent plane channel flow is examined. We show that particles larger than the smallest turbulence scales cause the suspension to deviate from the continuum limit in which its dynamics is well described by an effective suspension viscosity. This deviation is caused by the formation of a particle layer close to the wall with significant slip velocity. By assuming two distinct transport mechanisms in the near-wall layer and the turbulence in the bulk, we define an effective wall location such that the flow in the bul…
We simultaneously measure both spinning and tumbling components of rotation for long near-neutrally buoyant fibers in homogeneous and isotropic turbulence. The lengths and diameters of the measured fibers extend to several orders of the Kolmogorov length of the surrounding turbulent flow. Our measurements show that the variance of the spinning rate follows a -4/3 power law scaling with the fiber diameter ($d$) and is always larger than the variance of the tumbling rate. This behavior surprisingly resembles that observed previously for sub-Kolmogorov fibers. The general picture that emerges fro…
We consider the rotation of neutrally buoyant axisymmetric particles suspended in isotropic turbulence. Using laboratory experiments as well as numerical and analytical calculations, we explore how particle rotation depends upon particle shape. We find that shape strongly affects orientational trajectories, but that it has negligible effect on the variance of the particle angular velocity. Previous work has shown that shape significantly affects the variance of the tumbling rate of axisymmetric particles. It follows that shape affects the spinning rate in a way that is, on average, complementa…
We use an extended laser Doppler technique to track optically the velocity of individual particles in a high Reynolds number turbulent flow. The particle sizes are of the order of the Kolmogorov scale and the time resolution, 30 microseconds, resolves the fastest scales of the fluid motion. Particles are tracked for mean durations of the order of 10 Kolmogorov time scales. The fastest scales of the particle motion are resolved and the particle acceleration is measured. For neutrally buoyant particles, our measurement matches the performance of the silicon strip detector technique introduced at…
Suspended particles can alter the properties of fluids and in particular also affect the transition from laminar to turbulent flow. In the present experimental study, we investigate the impact of neutrally buoyant, spherical inertial particles on transition to turbulence in a pipe flow. At low particle concentrations, like in single phase Newtonian fluids, turbulence only sets in when triggered by sufficiently large perturbations and, as characteristic for this transition localized turbulent regions (puffs) co-exist with laminar flow. In agreement with earlier studies this transition point ini…
We successfully perform the three-dimensional tracking in a turbulent fluid flow of small asymmetrical particles that are neutrally-buoyant and bottom-heavy, i.e., they have a non-homogeneous mass distribution along their symmetry axis. We experimentally show how a tiny mass inhomogeneity can affect the particle orientation along the preferred vertical direction and modify its tumbling rate. The experiment is complemented by a series of simulations based on realistic Navier-Stokes turbulence and on a point-like particle model that is capable to explore the full range of parameter space charact…
We study the dynamics of neutrally buoyant particles with diameters varying in the range [1, 45] in Kolmogorov scale units (eta) and Reynolds numbers based on Taylor scale between 580 and 1050. One component of the particles' velocity is measured using extended Laser Doppler Velocimetry at the center of a Von-Karman (VK) flow, acceleration is derived by differentiation. We find that although the particle acceleration variance decreases with increasing their diameter with scaling close to (D/eta)^-2/3, in agreement with previous observations, the characteristic time of acceleration autocorrelat…
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…
