Finite-size Particles Research Articles

Models of interphase drag force from direct numerical simulations of upward turbulent particle-laden channel flows

Data from the interfaced-resolved direct numerical simulations (IR-DNSs) of upward turbulent channel flow laden with finite-size heavy particles at particle concentration ranging from 0.84% to 2.36% are used to develop improved drag correlations which account for the effect of turbulence on drag enhancement. First, the contribution of drag nonlinearity to drag enhancement for the turbulent flow over a fixed sphere is analyzed with the consideration of velocity fluctuation anisotropy. The nonlinear drag enhancement is generally smaller than the actual drag enhancement in our numerical simulations. Second, several models for turbulence correction are presented with different choice of model parameters, and it is found that the turbulent intensity normalized by the mean slip velocity and the particle size normalized by the Kolmogorov scale are most important for modeling the effect of turbulence on particle drag, while the anisotropy of fluctuating velocity and the particle Reynolds number are less important.

Influence of finite-size particles on fluid velocity and transport through porous media

Influence of finite-size particles on fluid velocity and transport through porous media

Impact of the inner solute structure on the electrostatic mean-field and strong-coupling regimes of macromolecular interactions.

The structural diversity of the solute molecules involved in biomolecular processes necessitates the characterization of the forces between charged macromolecules beyond the point-ion description. From the field-theoretic partition function of an electrolyte confined between two anionic membranes, we derive a contact-value identity valid for general intramolecular solute structure and electrostatic coupling strength. In the electrostatic mean-field regime, the inner charge spread of the solute particles is shown to induce the twofold enhancement of the short-range Poisson-Boltzmann level membrane repulsion and a longer-range depletion attraction. Our contact theorem indicates that the twofold repulsion enhancement by solute size is equally present in the opposite strong-coupling regime of linear and spherical solute molecules. Upon the inclusion of the dielectric contrast between the electrolyte and the interacting membranes, the emerging polarization forces substantially amplify the solute specificity of the macromolecular interactions. Namely, the finite size of the dumbbell-like solute particles composed of similar terminal charges weakens the intermembrane repulsion. However, the extended structure of the solute molecules carrying opposite elementary charges such as ionized atoms and zwitterionic molecules enhances the membrane repulsion by several factors. We also show that these polarization forces can extend the range of the solute structure effects up to intermembrane distances exceeding the solute size by an order of magnitude. This radical alteration of the intermembrane interactions by the salt structure identifies the solute specificity as a key ingredient of the thermodynamic stability in colloidal systems.

An improved method for estimating the dissipation rate of turbulent kinetic energy using structure functions evaluated from the motion of finite-sized neutrally buoyant particles

Statistical relations used for estimating the dissipation rate of turbulent kinetic energy (TKE) in isotropic turbulence from the inertial subrange of Lagrangian temporal and spatial structure functions are extended here to the case of more realistic turbulence spectra that include low-frequency and low-wavenumber ranges. It is shown that using the traditional relations based only on the inertial subrange substantially underestimates the dissipation. The improved relations are better constrained by experimental data from which the dissipation is evaluated, enabling more accurate dissipation estimates. The concept is illustrated using laboratory data from water tank experiments of turbulence generated by an oscillating cylinder, where the dissipation is evaluated in three independent ways: from Lagrangian spectra and from Lagrangian temporal and spatial structure functions calculated from the motion of neutrally buoyant finite-sized particles. An additional correction to the relations for estimating the dissipation from the spatial structure functions is applied to take into account the filtering effect of the particles due to their finite size. It is found that, for these particular experiments, the TKE dissipation rate scales well with dimensionally consistent quantities built using the amplitude of the oscillation of the cylinder and the period of its motion, and the constant of proportionality in this scaling relation is determined using the method proposed here. Although the turbulence under consideration is quite anisotropic, the adopted theoretical framework, which assumes isotropic turbulence, seems to be applicable to the experimental data as long as the turbulence statistics are averaged over the three main flow directions.

Drag model of finite-sized particle in turbulent wall-bound flow over sediment bed

Drag force acting on a particle is vital for the accurate simulation of turbulent multiphase flows, but the robust drag model is still an open issue. Fully resolved direct numerical simulation (DNS) with an immersed boundary method is performed to investigate the drag force on saltating particles in wall turbulence over a sediment bed. Results show that, for saltating particles, the drag force along the particle trajectories cannot be estimated accurately by traditional drag models originally developed for an isolated particle that depends on the particle-wall separation distance or local volume fraction in addition to the particle Reynolds number. The errors between the models and DNS are especially clear during the descending phase of the particles. Through simple theoretical analysis and DNS data fitting, we present a corrected factor using the classical, particle Reynolds number dependent drag force model as the benchmark model. The new drag model, which takes the particle vertical velocity into account, can reasonably predict the mean drag force obtained by DNS along a particle trajectory.

Magnetic density separation of particles in honeycomb-generated wake turbulence

Magnetic density separation (MDS) is a technique for separating granular materials based on mass density. MDS uses magnetically responsive fluids and engineered magnetic fields to create a vertical gradient of apparent mass density inside the fluid. We present a numerical study to investigate the effect of honeycomb wake turbulence on the motion of almost neutrally buoyant spherical particles in a magnetized fluid. A four-way coupled Euler-Lagrange approach is used where particles are effectively treated as finite-size point particles. It is shown that the honeycomb-generated wake turbulence increases the levitation time of the particles. The presence of particles results in an earlier break-up of the individual velocity profiles stemming from the honeycomb cells. The effects of honeycomb geometry and cell Reynolds number on the collective motion of particles and turbulence properties are investigated, where the choice for the best honeycomb is a trade-off between the separation error and the particle flux.

Parameterization of turbulence modulation by finite-size solid particles in forced homogeneous isotropic turbulence

Turbulence modulation by finite-size particles in homogeneous isotropic turbulence (HIT) has been investigated numerically and experimentally in many studies, but its controlling parameters are not fully clear. In this work, four non-dimensional parameters governing the turbulent modulation by non-settling particles, i.e. $Re_\lambda$ of the background HIT, the particle-to-fluid density ratio $\rho _p/\rho _f$ , the relative particle size $d_p/\eta$ and the particle volume fraction $\phi _v$ , are identified through dimensional analysis. Then, a parameterization study is conducted based on results from fully resolved direct numerical simulations to investigate the influence of the above non-dimensional parameters on the modulation of turbulent kinetic energy (TKE) and viscous dissipation rate. Empirical models that quantitatively predict the modulation of TKE and dissipation rate are then developed by fitting in the simulation results. These models are used to examine the turbulence modulation results reported in the literature. The model predictions and the data points of TKE modulation show reasonable agreement, but the model predicting the modulation of dissipation rate needs further deliberation as the credibility of the available data points is currently difficult to assess. The generality and the physics behind these empirical models also require further investigation.

Modeling and Experiments of Droplet Evaporation with Micro or Nano Particles in Coffee Ring or Coffee Splat.

Experimental and numerical experiments were carried out to study the coffee rings or coffee splats formed by droplet evaporation with micro or nano polystyrene sphere particles (Dp = 10 μm or 100 nm). Particle image velocimetry (PIV) and a high-resolution camera were used in this experiment, along with a temperature-controlled heater and a data-acquisition computer. The results showed that a nano particle could form a homogeneous coffee splat, instead of the common coffee ring formed when using micro particles. In order to account for this phenomenon, this paper developed a complex multiphase model, one which included the smooth particle hydrodynamics (SPH) fluid model coupled with the van der Waals equation of state for droplet evaporation, the rigid particle model of finite-size micro particles, and the point-particle model of the nanometer particles. The numerical simulation was operated on a GPU-based algorithm and tested by four validation cases. A GPU could calculate 533 times the speed of a single-core CPU for about 300,000 particles. The results showed that, for rigid solid particles, the forms emerged spontaneously on the wall, and their structure was mainly affected by the boundary wettability, and less affected by the fluid flow and thermal condition. When the wall temperature was low, it was easier for the particles to be deposited on the contact line. At high wall temperature, the coffee ring effect would be weakened, and the particles were more likely to be deposited in the droplet center. The hydrophilic surface produced a larger coffee ring compared to the hydrophobic surface. The experimental and numerical results proved that particle size could play a significant role during the particle deposition, which may be a possible route for producing uniform-distributed and nano-structure coatings.

Particle laden flows around a circular cylinder from the hydrodynamic to granular regime

The flow around a circular cylinder is studied with the presence of solid finite-size spherical particles. The simulations of suspension flows are based on highly efficient simulation algorithms to generate scalable Lattice Boltzmann Method calculations. Simulations of particle resolved dynamics with up to 4800 million grid cells and 1.8 million spherical particles are carried out for different flow regimes and particle concentrations (from dilute, 5% volume concentration to semi-dilute regime, 20%). We investigated a range of parameters that spans from suspensions of iso-dense particles to highly inertial particles in a granular flow, while considering particle to cylinder diameter ratios of 5 and 10.The flow response is described by characteristic properties such as vortex shedding frequency or wake recirculation length. Flow regimes with iso-dense particles can be rationalized by means of mixture material properties while we observe a progressive transition to granular flow for inertial particles. Drag and lift forces acting onto the cylinder are presented in time and frequency domains and the physical analysis is based on the respective hydrodynamic and particle collision contributions.

Taylor-Couette flow of hard-sphere suspensions: overview of current understanding.

Although inertial particle-laden flows occur in a wide range of industrial and natural processes, there is both a lack of fundamental understanding of these flows and continuum-level governing equations needed to predict transport and particle distribution. Towards this effort, the Taylor-Couette flow (TCF) system has been used recently to study the flow behaviour of particle-laden fluids under inertia. This article provides an overview of experimental, theoretical and computational work related to the TCF of neutrally buoyant non-Brownian suspensions, with an emphasis on the effect of finite-sized particles on the series of flow transitions and flow structures. Particles, depending on their size and concentration, cause several significant deviations from Newtonian fluid behaviour, including shifting the Reynolds number corresponding to transitions in flow structure and changing the possible structures present in the flow. Furthermore, particles may also migrate depending on the flow structure, leading to hysteretic effects that further complicate the flow behaviour. The current state of theoretical and computational modelling efforts to describe the experimental observations is discussed, and suggestions for potential future directions to improve the fundamental understanding of inertial particle-laden flows are provided. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

No room to hide: implications of cosmic-ray upscattering for GeV-scale dark matter

The irreducible upscattering of cold dark matter by cosmic rays opens up the intriguing possibility of detecting even light dark matter in conventional direct detection experiments or underground neutrino detectors. The mechanism also significantly enhances sensitivity to models with very large nuclear scattering rates, where the atmosphere and rock overburden efficiently stop standard non-relativistic dark matter particles before they could reach the detector. In this article, we demonstrate that cosmic-ray upscattering essentially closes the window for strongly interacting dark matter in the (sub-)GeV mass range. Arriving at this conclusion crucially requires a detailed treatment of both nuclear form factors and inelastic dark matter-nucleus scattering, as well as including the full momentum-transfer dependence of scattering amplitudes. We illustrate the latter point by considering three generic situations where such a momentum-dependence is particularly relevant, namely for interactions dominated by the exchange of light vector or scalar mediators, respectively, and for dark matter particles of finite size. As a final concrete example, we apply our analysis to a putative hexaquark state, which has been suggested as a viable baryonic dark matter candidate. Once again, we find that the updated constraints derived in this work close a significant part of otherwise unconstrained parameter space.

Attractors for the motion of a finite-size particle in a cuboidal lid-driven cavity

The motion of a finite-size particle in the cuboidal lid-driven cavity flow is investigated experimentally for Reynolds numbers $100$ and $200$ for which the flow is steady. These steady three-dimensional flows exhibit chaotic and regular streamlines, where the latter are confined to Kolmogorov–Arnold–Moser (KAM) tori. The interaction between the moving wall and the particle creates global particle attractors. For neutrally buoyant particles, these attractors are periodic or quasi-periodic, strongly attracting and located in or near KAM tori of the flow. As the density mismatch between particle and fluid increases, buoyancy and inertia become important, and the attractors evolve from those for neutrally buoyant particles, changing their shape, position and attraction rates.

Mathematical and computational modeling of electrohydrodynamics through a nanochannel

Fluid-ion transport through a nanochannel is studied to understand the role and impact of different physical phenomena and medium properties on the flow. Mathematically, the system is described through coupled fourth order Poisson–Nernst–Planck–Bikerman and Navier–Stokes equations. The fourth order-Poisson–Nernst–Planck–Bikerman model accounts for ionic and nonionic interactions between particles, the effect of finite size of the particles, polarization of the medium, solvation of the ions, etc. Navier–Stokes equations are modified accordingly to include both electroviscous and viscoelectric effects and the velocity slip. The governing equations are discretized using the lattice Boltzmann method. The mathematical model is validated by comparing the analytical and experimental ion activity while the numerical model is validated by comparing the analytical and numerical velocity profiles for electro-osmotic flow through a microchannel. For a pressure driven flow, the electroviscous and viscoelectric effects decrease the fluid velocity while the velocity slip enhances it. The acidity of the medium also influences the fluid velocity by altering the ζ potential and ion concentration. The finite size of the particle limits the concentration of ionic species, thus, reducing electroviscous effects. As the external concentration decreases, the impact of finite size of particles also reduces. The inhomogeneous diffusion coefficient also influences electroviscous effects as it changes the concentration distribution. The variation in external pressure does not influence the impact of steric and viscoelectric effects significantly. The maximum impact is observed for ΔP = 0 (electro-osmotic flow).

Improved modelling of interfacial terms in the second-moment closure for particle-laden flows based on interface-resolved simulation data

Correlations for the interfacial terms in the fluid dissipation rate equation and Reynolds stress equations are established for particle-laden flows, based on data from the interfaced-resolved direct numerical simulations of particle sedimentation in a periodic domain at a density ratio ranging from 0.01 to 1000, a particle concentration ranging from 2.3 % to 30.2 % and a particle Reynolds number below 250. The correlations for the mean drag and the pseudo-turbulent kinetic energy are also reported, which are used for the modelling of the interfacial term in the fluid dissipation rate equation. The interfacial term correlations obtained are then incorporated in the Reynolds stress model (RSM) (i.e. second-moment closure) for the simulation of vertical turbulent channel flows laden with the finite-size particles at relatively low particle volume fractions. The results show that the RSM with new interfacial term correlations can quantitatively predict particle-induced turbulence enhancement or suppression in vertical channel flows.

A correction procedure for self-induced velocity of a finite-sized particle in two-way coupled Euler–Lagrange simulations

The importance of incorporating a correction to undo the self-induced perturbation velocity of a particle, when its size becomes comparable to the Eulerian grid, in a two-way coupled Euler–Lagrange (EL) simulation is now well appreciated. The present work improves upon the prior correction procedures in a few important ways. First, the past correction procedures have been scalar-based with the assumption that the quasi-steady force is the source of self-induced velocity perturbation. Here we generalize to a vector correction procedure and thereby the directions of feedback force and relative velocity can be different. This allows the correction procedure to be used even in the presence of added-mass, history, and lift forces. Second, the effect of a nearby wall has been systematically included in the correction procedure. The correction procedure depends on fundamental Oseen solutions of streamwise and transverse regularized feedback forces. We present a Fourier transform-based analytical approach to obtaining these regularized Oseen solutions. We also present a step-by-step numerical procedure for obtaining the Oseen solutions in any EL code. With the analytical or numerical Oseen functions, the correction procedure can be easily implemented in any EL code. Iterations are required in solving the implicit correction equations and it is demonstrated that the correction procedure converges rapidly within three or four iterations. A simple empirical approach is also presented to account for unsteady effects in the correction procedure.

Numerical study of microscopic particle arrangement of suspension flow in a narrow channel for the estimation of macroscopic rheological properties

In a narrow channel, the apparent relative viscosity of a suspension with finite-size particles is strongly dependent on its microscopic particle arrangement. Relative viscosity increases when suspended particles flow near the channel wall; thus, a suspension in a narrow channel does not always exhibit the same rheological properties even if the concentration is the same. In this study, we focus on the inertia and concentration of particles in a narrow channel and consider their effects on the microscopic particle arrangement and macroscopic suspension rheology. Two-dimensional pressure-driven suspension flow simulations were performed using a two-way coupling scheme, and normalized particle density distribution (PDD) were implemented to consider their particle arrangements. The results demonstrated that the velocity profiles for the particle suspension were changed by the Reynolds number and particle concentration because of the interactions between particles according to the power-law index. These changes affected the particle equilibrium positions in the channel, and the subsequent changes in solvent layer thickness caused changes in the macroscopic apparent viscosity. The behavior of microscopic particles played important roles in determining macroscopic rheology. Thus, we have confirmed that a normalized PDD can be used to estimate and assess the macroscopic rheology of a suspension.

Theoretical Framework Based on Molecular Dynamics and Data Mining Analyses for the Study of Potential Energy Surfaces of Finite-Size Particles.

Nanoclusters are remarkably promising for the capture and activation of small molecules for fuel production or as precursors for other chemicals of high commercial value. Since this process occurs under a wide variety of experimental conditions, an improved atomistic understanding of the stability and phase transitions of these systems will be key to the development of successful technological applications. In this work, we proposed a theoretical framework to explore the potential energy surface and configuration space of nanoclusters to map the most important morphologies presented by those systems and the phase transitions between them. A fully automated process was developed, which combines global optimization techniques, classical molecular dynamics, and unsupervised machine learning algorithms. To showcase these capabilities of the approach, we explored the example of copper nanoclusters (Cun) where n = 13, 38, 55, 75, 98, 102, and 147. We not only reported a graphical potential energy surface for each size, but also explored the topology of the configuration space via structural and thermodynamic analyses. The effect of size on the potential energy surface and the critical temperature for solid-liquid phase transitions were also reported, highlighting the impact of magic numbers on those quantities.

The effect of particle anisotropy on the modulation of turbulent flows

We investigate the modulation of turbulence caused by the presence of finite-size dispersed particles. Bluff (isotropic) spheres versus slender (anisotropic) fibres are considered to understand the influence of the shape of the objects on altering the carrier flow. While at a fixed mass fraction – but different Stokes number – both objects provide a similar bulk effect characterized by a large-scale energy depletion, a scale-by-scale analysis of the energy transfer reveals that the alteration of the whole spectrum is intrinsically different. For bluff objects, the classical energy cascade shrinks in its extension but is unaltered in the energy content and its typical features, while for slender ones we find an alternative energy flux which is essentially mediated by the fluid–solid coupling.

Attenuation of turbulence in a periodic cube by finite-size spherical solid particles

To investigate the attenuation of turbulence in a periodic cube due to the addition of spherical solid particles, we conduct direct numerical simulations using an immersed boundary method with resolving flow around each particle. Numerical results with systematically changing particle diameters and Stokes numbers for a fixed volume fraction $\varLambda$ show that the additional energy dissipation rate in the wake of particles determines the degree of the attenuation of turbulent kinetic energy. On the basis of this observation, we propose formulae describing the condition and degree of the attenuation of turbulence intensity. We conclude that particles with size proportional to $\lambda /\sqrt {\gamma }$ , where $\lambda$ and $\gamma$ are the Taylor length and the mass density ratio between particles and fluid, most significantly reduce the intensity of developed turbulence under the condition that $\gamma$ and $\varLambda$ are fixed.

Chaotic rotation of a finite-size spheroidal particle in oscillating shear flows with fluid inertia

Rotational dynamics of a prolate spheroid in oscillating shear flows is studied by fully resolved direct numerical simulations with an immersed boundary method. In this flow configuration, we extend the work of Nilsen and Andersson [“Chaotic rotation of inertial spheroids in oscillating shear flow,” Phys. Fluids 25, 013303 (2013)] with focusing on the fluid inertia effect. We observe that the spheroid could rotate in chaotic and nonchaotic modes, which are identified by the sign of a largest Lyapunov exponent of the dynamic system. These two distinct rotation modes depend on both particle Reynolds number and oscillation frequency. For a certain Reynolds number, chaotic rotation appears when oscillation frequency is lower than a critical value, which decreases linearly with the increase of the particle Reynolds number. Based on this finding, we propose an empirical expression to predict the rotation mode. We, furthermore, discuss the mechanism of the emergence of the chaotic rotation, which is ascribed to a nonlinear interaction between time-varying orientation of the inertial spheroid and the oscillation of the shear rate.