We propose a pairwise influence framework for the complex unsteady compressible particle-laden flow problem by accounting for the scattered hydrodynamic waves emitting from neighboring particles in a Euler-Lagrange simulation. It has been observed from particle-resolved (PR) simulations of randomly dispersed particle beds under a loading shock that the compressible pseudoturbulence dominates the flow system even after the primary shock has passed, which causes fluctuations observed in the forces experienced by the particle. Moreover, the fact that each particle exists in the vicinity of a random arrangement of other particles modifies the time history of the drag force experienced by each particle during and after the passage of the shock. First, the scattering flow field due to an incoming shock interacting with a single sphere is constructed using an analysis of the flow in the acoustic limit. Then we examine the validity of the compressible Maxey-Riley-Gatignol force model by comparing the force prediction against a PR simulation of two interacting particles for various particle arrangements and incoming shock strength. Subsequently, the neighboring influences are stored as a library of maps that can be used readily in the calculation of the perturbation force. Finally, the pairwise interaction assumption is evaluated by comparing the force predicted with the model with PR simulations of a randomly packed particle bed of 10% volume fraction for both water and air as the fluid medium for an incoming shock Mach number 1.22. With a considerably lower cost for the implementation of the model compared to PR simulations, it is verified that the model is reasonably accurate in pinpointing particles whose peak force is significantly larger or smaller than the mean drag but also to capture the prolonged fluctuations after the initial shock.

The topology of multiscale turbulent motions in a high-pressure transcritical channel flow is studied using direct numerical simulations. In particular, the system analyzed corresponds to high-pressure ($P/P_c=2$) microconfined turbulence of ${\mathrm{N}}_2$ at transcritical conditions imposed by a temperature difference between the cold ($T/T_c=0.75$) and hot ($T/T_c=1.5$) walls for a friction Reynolds number of ${\text{Re}}_{\tau }=100$ (cold wall). The invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors are computed at different length scales. The joint probability density functions of the invariants are calculated and conditioned based on the distance from the walls and additionally compared against an equivalent low-pressure case at isothermal conditions. The results indicate that the presence of higher levels of vorticity close to the hot wall significantly impacts the flow topologies in the viscous sublayer. As a result, topology distributions of the velocity-gradient tensor typical from the outer region are observed in the vicinity of the hot wall. Moreover, the second invariants of the rate-of-strain and rate-of-rotation tensors indicate a large probability of vortex sheet events in the hot (supercritical gaslike) region. Finally, at lengths comparable to the density gradient scale, the presence of vortex sheet structures is diminished with respect to the reference low-pressure case to favor more tubelike flow motions. As inferred from the vorticity transport equation, this behavior is connected to the appearance of a baroclinic-type instability generated from the combination of the external force driving the flow and the large variation of density across the pseudoboiling region.

Fluid inertia is known to exert a dominant control over transport processes in fracture flows. In particular, recirculating flows readily arise in inertial rough fracture flows and have been shown to cause anomalous transport by trapping particles. However, understanding of the combined effects of fluid inertia and solute diffusion on reactive transport involving fluid-solid reactions has thus far been elusive. This study investigates reactive transport involving an irreversible fluid-solid bimolecular reaction for wide ranges of Reynolds (Re) and Péclet (Pe) numbers and elucidates how the interplay between inertia and diffusion effects controls the dynamics of reactive transport. Solute diffusion (Pe) controls mainly the total reaction amount, whereas fluid inertia (Re) governs the reaction dynamics by inducing complex flow structures such as flow channeling and recirculating flows. Specifically, recirculating flows are shown to facilitate fluid-solid reactions by increasing the residence time of particles near the fluid-solid interfaces, and such trapping effects increase as Pe increases. Further, flow channeling and recirculating flows exert dominant control over the transport of both reactants and products. We elucidate the reactive transport dynamics by analyzing particle trajectories and quantifying Lagrangian velocity statistics and reaction-related measures. Based on the improved understanding, we then propose an upscaled reactive transport model that incorporates Lagrangian velocity statistics and velocity-dependent reaction probability, and show that the upscaled model successfully captures reactive transport over wide ranges of Re and Pe.

The coalescence dynamics of two unequal-sized drops made of miscible but distinct liquids has been numerically simulated using the coupled level set and volume of fluid method. Effect of the surface tension ratio of two liquid drops, the Ohnesorge number and the diameter ratio of two parent drops on three different pinch-off regimes, namely, first-stage, second-stage, and no pinch-off, are explored. The result shows that the coalescence process of two miscible liquid drops exhibits a nonmonotonic behavior of partial coalescence from appearance to disappearance and then reappearance with decreasing surface tension ratio. The strong lifting force of the intense Marangoni flow causes the reappearance of partial coalescence at higher surface tension difference between two drops. When the Ohnesorge number increases, high viscous forces restrict the propagation of Marangoni flow and do not favor the pinch-off, even in the presence of a significant surface tension difference. The generation of secondary drops at a considerable surface tension difference is also prevented for small parent drop size ratio. A regime map for the distinct coalescence outcomes is presented for different surface tension ratios. The critical surface tension ratio necessary for partial coalescence to occur grows monotonically as the Ohnesorge number increases. In our simulation, the minimum value of critical surface tension ratio needed for partial coalescence to take place is 0.94 at small values of the Ohnesorge number and the Bond number.

The impact of drops on a thin liquid film is a phenomenon encountered in industrial applications, but also of particular interest in nature. Examples include the growth of stalagmites in karstic caves, a case where the drop feeds the film with ions that will subsequently precipitate. The mixing upon impact, which is witnessed both in the film and in the ejections, remains poorly understood. In the case of stalagmites, this short-term mixing directly affects the ion distribution in the film between impacts. In this work we investigate the mixing and ejection processes occurring during the impact of a free-falling drop on a thin, horizontal film of miscible liquid. We perform laboratory experiments and record side and top views of high-speed movies of impacts in a range of parameters close to impacts observed on stalagmites in caves. We observe that several outcomes arise from these impacts depending on the initial film thickness and Weber number. We relate the geometry of the splashing crown growth to the four scenarios observed. Additionally, the postimpact mixing patterns and film thickness variations are analyzed through an original colorimetry-based technique. From there we infer the size of the stain and quantity of water left by the drop in the film, as well as the total volume ejected away during the impact.

The slip boundary is usually realized by microstructured surfaces, where primary fluid flows over the microstructures being filled with a secondary immiscible fluid. The characteristics of the microstructures and the properties of the secondary fluid have a specific effect on the primary flow, which eventually affects the properties of the slip boundary. The coupled flow of two fluids needs to be considered, although it is challenging to theoretically solve the coupled flow problem. In the current work, we establish a theoretical framework for interfacial coupled flow on a slip boundary over a microstructured surface. Taking shear flow over a periodic microstructured boundary as an example, by finding integral relation between the slip velocity and the slip velocity gradient, we decouple the binary fluid system on the slip boundary and solve the slip problem under the low-Reynolds-number limit. It is found that a small viscosity ratio, large fluid interfacial fraction, or large depth-to-width ratio of a groove will result in a large vorticity flux in the groove, leading to a large slip length. Thus, we propose a method to enhance the slippage by introducing a jet flow in the grooves, which is verified by our theory. The current work provides a new method for theoretically solving the coupled flow problem, which can be extended to cases of high-speed flow.

Bubbles and droplets are ubiquitous in many areas of engineering, including microfluidics where they can serve as microreactors for screening of chemical reactions. They are often formed out of a constriction (a microfluidic channel or a cylindrical tube) by blowing a given volume of gas into a liquid phase. It is obviously crucial to be able to control their size, which is not always easy due to the coupling between the volume of the bubble and the gas pressure induced by the Laplace law. In this paper, we examine the size and formation dynamics of soap bubbles blown from a cylindrical tube, which is the paradigm geometry for bubble and droplet formation. To do so, one end of the tube is closed by a soap film, while the other end is connected to a large reservoir of variable volume filled with gas. To inflate the bubble, we reduce the volume of the reservoir, which mimics air inflation through the lung diaphragm or the flow-rate-driven bubble formation in microfluidics geometry such as flow-focusing. As the volume of the reservoir decreases, the soap film curves and takes the form of a spherical cap with a smaller and smaller radius of curvature, which leads to the increase of the gas pressure in the reservoir, according to Laplace's law. This quasistatic process continues until a critical pressure is reached for which the bubble is quasihemispherical. Beyond this pressure, the film undergoes a rapid topological transformation and swells very rapidly (in less than 100 ms) until it reaches its final volume. We describe this instability in particular by showing that this unstable regime appears when a dimensionless number, which depends on the volume of the reservoir, the radius of the tube, surface tension, and external pressure, reaches a critical value. Using a quasistatic model that we solve analytically, we predict the bubble growth dynamics and the amplitude of the unstable height increase for any reservoir volume and constriction size.

The flow field associated with cantilevered, low aspect ratio cylindrical pins having different chamfered free-ends were investigated using oil flow visualizations and stereoscopic particle image velocimetry at ${\text{Re}}_D=8\times {10}^3$. Two chamfered pins, where the chamfer encompassed either half of the pin's planform or its full planform, were analyzed with the chamfer at various skew angles with respect to the freestream and were compared with a pin without a chamfer. All pins exhibited a complex flow field, including an array of streamwise vortical structures. The chamfered pins resulted in two additional counter-rotating streamwise vortices, named chamfered induced vortices (CIVs). It was shown that changing the skew angle resulted in a change in the strength of these vortical structures, their direction of rotation, and as a result, the net circulation produced. Comparing the two chamfered pins, the pin where the chamfer encompassed half of its planform produced stronger CIVs. These effects are discussed in detail to provide insight into a future use of these pins as flow control devices.

Airway mucus is a complex material with both viscoelastic and viscoplastic properties that vary with healthy and pathological conditions of the lung. In this study, the effects of these conditions on airway closure are examined in a model problem, where an elastoviscoplastic (EVP) single liquid layer lines the inner wall of a rigid pipe and surrounds the air core. The EVP liquid layer is modelled using the Saramito-HB model. The parameters for the model are obtained for the mucus in healthy, asthma, chronic obstructive pulmonary disease (COPD), and cystic fibrosis (CF) conditions by fitting the rheological model to the experimental data. Then the liquid plug formation is studied by varying the Laplace number and undisturbed liquid film thickness. Airway closure is a surface-tension-driven phenomenon that occurs when the ratio of the pulmonary liquid layer thickness to the airway radius exceeds a certain threshold. In previous studies, it has been found that airway epithelial cells can be lethally or sublethally damaged due to the high peak of the wall stresses and stress gradients during the liquid plug formation. Here we demonstrate that these stresses are also related to the EVP features of the liquid layer. Yielded zones of the liquid layer are investigated for the different mucus conditions, and it is found that the liquid layer is in a chiefly unyielded state before the closure, which indicates that this phase is dominated by the elastic behavior and solvent viscosity. This is further confirmed by showing that the elastic coefficient is one of the most critical parameters determining whether the closure occurs. This parameter also largely affects the closure time. The wall stresses are also investigated for the pathological and healthy cases. Their peaks for COPD and CF are found to be the highest due to the viscoelastic extra stress contribution. Contrary to the Newtonian case, the wall stresses for COPD and CF do not smoothly relax after closure, as they rather remain effectively almost as high as the Newtonian peak. Moreover, the local normal wall stress gradients are smaller for the COPD and CF liquid layer due to their higher stiffness causing a smaller curvature at the capillary wave. The local tangential wall stress gradients are also shown to be smaller for these cases because of the slower accumulation of the liquid at the bulge.

The distribution of wave heights, and therefore the occurrence rate of extreme waves, depends on the shape of the surface elevation spectrum. In an idealized two-layer flow, e.g., fresh water overlaying salt water, the spectral shape of surface waves is modified by class-three triad interactions. We conduct numerical simulations of the wave field evolution on a two-layer stratified fluid. Starting from realistic deep-water JONSWAP spectra, the spectral density at high wavenumbers increases while the variance in the peak region decreases and the peak shifts slightly lower. The enhancement of the spectral tail grows rapidly with increasing initial wave steepness and is strongest for broad-banded spectra. Monte Carlo simulations of surface realizations are performed, where the surface is a linear superposition of wave components taken from the initial and the modified spectra. In all cases, the wave height and crest height distributions can be expressed by modified Rayleigh distributions. On a two-layer flow the probability of rogue waves can be up to two orders of magnitude lower than in the unstratified deep-water case, whereas the probability of rogue crests is nearly unaffected. The average crest-trough correlation, calculated from the spectra, is a good predictor for rogue wave probabilities even for strongly modified spectra with enhanced high-wavenumber spectral variance.

The present study aims at understanding the effect of external pulsations on the flow characteristics in the downhill region of an oblique jet impingement with the help of particle image velocimetry. The distance between nozzle exit and the wall is kept constant at $L=4D$ (D is the diameter of the nozzle) and $\mathrm{Re}=1900$ (based on nozzle diameter and the average jet exit velocity). The impingement angle is varied from $\theta ={90}^{\circ }$ (normal impingement) to ${30}^{\circ }$ and the Strouhal number ($\mathrm{St}=fD/U$, where $f$ is the external frequency and U is the average velocity) from 0 to 0.9. The wall jet corresponding to $\mathrm{St}=0.44$ shows highest jet growth as compared to other jet pulsations. The wall jet at $\mathrm{St}=0.9$ is observed to show similar behavior to that of the steady jet $(\mathrm{St}=0)$. A quadrant analysis shows that instability causes ejection motion to occur nearest to the impingement region when $\mathrm{St}=0.44$. The ejection motion leads to an expansion of the wall jet region in the wall-normal direction which is also observed in the increase in jet half-width. Further, it is observed that the maximum wall jet velocity increases with decreasing $\theta$. The location of the occurrence of the ejection motion depends strongly on $\theta$, shifting downstream of the wall as $\theta$ decreases. A proper orthogonal decomposition analysis reveals that the dominant structures of the wall jet flow occur at the location where the ejection motion is initiated. A higher jet momentum is responsible for delay in the ejection motion and development of coherent structures in the case of a wall jet with lower impingement angles. These results provide some relatively important insights on the behavior of the wall jet under different pulsations in the case of oblique jet impingements which can be of practical interest for heat transfer studies as well as heat transfer applications involving jet impingement cooling and mixing.

Polymers in nonuniform flows undergo strong deformation, which in the presence of persistent stretching can result in the coil-stretch transition. This phenomenon has been characterized by using the formalism of nonequilibrium statistical mechanics. In particular, the entropy of the polymer extension reaches a maximum at the transition. We extend the entropic characterization of the coil-stretch transition by studying the differential entropy of the polymer fractional extension in a set of laminar and random velocity fields that are benchmarks for the study of polymer stretching in flow. In the case of random velocity fields, a suitable description of the transition is obtained by considering the entropy of the logarithm of the extension instead of the entropy of the extension itself. Entropy emerges as an effective tool for capturing the coil-stretch transition and comparing its features in different flows.

In this paper, we present direct numerical simulations of viscoelastic fluid flow in a cavity with an ion conduction-driven mechanism. The flow patterns, oscillation amplitudes, force competition mode, and power-law spectral scaling accompanying oscillatory flow are examined. The dimensionless parameter $\beta$ (elucidating the electric-field-enhanced dissociation) together with conduction number $C_0$ determines the limiting operating regimes (ohmic and saturation). The results demonstrate that asymmetric unsteady flow patterns are observed in perfectly symmetric geometry. Different transition sequences are discussed under two operating regimes, by velocity oscillation and power-law decay. The commensurability magnitudes of the elastic stress and Coulomb forces significantly alter the convective mode, leading to discrepancies in the electroelastic instability paths. The kinetic and elastic energies of the associated driving parameters are quantified, and the flow patterns are divided into five subregions. The dynamic behavior above is related to the strong electroconvective flow within the heterogeneous charge layers.

Droplet breakup is an important phenomenon in the field of microfluidics to generate daughter droplets. In this work, a novel breakup regime in the widely studied T-junction geometry is reported, where the pinch-off occurs laterally in the two outlet channels, leading to the formation of three daughter droplets, rather than at the center of the junction for conventional T-junctions which leads to two daughter droplets. It is demonstrated that this new mechanism is driven by surface tension, and a design rule for the T-junction geometry is proposed. A model for low values of the capillary number Ca is developed to predict the formation and growth of an underlying carrier fluid pocket that accounts for this lateral breakup mechanism. At higher values of Ca, the conventional regime of central breakup becomes dominant again. The competition between the new and the conventional regime is explored. Altogether, this novel droplet formation method at T-junction provides the functionality of alternating droplet size and composition, which can be important for the design of new microfluidic tools.

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. The main motivation is the study of phytoplankton and oceanic particles in turbulent flows. 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 their dynamics and show that small neutrally buoyant particles in these flows tend to cluster in regions of low local vorticity. The particles, albeit small, behave fundamentally differently than tracers.

The study of the transitions among different regimes in thermal convection has been an issue of paramount importance in fluid mechanics. While the bifurcations at low Rayleigh number, when the flow is laminar or moderately chaotic, have been fully understood for a long time, transitions at higher Rayleigh number are much more difficult to be clearly identified. Here, through a numerical study of the two-dimensional Rayleigh-Bénard convection covering four decades in Rayleigh number for two different Prandtl numbers, we find a clear-cut transition by considering the fluctuations of the heat flux through a horizontal plane, rather than its mean value. More specifically, we have found that this sharp transition is displayed by a jump of the ratio of the root-mean-square fluctuations of the heat flux to its mean value and occurs at $\mathrm{Ra}\text{/}\mathrm{Pr}\approx {10}^9$. Above the transition, this ratio is found to be constant in all regions of the flow, while taking different values in the bulk and at the boundaries. Below the transition instead, different behaviors are observed at the boundaries and in the bulk: at the boundaries, this ratio decreases with respect to the Rayleigh number whereas it is found to be constant in the bulk for all values of the Rayleigh number. Through this numerical evidence and an analytical reasoning we confirm what was already observed in experiments; that is, the decrease of the ratio of root-mean-square fluctuations of the heat flux to its mean value, observed at the boundaries below the transition, can be understood in terms of the law of large numbers.

Wave breaking is the main mechanism that dissipates energy from ocean waves by wind. Its effects on the frequency spectrum cause a downshift of the spectral peak and dissipation of the total energy of the spectrum. Various reduced-form wave breaking models have been developed to capture wave breaking in envelope-based wave evolution equations for perturbed plane-wave systems, but their applicability to waves with a continuous spectrum has not been examined. In this paper we perform modified nonlinear Schrödinger equation simulations to study four existing wave breaking models and compare the results with new experimental data for breaking unidirectional wave groups. We first compare the different wave breaking models for perturbed plane-wave simulations and then examine their potential extension to waves with a continuous spectrum. We find that most existing models are able to model breaking in perturbed plane waves, but none produce the correct spectral dissipation for focused wave groups. We propose a modification to the breaking model by Kato and Oikawa [J. Phys. Soc. Jpn. 64, 4660 (1995)] in order to model breaking in focused wave groups. The modified model incorporates both a breaking criterion, which activates and deactivates the dissipation term proposed by Kato and Oikawa, and a heuristic spectral weighting function that is obtained by fitting to experimental data. The modified model also predicts breaking in perturbed plane waves well.

The quasisteady thermophoretic motion of a spherical aerosol particle situated at an arbitrary position in a microchannel with naturally permeable plane walls bounding a porous medium is studied semianalytically. The applied temperature gradient is constant and perpendicular to the walls of the channel. The appropriate field equations of energy and momentum for the system are solved using a boundary collocation technique in the limit of small Péclet and Reynolds numbers. The effect of thermal stress slip at the surface of the particle is included in this paper in addition to temperature jump, thermal creep, and frictional slip. This paper is motivated by a wide variety of flows such as the deposit of particles in reverse osmosis processes, dialysis, or various biological organs where fluid passes through membranes or cell walls. The collocation results of the normalized thermophoretic velocity are obtained with adequate accuracy for a wide range of values of the relative thermal conductivity, permeability of the walls, and surface properties of the particle. Thermophoretic velocity is also obtained for the particular case of the migration of a spherical particle in an unbounded fluid medium in the presence of a single permeable plane surface and it is found in perfect agreement with the corresponding data available in the literature. The normalized thermophoretic velocity of the confined particle decreases significantly when the particle is in near contact with the microchannel walls. It decreases also as the permeability parameter of the walls increases. It is also found that the thermal stress slip coefficient has a significant rule on the normalized thermophoretic velocity.

The flow downstream of a linearly tapered cylinder executing rotational oscillations is experimentally studied at Reynolds number (based on mean diameter) of 250. The tapered cylinder is forced to rotationally oscillate at various oscillation amplitudes and normalized forcing frequencies. The hydrogen bubble technique is used for visualizing the spanwise wake structure, and the laser-induced fluorescence technique is used for visualizing the streamwise wake structure. The cylinder used in the current study has a taper ratio of 70:1 with a mean diameter of 8 mm. Oblique shedding with an oblique angle of ${16}^{\circ }$ is seen for a stationary cylinder which gradually reduces and eventually changes to parallel shedding with an increase of forcing frequency up to a certain forcing frequency which is also dependent on the oscillation amplitude. Flow visualization revealed the forcing frequencies and amplitudes for which the flow becomes two-dimensional. Spanwise cellular structures are observed for some specific forcing parameters. For an oscillation amplitude of $3\pi /4$ and normalized forcing frequency of 2, a three-dimensional mode is formed at the upper half of the cylinder with a spanwise wavelength of 1.6. Frequency content of the wake measured by hot-film anemometry showed that the flow is governed by multiple frequencies when cellular structures in the wake are observed. It is seen from hot-film measurements that the range of forcing frequencies for which the wake undergoes lock-on increases with increasing oscillation amplitude. A direct drag measurement technique showed that the drag for a stationary tapered cylinder is $\sim 10\%\text{–}20\%$ less than that of a stationary straight cylinder. Particle image velocimetry (PIV) data revealed that the circulation of spanwise vortices loses its strength as we move from the larger diameter end to the smaller diameter end. The drag coefficient for forcing cases is estimated using the momentum deficit formula by finding the mean and fluctuating velocities obtained from PIV. When the forcing frequency enters the lock-on initiation zone, the coefficient of drag becomes maximum, and with further increase in forcing frequency the drag coefficient decreases. The maximum value of the drag coefficient increases as the oscillation amplitude is increased from $\pi /2$ to $3\pi /4$.

We present laboratory experiments on turbulence in a linearly stratified fluid driven by an ensemble of internal gravity waves which approaches statistical homogeneity and axisymmetry. In a way similar to several recent experimental works, nonlinearities develop through the establishment of a set of internal wave modes at discrete frequencies, when the forcing amplitude is increased. We show that the most energetic of these modes are resonant eigenmodes of the fluid domain. The discretization of the energy in frequency and wave number associated to the emergence of these modes prevents the flow from approaching a regime described by the weak/wave turbulence theory, in which a forward cascade carried by a statistical ensemble of weakly nonlinear waves in an infinite domain forms an energy continuum in the frequency and wave-number spaces. We then show that the introduction of slightly tilted panels at the top and at the bottom of the fluid domain allows to inhibit the emergence of the discrete wave modes. In this new configuration, the nonlinear regime results in a continuum of energy over one decade of frequencies which is mainly carried by internal gravity waves verifying the dispersion relation. We therefore achieved a turbulent flow approaching a three-dimensional internal wave turbulence regime with no discretization of the energy in the frequency and wave-number domains. These results constitute a significant step forward in the search of the laboratory observation of a fully developed weakly nonlinear internal-gravity-wave turbulence.