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Mass transport of the Knudsen gas in a porous medium is investigated on the basis of the kinetic theory of gases. First, the mass flow conductance is computed numerically for various porosities and solid grain sizes by stochastic particle simulations (SPS). Then, a kinetic model with a homogeneous scatterer is introduced, which contains the reference Knudsen number as the sole parameter that characterizes the collision frequency of gas molecules with the micro-structural solid surface. With the aid of the standard asymptotic analyses for small and large Knudsen numbers combined with the percolation theory, the effective reference Knudsen number is identified to reproduce the SPS results for a wide range of porosities., This paper is part of the Special Topic, Advances in Micro/Nano Fluid Flows: In Memory of Prof. Jason Reese.

We study the motion of radially driven fluid-immersed particles in a novel Hele-Shaw cell with open boundaries. The initially uniform suspension forms a striped pattern within a specific range of horizontal oscillation frequencies and for sufficiently large amplitudes. We observe that the initial coarsening dynamics of the stripes gradually slows down and the pattern reaches a steady state after a few minutes. The distance between the stripes in the steady state exhibits an exponentially saturating increase with increased oscillation amplitude or frequency. The width of the stripes decreases as a power-law with the frequency while its amplitude dependence follows a logistic function. We propose a mechanism -- based on the interplay between shear stress, hydrodynamic interactions, and frictional forces -- to link the structural characteristics of the stripes to the properties of the oscillatory external drive., Comment: 7 pages, 4 figures

Binary collision rates are calculated for the permeable particles undergoing (i) Brownian motion, (ii) gravity sedimentation, (iii) uniaxial straining flow, and (iv) shear flow. Darcy's law is used to describe the flow inside the permeable particles, and no-slip boundary conditions are applied at particle surfaces. A leading-order asymptotic solution of the problem is developed for the weak permeability regime K=k/a2≪1, where k=12(k1+k2) is the mean permeability and a=a1a2/(a1+a2) is the reduced radius; ai, ki (i = 1, 2), respectively, is the radius and permeability of each particle. The resulting collision rates are given by the quadrature of the pair mobility functions for permeable particles in the near-contact lubrication region and size-ratio-dependent parameters obtained from standard hard-sphere pair mobility functions. Collision rates in shear flow vanish below a critical value of the permeability parameter K* that increases with diminishing size ratio. The analogous problem of pair collision rates of particles with small-amplitude surface roughness δa is also analyzed. The formulas for the collision rates of rough particles provide accurate analytical approximations for the collision rates of permeable particles for all four aggregation mechanisms and a wide range of size ratios using an equivalent roughness δ=0.72K2/5.

Collision of two vortex rings (VR) initially arranged in axis-offset and orthogonal configurations at Reynolds numbers ( ReΓ) in the range of 5000–200 000 was simulated to investigate turbulent energy cascade associated with their reconnection. Two elliptical VRs are generated by joining each part of the first VR with another part of the second VR for the axis-offset collision, while two VRs associate to form a double U-shaped vortex, and this vortex reconnects itself at two points to form three elliptical VRs linked by the vortex filaments for the orthogonal collision. Many vortex structures in various scales and shapes, including small-scale VRs and horseshoe vortices, are observed in connection regions for both cases. As ReΓ increases, the energy of formed small vortices raises and their wavenumber (k) range enlarges. The flow energy spectrum approaches a k−5/3 slope of the Kolmogorov hypotheses at low wavenumbers. For the axis-offset collision, the energy spectrum at medium wavenumbers continuously changes from k−3.0 at ReΓ= 5000 to k−1.8 at ReΓ= 200 000, and the exponent (α) of the wavenumber is determined by a function as α=0.3304 ln(ReΓ)−5.6538. Meanwhile, the energy spectrum at two medium-wavenumber subranges for the orthogonal collision with ReΓ≥ 20 000 approaches the slopes of k−3.0 and k−2.6. Turbulent mixing performance due to the axis-offset collision of two vortex rings is better than that with the orthogonal one.

In the time since the Navier–Stokes equations were introduced more than two centuries ago, their application to problems involving real gas effects has relied on appropriate closure for the mass, momentum, and energy transport fluxes via the constitutive laws. Determination of the corresponding transport coefficients, most readily obtained through generalized Chapman–Enskog theory, requires knowledge of the intermolecular potentials for rotationally and vibrationally excited molecules. Recent advances in computational chemistry provide extraordinary detail of interactions involving rovibrationally excited molecules, offering a means for transport flux closure with unprecedented accuracy. Here, the bracket integrals for rovibrationally resolved molecular states are developed, and the resulting transport flux closure is presented for the rovibrationally resolved Navier–Stokes equations. The accompanying continuum breakdown parameters are also derived as a rigorous metric to establish the range of applicability of the aforementioned equations in flow conditions approaching the rarefied regime.

In this study, the coalescence dynamics of two unequal sized vertically inline bubbles rising in a liquid column have been investigated using the coupled level-set and volume-of-fluid (CLSVOF) method. A wide range of bubble radius ratios of trailing bubble and leading bubble ( 0.25 ≤ R ≤ 2.0) and separation distances between the bubbles ( 2.5 ≤ S ≤ 3.5) have been deployed to investigate the evolution of the bubble wakes and bubble shapes. It is discovered that the coalescence time increases with R, the maxima being around 0.75 ≤ R ≤ 1, and then it decreases. With the increase in S, the coalescence time gradually increases. The existence of a pair of counter-rotating vortex rings has been observed between the bubbles, which are seen to accelerate the bubble coalescence process. For the present range of R and S, we show a regime map with four distinct coalescence pathways: coalescence with liquid entrapment, coalescence without liquid entrapment, penetration of the leading bubble, and premature splitting of the trailing bubble.

The effect of finite inertia on the particle distribution of mono and bidisperse suspensions under a wall-bounded linear shear flow has been numerically studied using lattice Boltzmann simulations in the range of the particle Reynolds number (Rep) up to approximately 1 at moderate volume fractions ( ϕ ¯ = 0.2). We found that the channel-to-particle size ratio ( H / a p) plays an important role in the monodisperse particle distribution at R e p > 0.1, such that the particles with H / a p = 19 maintain a uniform distribution even at finite inertia, while those with H / a p = 32 accumulate in the mid-plane, and the accumulation increases with increasing H / a p and decreasing ϕ ¯. The bidisperse particle suspension comprising a mixture of large ( H / a l = 19) and small ( H / a s = 32) particles with ϕ l ¯ = 0.05 and ϕ s ¯ = 0.15 was also examined, where the subscripts l and s denote large and small particles, respectively. The particle distribution of the mixture was strikingly different from that expected for monodisperse suspensions, such that the net migration of large particles was reversed toward the walls at R e s > 0.1. Further, it was demonstrated that the inertia-driven concentration gradient of small particles leads to the diffusiophoretic migration of large particles moving toward the walls.

The impact dynamics of a water droplet on a flexible substrate is useful for designing pesticide sprays and understanding insects flying in rainfall. We experimentally analyze the impact dynamics of a microliter water droplet on a superhydrophobic cantilever beam for Weber number in the range of 30–76. A thin copper sheet was coated with a commercial coating to render it superhydrophobic and high-speed imaging was used for visualization. During the impact, the spreading droplet converts its inertial energy into surface energy and elastic energy of the substrate. While retraction of the contact line, the latter energies convert to the kinetic energy of the droplet, and the droplet could bounce off the deforming cantilever beam. The characteristics timescales of droplet and cantilever beams are varied by changing the droplet diameter and impact velocity, and beam length, respectively. We show that the overall system dynamics, i.e., bouncing of the droplet and oscillations of the cantilever, is dependent on the interplay of these two timescales. A spring-mass system has been used to model this coupling and to explain the experimental observations. These findings can help to design systems to achieve desirable contact time, droplet rebound kinetic energy, energy transfer to the cantilever beam, and the droplet spreading diameter.

Liquid drops sliding on surfaces are ubiquitous both in the natural and industrial world. The prediction of such drop motions has far-reaching implications in many fields of application, including microfluidics, phase change heat transfer, or coating technology. We present a numerical model based on the particle finite element method for the prediction of the sliding motion of liquid drops. The model includes the effect of a retention force which acts in the vicinity of the drop's contact line. This effect is found to be essential to obtain realistic spatiotemporal evolution of the drop. Thus far limited to two-dimensional simulations, the proposed model is validated by using experimental data found in the published literature, covering a wide range of drop size and physical properties. The numerical results are found to be mesh-independent and in good agreement with the experiments.

In electrolyte solutions, charged nanoscale pores or channels with overlapping electrical double layers are charge selective, thereby benefiting a wide range of applications such as desalination, bio-sensing, membrane technology, and renewable energy. As an important forcing mechanism, a gradient of electrolyte concentration along a charged nano-confinement can drive flow without an external electrical field or applied pressure difference. In this paper, we numerically investigate such a diffusioosmotic nanoflow, particularly for dilute electrolyte concentrations (0.01 mM–1 mM), and calculate the corresponding electrical and concentration fields in a charged nanochannel connecting two reservoirs of different salt concentrations—a typical fluidic configuration for a variety of experimental applications. Under a wide range of parameters, the simulation results show that the flow speed inside the nanochannel is linearly dependent on the concentration difference between the two reservoir solutions, Δc, whereas the flow direction is primarily influenced by three key parameters: nanochannel length (l), height (h), and surface charge density (σ). Through a comparison of the chemiosmotic (due to ion-concentration difference) and electroosmotic (as a result of the induced electric field) components of this diffusioosmotic flow, a non-dimensional number ( C = h / l λ G C) has been identified to delineate different nanoscale flow directions in the charged nanochannel, where λGC is a characteristic (so-called Gouy–Chapman) length associated with surface charge and inversely proportional to σ. This critical dimensionless parameter, dependent on the above three key nanochannel parameters, can help in providing a feasible strategy for flow control in a charged nanochannel.

The generation of monodispersed droplets in T-junction microchannels has wide range applications in biochemical analysis and material synthesis. While the generation of these monodispersed droplets was previously considered to be a balance between forces acting from continuous phase and interfacial force, it is shown here that the inertial force from the dispersed phase also plays an important role in determining the size of the generated droplets. A theoretical analysis for the size of monodisperse droplets generated in a microfluidic T-junction device is developed, and it is validated with a large set of experimental observations. The theoretical analysis accounts for the inertial forces from the dispersed phase along with the forces from the continuous phase and the interfacial forces to define the non-dimensional numbers that govern the droplet breakup in the T-junction microchannel.

We consider thermocapillary instability in a three-dimensional liquid layer with a deformable interface with an ambient gas phase and subjected to an oblique temperature gradient when the temperature gradient at the substrate is prescribed. We demonstrate that this configuration leads to a drastic change in the instability features with respect to those emerging when either a purely vertical temperature gradient (VTG) or a purely horizontal temperature gradient (HTG) is present. In the case of the return flow as the base state, the spanwise long-wave instability mode dominates except for the range of small Bond numbers Bo. Slippage at the substrate has a stabilizing (destabilizing) effect on streamwise (spanwise) long-wave modes in the presence of a HTG. In the case of linear flow as the base state, both streamwise and spanwise long-wave modes play a major role in the instability onset depending on the ratio between the HTG and the VTG η for higher values of the capillary number Ca, e.g., Ca > 0.001. However, for lower values of Ca, e.g., Ca < 0.001, streamwise and spanwise instability modes become finite-waves at large η. In contrast to the return flow, for the linear flow, slippage at the substrate destabilizes both long-wave modes.

This study is devoted to the numerical analysis of the result of light distribution after passing it through a shock wave, depending on the degree of gas rarefaction. The obtained numerical results allowed reproducing the experimental shadowgraph images obtained in our study. The range of shock wave thickness (from 0 mm to 20 mm) allowed considering the qualitative change in the light distribution on the screen during switching from the regime where the wave nature of light has the greatest influence on the distribution of light to the regime of the geometric optics approach. As a result, the criteria for the applicability of the shadowgraphy technique for the experimental description of the shock wave internal structure were obtained.

The existence of cavitation nuclei is one of the necessary conditions for liquid cavitation. Bubble nucleus is the most basic cavitation nucleus, and bubble nuclei size distribution is a parameter describing the population of gas nuclei. To study the dynamics of bubble nuclei population after artificial seeding under reduced pressure, a decompression chamber was built, combined with the artificial seeding system and the acoustic nuclei measurement system. After the nuclei seeding, the experimental study of the nuclei population dynamics with pressure and time was carried out. It is found that as the pressure decreases, the number density of larger size nuclei decreases, while the number density of smaller size nuclei increases. In the measured size range, the maximum value of number density of the nuclei size distribution increases. In addition, based on the theory of bubble dynamics, the growth process of the nucleus under reduced pressure is calculated and analyzed, which can realize the preliminary prediction of the nuclei population dynamics under reduced pressure.

The present paper elaborates on the experimental study of jet-excited pressure fluctuations in a Helmholtz oscillator model with two openings in a cylindrical cavity. The length of the cylindrical nozzle in the front cover lN normalized by the nozzle diameter dN was lN/dN = 0.125, 0.33, 0.47, and 0.67. The diameter of the outlet opening in the back cover dOUT was in the range dOUT/dN = 1–2.5. The length of the cylindrical cavity LCH determined the jet length LJET in the spacing between the covers, LCH/dN = 0.5–3.5. The amplitude–frequency spectra were studied when the oscillator configuration was changed in the indicated intervals. From the generation amplitude, the best ratio of the sizes of the nozzle, chamber, and outlet was determined. The appearance of the jet tone of the hole and the alternation of acoustic modes were observed with a smooth increase in the Reynolds number to ∼8 · 104. The measurements showed very high amplitude of pressure fluctuations in an oscillator with a short nozzle and a short chamber at a significant jet velocity. A slight increase in the length of the chamber led to a rapid decrease in the generation amplitude. It is determined that the tone frequency is usually much lower than the resonance frequency in the chamber. Moreover, the tone frequency gradually increases with increasing jet velocity, while the resonance frequency remains unchanged, close to the natural frequency of the cavity chamber.

Micro lubrication of a gas between two walls with an arbitrary temperature difference is studied on the basis of the Bhatnagar–Gross–Krook–Welander model of the Boltzmann equation. Applying the slowly varying approximation, the kinetic equation is studied analytically when the Knudsen number based on the gap size is large. The leading order approximation, which ought to be the solution of the nonlinear heat transfer problem, is replaced by its free molecular solution. Due to this crude approximation, a macroscopic lubrication model of Reynolds-type equation is derived in a closed form. For an assessment of the model, a direct numerical analysis of the kinetic equation is also conducted. The lift calculated using our model approximates that of the direct numerical analysis within the error of 4% uniformly in the range of the temperature ratio between 0.75 and 2 and the Knudsen number Kn between 0.1 and 10. A heating of the moving wall reduces the lift acting on the other wall when Kn is sufficiently large, whereas it is enhanced when Kn is sufficiently small.

Dynamics of a single porous, rigid, two-dimensional (2D) elliptic particle settling in a narrow vertical channel filled with a Newtonian fluid is numerically studied using the lattice-Boltzmann method. The main objective of the work is to investigate the role played by the particle’s permeability on its trajectory, orientation, and terminal velocity when released from the rest state with prescribed initial conditions. Assuming that the flow induced in the fluid surrounding the particle is laminar, incompressible, isothermal, and two-dimensional, numerical results could be obtained over a wide range of parameter settings suggesting that permeability can strongly affect the modes of sedimentation reported in the literature for impermeable elliptic particles provided that the particle’s permeability is larger than a threshold. Above this threshold, permeability is predicted to increase the terminal velocity of the particle with its severity depending on the blockage ratio. It is also predicted that a permeable particle is less sensitive to initial orientation and position as compared with an impermeable particle.

Energy dynamics in elastoinertial turbulence is investigated by performing different direct numerical simulations of stationary, homogeneous isotropic turbulence for the range of Weissenberg numbers 0 ≤ Wi ≤ 9. Viscoelastic effects are described by the finite extensibility nonlinear elastic-Peterlin model. It is found that the presence of the polymer additives can nontrivially modify the kinetic energy dynamics by suppressing the rate of the kinetic energy transfer and altering the locality nature of this energy transfer. Spectral representation of the elastic field revealed that the elastic energy is also transferred locally through different elastic degrees of freedom via a dominantly forward energy cascade. Moreover, the elastic energy spectrum can display a power-law behavior, k−m, with the possibility of different scaling exponents depending on the Wi number. It is observed that the energy exchange between macro- and microstructures is a two-directional process: there is a dominant energy transfer from the solvent large-scale structures to the polymers alongside a weak energy transfer from polymers to the solvent small-scale structures. This energy exchange consists of three different fluxes. Two of these fluxes equally transfer a small fraction of the kinetic energy into the mean and fluctuating elastic fields. However, the main energy conversion takes place between fluctuating kinetic and elastic fields through a completely nonlocal energy transfer process.Energy dynamics in elastoinertial turbulence is investigated by performing different direct numerical simulations of stationary, homogeneous isotropic turbulence for the range of Weissenberg numbers 0 ≤ Wi ≤ 9. Viscoelastic effects are described by the finite extensibility nonlinear elastic-Peterlin model. It is found that the presence of the polymer additives can nontrivially modify the kinetic energy dynamics by suppressing the rate of the kinetic energy transfer and altering the locality nature of this energy transfer. Spectral representation of the elastic field revealed that the elastic energy is also transferred locally through different elastic degrees of freedom via a dominantly forward energy cascade. Moreover, the elastic energy spectrum can display a power-law behavior, k−m, with the possibility of different scaling exponents depending on the Wi number. It is observed that the energy exchange between macro- and microstructures is a two-directional process: there is a dominant energy transfer fr...

In this paper, the thermodynamic effect is systematically studied by Venturi cavitation in a blow-down type tunnel for the first time, using water at temperatures up to relatively high levels and at controlled dissolved gas contents in the supply reservoir (measured by dissolved oxygen, DO). The mean attached cavity length Lcav is chosen to reveal the thermodynamic effect, and the cavitation characteristics are analyzed from the experiments. With an increase in the thermodynamic parameter Σ*, a decrease in Lcav vs the pressure recovery number κ is observed, which is consistent with suppression of cavitation by the thermodynamic effect, but the decrease is related not only to this effect. Based on the experimental results, a model is presented of the attached cavity cloud that develops from the Venturi throat. It is found that either the length of this cloud oscillates stably around a mean value or the cloud breaks regularly at some upstream position, allowing that a detached cavity cloud is shed, flows downstream, and collapses while the remaining attached cloud regenerates. Applying this model to experimental results obtained first with cold water, then with hot water, we find that when the mean length of the attached cavity cloud oscillates stably, temperature increase causes reduction of the mean cavitation length. This is interpreted to be a consequence of the thermodynamic effect. When detachment of large cavity clouds occurs, the mean length is increased at temperature increase. This is a consequence of cloud configuration changes being superposed on changes due to the thermodynamic effect. These observations explain conflicting results reported for attached cavity clouds in relation to the thermodynamic effect. The gas content in the water is found to be without significance within the range of DO tested.

It is known from recent studies that evaporation induces flow around a droplet at atmospheric conditions. This flow is visible even for slowly evaporating liquids like water. In the present study, we investigate the influence of the ambient gas on the evaporating droplet. We observe from the experiments that the rate of evaporation at atmospheric temperature and pressure decreases in a heavier ambient gas. The evaporation-induced flow in these gases for different liquids is measured using particle image velocimetry and found to be very different from each other. However, the width of the disturbed zone around the droplet is seen to be independent of the evaporating liquid and the size of the needle (for the range of needle diameters studied), and only depends on the ambient gas used.It is known from recent studies that evaporation induces flow around a droplet at atmospheric conditions. This flow is visible even for slowly evaporating liquids like water. In the present study, we investigate the influence of the ambient gas on the evaporating droplet. We observe from the experiments that the rate of evaporation at atmospheric temperature and pressure decreases in a heavier ambient gas. The evaporation-induced flow in these gases for different liquids is measured using particle image velocimetry and found to be very different from each other. However, the width of the disturbed zone around the droplet is seen to be independent of the evaporating liquid and the size of the needle (for the range of needle diameters studied), and only depends on the ambient gas used.

In this study, the spreading characteristics of water droplets impacted on a solid spherical target have been investigated experimentally and theoretically. Droplet impact and postimpact feature studies have been conducted on hydrophilic and superhydrophobic spherical surfaces. Effects of the impact Weber number and target-to-drop diameter ratio on the spreading hydrodynamics have been discussed. Postcollision dynamics are explored with side and top views of impaction phenomenon using a high speed imaging technique. The morphological outcome of this impingement process has been quantitatively discussed with three geometric parameters, namely, liquid film thickness at the north-pole of the target surface, spread factor, and the maximum spread angle. Observations revel that spread factor and the maximum spread angle increases with the decrease in the size of the spherical target, whereas opposite of this is true for liquid film thickness at the north-pole of the target surface. Temporal variations of liquid film thickness at the north pole of the target have been plotted and found in agreement with the theoretical predictions made in the earlier studies. Finally, a mathematical model based on the energy balance principle has been proposed to predict the maximum spread angle on spherical targets. The theoretical values are found in good agreement with the experimental results for a wide range of spherical diameters studied. The findings may have implications toward a better understanding of fluid wetting, spraying, and coating behavior of complex shapes and geometries.

This letter investigates the clustering of particles in isotropic turbulence sustained by linear and spectral forcing. The Stokes numbers range from 0.1 to 100. The time series of particles are ana...

The effect of internal-kinetic energy exchange on transient spectral energy transfer in compressible turbulence is investigated. We derive the spectral evolution equations for kinetic energy and pressure fields to highlight the key mechanisms that affect the turbulence spectral evolution. Direct numerical simulations of decaying isotropic turbulence are performed from solenoidal, dilatational, and mixed velocity initial conditions. It is shown that internal-kinetic energy exchange arising due to pressure-dilatation renders the dilatational kinetic energy amplitudes at large scales of motion to be oscillatory. The oscillatory behavior of amplitude diminishes with increasing wavenumber. The dilatational energy spectrum also exhibits a wider range of scales due to its inherent tendency to form shocks. The findings are expected to lead to an improved understanding of energy dynamics in high-speed compressible flows.The effect of internal-kinetic energy exchange on transient spectral energy transfer in compressible turbulence is investigated. We derive the spectral evolution equations for kinetic energy and pressure fields to highlight the key mechanisms that affect the turbulence spectral evolution. Direct numerical simulations of decaying isotropic turbulence are performed from solenoidal, dilatational, and mixed velocity initial conditions. It is shown that internal-kinetic energy exchange arising due to pressure-dilatation renders the dilatational kinetic energy amplitudes at large scales of motion to be oscillatory. The oscillatory behavior of amplitude diminishes with increasing wavenumber. The dilatational energy spectrum also exhibits a wider range of scales due to its inherent tendency to form shocks. The findings are expected to lead to an improved understanding of energy dynamics in high-speed compressible flows.

A three-roll mill is used in various engineering fields to manufacture high-value-added products. This mill has three horizontally positioned rolls with different rotational velocities. In the mill, viscous materials (or pastes) pass through the narrow gap between the rolls to be mixed, refined, dispersed, and/or homogenized. The viscous materials tend to consist of wet-particles connected by liquid bridges. Although viscous materials always adhere to a faster roll in the three-roll mill, the mechanism has not yet been clarified. Herein, the adhesion mechanism is clarified scientifically by numerical simulation. In the calculations, a Lagrangian method, such as the discrete element method, is used to analyze the specific phenomena in the particle–particle and the particle–wall interaction. A latest liquid bridge force model is used in this study to examine the effect of a wide range of liquid volumes on the adhesion phenomena. In the calculation, a lump of wet-particles is fed into the gap between the two rolls and the roll speed is changed to investigate its influence on the adhesion phenomena. Through numerical examples, it is proven that wet-particles always adhere to a fast roll because the liquid bridge force that acts on the faster roll is larger than that on the slower roll after the compression force is released. This is because the extension of the wet-particles is larger on the faster roll because of the speed difference between the two rolls. Consequently, the adhesion mechanism of the wet-particles in the three-roll mill is proven scientifically to be the force balance due to the liquid bridge force.

This paper is devoted to the instability mechanisms of the thermocapillary flow in an annular pool. The stability limit of the axisymmetric basic state was studied over a wide range of Prandtl numbers (0.001 ≤ Pr ≤ 6.7) using linear stability analysis based on the spectral element method. The results demonstrate five types of instabilities, and the corresponding instability mechanisms were revealed by disturbance energy analysis. In particular, in the narrow range 1.4 ≤ Pr ≤ 1.53, with the increase in the Marangoni number, three transitions between the axisymmetric steady flow and the three-dimensional oscillatory flow were found, owing to the coupling and interaction of the hydrodynamic and hydrothermal instability mechanisms.

Experimental investigation of particle pair separation is conducted in two types of laboratory two-dimensional turbulence under a broad range of experimental conditions. In the range of scales corresponding to the inverse energy cascade inertial interval, the particle pair separation exhibits diffusive behaviour. The analysis of the pair velocity correlations suggests the existence of coherent bundles or clusters of non-diverging fluid particles. Such bundles are also detected using a recently developed topological tool based on the concept of braids. The bundles are observed as meandering streams whose width is determined by the turbulence forcing scale. In such locally anisotropic turbulence, the particle pair dispersion depends on the initial particle separation and on the width of the bundles.

In Stokesian Dynamics, particles are assumed to interact in two ways: through long-range mobility interactions and through short-range lubrication interactions. To speed up computations, in shear-driven concentrated suspensions, often found in rheometric contexts, it is common to consider only lubrication. We show that, although this approximation may provide acceptable results in shear-driven, periodic suspensions, for bidisperse suspensions where the particles are exposed to an external force, it can produce physically unreasonable results. We suggest that this problem could be mitigated by a careful choice of particle pairs on which lubrication interactions should be included., 17 pages, 12 figures

Temperatures of the attainable superheating of liquid n-butane have been determined at pressures from 0.4 to 2.0 MPa in the range of nucleation rates J = 104–108 s−1 m−3. The data obtained have been compared with classical nucleation theory (CNT). At J > 106 s−1 m−3, satisfactory agreement between theory and experiment has been noted in both the value of the limiting superheating and the slope of the temperature dependence of the nucleation rate. It is shown that temperatures of the attainable superheatings of hydrocarbons of the methane series satisfy the one-parameter similarity. The possibility of manifestation of heterogeneous nucleation in experiment is discussed.

Shapes and paths of an air bubble rising inside a liquid are investigated experimentally. About three hundred experiments are conducted in order to generate a phase plot in the Galilei and Eotvos numbers plane, which separates distinct regimes in terms of bubble behaviour. A wide range of the Galilei and Eotvos numbers are obtained by using aqueous glycerol solutions of different concentrations as the surrounding fluid, and by varying the bubble size. The dynamics is investigated in terms of shapes, topological changes and trajectories of the bubbles. Direct numerical simulations are conducted to study the bubble dynamics, which show excellent agreement with the experiments. To the best of our knowledge, this is the first time an experimentally obtained phase plot showing the distinct behaviour of an air bubble rising in a quiescent medium is reported for such a large range of Galilei and Eotvos numbers., Comment: 13 pages, 13 figures

Collisions between two thin floating disks forced by regular water waves are studied for a range of wave amplitudes and lengths, using laboratory wave basin experiments and a mathematical model. Three collision regimes are identified from the experiments in terms of collision frequency and strength, and the collisions are shown to be caused by drift for short incident wavelengths and relative surge motion between the disks for longer incident waves. The model is based on slope-sliding theory for the wave-induced disk motions and rigid-body collisions. It is shown to predict collision frequencies and velocities accurately for intermediate-long incident wavelengths. Incorporating drift and wave scattering forces into the model is shown to capture the collision behaviours for short incident wavelengths. Published version

International audience; We discuss the phenomenology of the split energy cascade in a three-dimensional thin fluid layer by mean of high resolution numerical simulations of the Navier-Stokes equations. We observe the presence of both an inverse energy cascade at large scales, as predicted for two-dimensional turbulence , and of a direct energy cascade at small scales, as in three-dimensional turbulence. The inverse energy cascade is associated with a direct cascade of enstrophy in the intermediate range of scales. Notably, we find that the inverse cascade of energy in this system is not a pure 2D phenomenon, as the coupling with the 3D velocity field is necessary to guarantee the constancy of fluxes.

In the last 10 years, laser-driven fusion experiments performed on atomic clusters of deuterium have shown a surprisingly high neutron yield per joule of input laser energy. Results indicate that the optimal cluster size for maximizing fusion events should be in the 0.01–1 μm diameter range, but an appropriate source of droplets of this size does not exist. In an attempt to meet this need, we use ultrasonic atomization to generate micron-scale droplet aerosols of high average density, and we have developed and refined a reliable droplet sizing technique based on Mie scattering. Harmonic excitation of the fluid in the MHz range yields an aerosol of droplets with diameters of a few microns. The droplet diameter distribution is well-peaked and the relationship between average droplet size and forcing frequency follows an inviscid scaling law, predictable by dimensional analysis and consistent with the linear theory for Faraday excitation of an infinitely deep fluid.

A three-dimensional kinematic simulation (KS) model is used to study one- and two-particle diffusion in turbulent flows. The energy spectrum E(k) takes a power law form E(k)∼k−p. The value of this power p is varied from 1.2 to 3, so that its effects on the diffusion of one and two particles can be studied. The two-particle diffusion behaves differently depending on whether the two-particle separation is larger or smaller than the smallest scale of turbulence (Kolmogorov length scale η). When the two-particle mean square separation 〈Δ2(t)〉 is smaller than η2 it experiences a time exponential growth 〈Δ2(t)〉=Δ02eγ(t/tη) but for a very short time. For longer times, when η2

The dielectrophoretic forces acting on and the resulting velocities of cylindrical and spherical particles embedded in perfectly dielectric viscous fluids are calculated analytically. The fluids are confined in cylindrical/spherical shells and in semi-infinite media with prescribed potential distributions along the surfaces of the media. The forces are calculated by evaluating the Maxwell stress tensor. The velocities of the particles are obtained by solving the Stokes equation for creeping flow. The range of validity of force calculations based on the dipole-moment approximation is estimated.

Simplified models are often used for the short-range interaction of spherical particles in dilute, liquid–solid suspensions. These may range from simple collision barriers to a more detailed inclusion of viscous lubrication forces. Results are given to illustrate the sensitivity of mean particle velocity, fluctuation levels, and microstructure to different parameters and barrier models.

Vortex rings were formed with a piston-cylinder mechanism in the presence of uniform background co-flow supplied through a shroud surrounding the cylinder. The jet and co-flow were started simultaneously. Ratios of the co-flow to jet velocity (Rv) in the range 0–1 were considered. The formation number (F) as a function of Rv was determined using the procedure of Gharib et al. [J. Fluid Mech. 360, 121 (1998)] and a generalized definition of formation time. The results show a sharp decrease in F as Rv increases from 0.5–0.75, suggesting possible performance limitations for pulsed-jet propulsion.

The friction factor of a water laminar flow through fused silica microtubes with diameters ranging from 50 to 530 μm is investigated experimentally. The existing works in the literature are analyzed. They show a range of experimental results which agree or not with the conventional theory. Pressure drops and flowing masses are measured to determine the flow characteristics using a transient method. Several experiments are developed for two fluids (distilled and tap water) and tube compositions. The experimental results are discussed. The disparity from the classical theory is found to be due to the fluid’s ionic composition. The experimental results for tap water and classical fused silica surfaces indicate a disparity from the conventional theory. A friction factor increase with small uncertainties (

Temporal stability analysis of particle-laden mixing layers with uniform and nonuniform particle loadings is presented. New analytical results have been derived in the limit of small and large Stokes numbers using small-parameter expansions. A dichotomy in the behavior of the fluid–particle system, based on whether the particle diameter or density is increased to achieve large Stokes numbers, is clarified. Good agreement between the limiting analytical expressions and numerical results is obtained. Additional unstable modes are observed for nonuniform particle loadings for large Stokes numbers and high mass loadings conditions. The effect of the steepness of the nonuniformity is presented for the first time. The primary effect of nonuniformity, is an increase in the range of unstable wave numbers for small to intermediate Stokes numbers, and a change in the nature of the dominant Kelvin–Helmholtz instability from stationary to dispersive. The value of the most unstable wave number is shown to remain unaffected by the nonuniformity.

An in-depth understanding of the liquid transport in roll-based printing systems is essential for advancing the roll-based printing technology and enhancing the performance of the printed products. In this study, phase-field simulations are performed to characterize the liquid transport in roll-based printing systems, and the phase-field method is shown to be an effective tool to simulate the liquid transport. In the phase-field simulations, the liquid transport through the ink transfer rollers is approximated as the stretching and splitting of liquid bridges with pinned or moving contact lines between vertically separating surfaces. First, the effect of the phase-field parameters and the mesh characteristics on the simulation results is examined. The simulation results show that a sharp interface limit is approached as the capillary width decreases while keeping the mobility proportional to the capillary width squared. Close to the sharp interface limit, the mobility changes over a specified range are ob...

This paper presents results for the behavior of particle-laden gases in a small Reynolds number vertical channel down flow. Results will be presented for the effects of particle feedback on the gas-phase turbulence and for the concentration profile of the particles. The effects of density ratio, mass loading, and particle inertia will be discussed. The results were obtained from a numerical simulation that included the effects of particle feedback on the gas phase and particle–particle collisions. The resolution of the simulation was comparable to the smallest scales in the particle-free flow, but the grid spacings were larger than the particle size. Particle mass loadings up to 2 and both elastic and inelastic collisions were considered. Particle feedback causes the turbulent intensities to become more anisotropic as the particle loading is increased. For small mass loadings, the particles cause an increase in the gas flow rate. It will be shown that the particles tend to increase the characteristic length scales of the fluctuations in the streamwise component of velocity and that this reduces the transfer of turbulent energy between the streamwise component of velocity and the components transverse to the flow. Particle–particle collisions greatly reduce the tendency of particles to accumulate at the wall for the range of mass loadings considered. This was true even when the collisions were inelastic.

A spectral closure analysis and numerical simulations suggest that there may be a class of two-dimensional turbulence in which the energy spectrum E(k) scales with the wave number k like E(k)=Ak−3 in the enstrophy transfer range in accordance with the Kraichnan–Leith–Batchelor (KLB) spectrum, but the prefactor A is different from the KLB spectrum and depends in a nontrivial way on the flow conditions at large scales.

By replacing the “heavy” silicone oil used in the oil phase of Saksena, Christensen, and Pearlstein [“Surrogate immiscible liquid pairs with refractive indexes matchable over a wide range of density and viscosity ratios,” Phys. Fluids 27, 087103 (2015)] by one with a twentyfold higher viscosity, and replacing the “light” silicone oil in that work by one with a viscosity fivefold lower and a density about 10% lower, we have greatly extended the range of viscosity ratio accessible by index-matching the adjustable-composition oil phase to an adjustable-composition 1,2-propanediol + CsBr + H2O aqueous phase and have also extended the range of accessible density ratios. The new system of index-matchable surrogate immiscible liquids is capable of achieving the density and viscosity ratios for liquid/liquid systems consisting of water with the entire range of light or medium crude oils over the temperature range from 40 °F (4.44 °C) to 200 °F (93.3 °C) and can access the density and viscosity ratios for water with some heavy crude oils over part of the same temperature range. It also provides a room-temperature, atmospheric-pressure surrogate for the liquid CO2 + H2O system at 0 °C over almost all of the pressure range of interest in sub-seabed CO2 sequestration.

Intrinsic instability and cell formation of premixed flames at high Lewis numbers (Le=1.0–3.0) are studied by two-dimensional, unsteady calculations of reactive flows. The relation between the growth rate and the wave number, i.e., the dispersion relation, is obtained to study intrinsic instability due to hydrodynamic and diffusive-thermal effects. The growth rate is positive at small wave numbers, and the marginal wave number separating stable and unstable ranges is found. The growth rate decreases and the unstable range narrows as the Lewis number becomes higher, since the diffusive-thermal effect has a stabilizing influence at Lewis numbers higher than unity. Positive growth rates caused by the hydrodynamic effect form a cellular flame. To study the formation of cellular flames, the disturbance with the linearly most unstable wave number is superimposed on a plane flame. The superimposed disturbance evolves, and eventually a cellular flame front is formed. The higher the Lewis number, the greater the cell size and cell depth. In addition, a stationary cellular flame is obtained when the inlet velocity of the unburned gas is set to the flame velocity, since cells on flame do not move laterally.

For surface waves in brimful right circular cylinders with clean interfaces and pinned contact lines, damping rates and frequencies are measured for the six lowest frequency surface-wave modes over a two-decade range of the inverse Reynolds number C. Asymptotic calculations that include viscous dissipation in both Stokes boundary layers and the bulk show good agreement with measurements for small C; the theory typically overpredicts the measured damping rates for C large. Our measurements suggest interfacial contamination may account for a previously reported discrepancy between theory and experiment.

An experimental study of the rimming flow established inside a partially fluid-filled cylinder rotating around a horizontal axis of rotation is described. For the first time effects of granular additives on transition boundaries between flow states adopted by the fluid for different experimental conditions are studied. For the granule-free fluid and low filling levels we confirm results of previous authors showing that the ratio of viscous stresses and gravitational force remains constant along the transition boundaries considered. For higher filling levels our new data indicate, however, that the gravitational force becomes increasingly more important. For the solid–liquid two-phase flow our data reveal that even small amounts of granular additives can have a significant effect on a suitable parameter defined to characterize the transition boundaries. Granular additives can lead to the stabilization of states and to the extension of the parameter range over which certain states can be observed. It is sho...

The classical Blake threshold indicates the onset of quasistatic evolution leading to cavitation for gas bubbles in liquids. When the mean pressure in the liquid is reduced to a value below the vapor pressure, the Blake analysis identifies a critical radius which separates quasistatically stable bubbles from those which would cavitate. In this work, we analyze the cavitation threshold for radially symmetric bubbles whose radii are slightly less than the Blake critical radius, in the presence of time-periodic acoustic pressure fields. A distinguished limit equation is derived that predicts the threshold for cavitation for a wide range of liquid viscosities and forcing frequencies. This equation also yields frequency-amplitude response curves. Moreover, for fixed liquid viscosity, our study identifies the frequency that yields the minimal forcing amplitude sufficient to initiate cavitation. Numerical simulations of the full Rayleigh-Plesset equation confirm the accuracy of these predictions. Finally, the implications of these findings for acoustic pressure fields that consist of two frequencies will be discussed., 14 pages, Presented at APS/DFD conference in Philadelphia 1998

The datasets on the forced two-dimensional turbulence on a rotating sphere obtained in our recent direct numerical simulations were analyzed to study the spectral anisotropy due to the rotation of the sphere. The results were also compared with those previously obtained in some β-plane experiments to assess the β-plane approximation of the rotating sphere. Owing to the effect of rotation the upward energy cascade ceases around a characteristic total wavenumber nβ at which the linear “β-term” is comparable to the nonlinear Jacobian term. The energy density of zonal components (m=0) is dominant in the range of n≲nβ while the energy is very small in an airfoil-shaped region at the lower edge in the wavenumber space (m,n). Anisotropic distribution of the energy is also found in the high wavenumber region n≳nβ; the energy density decreases as the zonal wavenumber m increases. The flow field in the spherical geometry is projected on some tangential planes from the equator to the poles to compare the spherical r...

The transport in vortical and stagnation point flow fields is analyzed for particles across the entire range of density ratios, based on the Maxey–Riley equation [Phys. Fluids 26, 883 (1983)] without history effects. For these elementary flow fields, the governing equations simplify substantially, so that analytical progress can be made towards quantifying ejection/entrapment trends and accumulation behavior. For a solid body vortex, the analysis shows that optimal ejection or entrapment occurs for all density ratios, as the difference between inward and outward forces reaches a maximum for intermediate values of the Stokes number. The optimal Stokes number value is provided as a function of the density ratio. Gravity is shown to shift accumulation regions, without affecting the entrapment or ejection rates. For a point vortex flow, the existence of up to three different regimes is demonstrated, which are characterized by different force balances and ejection rates. For this flow, optimal accumulation is ...

Streamwise high vorticity rolls and streaks in the turbulent channel flows have been the subject of many studies due to their important role in turbulence production, as a result of sweeping, ejection, and bursting of these structures. Understanding the physics of these streamwise structures is important in controlling drag producing events. Investigations of the average streak spacing of the low‐speed streaks have resulted in the generally accepted range of λ+=λuτ/ν=100±20, where λ is the mean spanwise spacing between streaks, normalized to the viscous length ν/uτ. It is also reported, for y+≤30, that the streak spacing grows nearly linearly with distance from the wall. The previous studies mostly have focused on distances close to the wall. Here we report on correlation measurements extended into the log layer, which show that the linear growth of the vortex diameter and the streak spacing extends well in the log layer. Arguments are presented to distinguish these two measures.

An analytical study is presented for the diffusiophoretic motion of two colloidal spheres in a constant gradient of a nonionic solute using a method of reflections. The particles are oriented arbitrarily relative to the gradient, and they are allowed to differ in radius and in surface properties. The range of the interaction between the solute and the particle surfaces is assumed to be small compared to the radius of each particle and to the gap width between the particles, but the polarization effect in the thin particle–solute interaction layers caused by the strong adsorption of the solute is incorporated. A normal flux of the solute and a slip velocity of the fluid at the outer edge of the thin diffuse layer are used as the boundary conditions for the fluid domain outside the diffuse layers. The method of reflections is based on an analysis of the solute concentration and fluid velocity disturbances generated by a single sphere placed in an arbitrarily varying concentration field. The quasisteady resu...