Drainage flow of a viscous compressible gas from a semisealed narrow conduit is a pore-scale model for studying the fundamental flow physics of fluid recovery from a porous reservoir without fluid injection. The drainage flow is driven by the volumetric expansion of the gas and its mass flow rate has been found previously to be sliplike and proportional to the kinematic viscosity of the gas. Thermal effect on such a drainage flow is studied here by simultaneously solving the linearized continuity, momentum, and energy equations for a semisealed narrow channel with adiabatic walls. It is shown that even in the absence of an imposed temperature drop, gas expansion induces a transient temperature decrease inside the channel, which slows down the drainage process compared to the isothermal model and Lighthill's model. For a given density drop, gas drains out faster as the initial-to-final temperature ratio increases; the transient density can undershoot the final equilibrium value. It is concluded that thermal effect should be carefully considered in order to accurately predict the drainage rate.

The effect of void fraction on turbulent multifluid flows undergoing topology changes in a vertical channel is examined by numerical simulations using a front tracking and finite volume method. Several blobs or bubbles of the light fluid are initially placed in a turbulent channel flow. When the blobs collide and the liquid film between them becomes very thin it is ruptured, and the blobs are allowed to coalesce. The rupture is done for a predetermined film thickness selected in such a way that the results are relatively insensitive to its exact value. For the parameters used here, the blobs generally break up after the initial coalescence, and five simulations for void fractions from about 5% to 25% are carried out until the flow has reached an approximately steady state. The evolution of various integral quantities, such as the average flow rate, wall shear, and interface area, are monitored and compared. Various averages of the flow field and the phase distribution, over planes parallel to the walls, are then examined at late times, when the flow has reached an approximate statistically steady state. At steady state, the probability distribution of blob volumes is similar, and the light fluid is contained in blobs with an average Eötvös number of about 3.5, for all the void fractions. However, the deformation and the surface area of the largest blobs are much larger for the higher void fractions, suggesting that the flow starts to depart from the bubbly regime at a void fraction of about 15%.

The flow in anatomically accurate rhesus macaque airways is studied using large eddy simulation. The deposition of inhaled 1- to 10-$\mu \text{m}$-diameter particles in the flow is also presented. The geometries comprise the nasal cavity, maxillary sinus cavities, pharynx, larynx, and trachea. Simulations are carried out for constant inspiratory flow rates of 2, 4, and 6 L/min, corresponding to Reynolds numbers of 351, 702, and 1053 for a nominal tracheal diameter of 0.8 cm. Unsteady flow is seen at certain flow rates, with the onset of turbulence occurring at constrictions in either the pharynx or glottis. The computed particle deposition results are compared extensively with experimental measurements carried out in models of the same computed tomography-based geometries, showing good agreement in the majority of cases. We observe significant deposition in the nasal airways as well as in the pharyngeal and laryngeal jet regions which dominate deposition for most particle sizes and flow rates. Inclusion of the pharynx and larynx regions of the upper airway in simulations is critical for accurately capturing the unsteady flow entering the lower airways, as well as predicting the fraction of inhaled particles that is filtered by the upper airways. Variability in airflow features, total particle deposition, and deposition locations between three monkeys is presented. These findings will allow better characterization of exposure dosages of inhaled compounds in animal experiments.

In this study, we experimentally investigate the mechanical process of a self-propelled helical swimmer to move across an interface between two immiscible fluids. This configuration is aimed to emulate some aspects of the process used by bacteria to trespass mucus layers or epithelial cell membranes to cause infections. We consider two configurations: head-first and tail-first. We find that, in both cases, the head of the swimmer deforms the interface generating a meniscus that induces a significant reduction of the swimming speed, that lasts until the interface is pierced. In both cases, the dynamics of penetration is complex leading to significant variations of the swimming speed during the process. We observed interesting differences in the penetration dynamics for the two cases; we argue that the differences arise from the significantly different shape and direction of the menisci that forms during the penetration process. A model that accounts for thrust, drag, buoyant, and capillary forces is used to rationalize the results.

The outer region of fully developed turbulent boundary layers can be viewed as a collection of uniform momentum zones separated by thin (but finite-thickness) shear layers referred to as momentum internal interface layers (MIILs). We first show the existence of such interfacial layers under transcritical thermodynamic conditions and introduce their thermal counterpart, named uniform thermal zones (UTZs), based on temperature. The UTZs, and the corresponding thermal internal interfacial layers (TIILs), are studied for a database of turbulent channel flow at transcritical thermal conditions [K. Kim et al., J. Fluid Mech. 871, 52 (2019)]. The thermal and vortical interfaces are identified using a recently proposed clustering approach by Fan et al. [D. Fan et al., J. Fluid Mech. 872, 198 (2019)]. It is shown that the MIILs and TIILs are correlated, but not collocated; their location is related to the underlying turbulent structures in the flow. On average, the TIILs are located about halfway between the wall and the MIIL, and the relationship between these layers is studied from the perspective of the attached eddy model. Under high near-wall thermal gradients the pseudoboiling line and the outer MIIL are collocated, which is explained using a shear stress balance analysis. Ultimately, the study of the thermal layering permits a simplification of the wall scaling in the presence of complex transcritical thermodynamics.

We analyze a large-eddy simulation data set of wakes of a towed sphere of diameter $D$ at speed $U$ in a uniformly stratified Boussinesq fluid with buoyancy frequency $N$ and kinematic viscosity $\nu$. These temporally evolving wakes are simulated using a spectral multidomain penalty-method-based incompressible Navier-Stokes solver for $\text{Fr}\equiv 2U/ND\in \{4,16,64\}$ and $\text{Re}\equiv UD/\nu \in \{5\times {10}^3,{10}^5,4\times {10}^5\}$, enabling a systematic examination of stratified wakes at three different values of $\text{Re}$ sufficiently separated in magnitude. As such, particular attention is paid to the effects of varying $\text{Re}$ on the evolution of large-scale characteristics of stratified wake turbulence. We examine the evolution of horizontal and vertical integral length scales (${\ell }_h$ and ${\ell }_v$), horizontal and vertical fluctuation velocities ($\mathcal{U}$ and $\mathcal{W}$), local vertical shear, as well as the resulting dimensionless parameters based on the above quantities. In particular, the vertical turbulent Froude number ${\text{Fr}}_v^{★}\equiv 2\pi \mathcal{U}/N{\ell }_v$ is found to be of order unity, a signature of the dynamics in the strongly stratified regime where shear instabilities develop between anisotropic flow layers. The horizontal turbulent Reynolds number ${\text{Re}}_h\equiv \mathcal{U}{\ell }_h/\nu$ stays approximately constant in time and the horizontal turbulent Froude number ${\text{Fr}}_h\equiv \mathcal{U}/N{\ell }_h$ decays in time as ${\left(Nt\right)}^{-1}$, consistent with scaling analysis of freely decaying turbulence. We characterize the transitions between distinct stratified flow regimes and examine the effects of body-based parameters $\text{Re}$ and $\text{Fr}$ on these transitions. The transition from the weakly to the strongly stratified regime, which is marked by ${\text{Fr}}_v^{★}$ decaying to unity, occurs when ${\text{Fr}}_h\simeq O\left(0.01\right)$. We further show that the initial value of ${\text{Re}}_h$ at which the flow completes the above transition scales as $\text{Re}{\text{Fr}}^{-2/3}$, which provides a way to predict the possibility of accessing the strongly stratified regime for a wake of given $\text{Re}$ and $\text{Fr}$. The analysis reported here constitutes an attempt to obtain the predictive capability of stratified wake turbulence in terms of Reynolds number $\text{Re}$, applying select elements of strongly stratified turbulence theory, so far typically utilized for homogeneous turbulence, to a canonical inhomogeneous turbulent free-shear flow.

We consider the steady flow of a viscoelastic liquid film over an inclined wall with sinusoidal corrugations of arbitrary wavelength and depth. We develop a computational model and carry out detailed numerical simulations based on the finite-element method to investigate this flow. To this end, we solve the two-dimensional momentum and mass conservation equations while employing the Phan-Thien-Tanner (PTT) constitutive model to account for the rheology of the viscoelastic material. An elliptic grid generation scheme is used to follow the large deformations of the liquid film. We perform a thorough parametric analysis to investigate the combined effects of elasticity, inertia, and capillary and viscous forces on the characteristics of the steady flow. The results of our simulations indicate that fluid elasticity suppresses interfacial deformation at low flow rates, whereas at moderate values of $\mathrm{Re}$ it enhances the deformation considerably. In the latter case, elastic forces may even give rise to the formation of a static hump and a cusp at the free surface, the size of which increases with the relaxation time of the liquid. The resonance of the liquid film with the substrate undulations is also enhanced by shear thinning. Interestingly, it is predicted that under certain conditions the transition to the inertia regime is not smooth and a hysteresis loop arises, which is the signature of an abrupt change of the film shape, since its high deformations cannot be sustained. Additionally, we have performed calculations for a wide range of different geometrical characteristics of the substrate. We find that viscoelastic effects become more pronounced in the case of long-wavelength wall undulations, while for substrates with short wavelengths the effect of shear thinning is less significant due to the presence of vortices inside the corrugations.

The linear hydrodynamic stability of a film of viscoelastic fluid flowing down an inclined wavy surface is studied. We investigate the stability of the flow with respect to infinitesimal two- and three-dimensional (2D and 3D) disturbances and employ the Floquet-Bloch theory to examine the effect of periodic disturbances of any wavelength. The study is based on the numerical solution of the momentum equations along with the Phan-Thien–Tanner (PTT) model to account for material viscoelasticity. The generalized eigenvalue problem is solved using Arnoldi's algorithm, in a Newton-like implementation in order to calculate faster the critical conditions for the onset of the instability. Our results are in excellent agreement with the previous experimental and theoretical results in the case of Newtonian liquids flowing over flat and undulating substrates and viscoelastic liquids over flat substrates. We present detailed stability maps for finite amplitude of the wall corrugations and a wide range of material parameters. Our calculations indicate that fluid elasticity is primarily stabilizing, while shear thinning of the fluid tends to destabilize the fluid flow. In order to investigate the mechanisms involved, we perform an energy analysis of the flow under long-wave disturbances indicating that the convection of stress-gradient disturbances provides an additional viscoelastic mechanism for the destabilization of the flow, in contrast to the base state stress gradients which contribute to stabilization of the flow. Besides the usual long-wave instability, conditions are identified which lead to unstable disturbances of wavelength equal or smaller than the wavelength of the substrate. Experimental observations for Newtonian liquids have indicated that these short-wave instabilities will dominate and a similar behavior is predicted for viscoelastic liquids. Sometimes, before the short-wave instabilities, a hysteresis loop in the steady flow can be identified, which leads to a sharp change in the critical frequency. Finally, we examine the stability of the flow when subjected to disturbances in the spanwise direction and show that for highly elastic liquids 3D instabilities may arise.

The passage of microfluidic droplets in miscible thread-forming flows is shown to improve the mixing efficiency of low- and high-viscosity fluids at the small scale. Hydrodynamic interactions between recirculating flow patterns and viscous core-annular flows are experimentally investigated in square microchannels. The deformation of thick segmented flows injected in thin fluids is examined through the evolution of droplet size, spacing, and velocity along a square microchannel. Droplets also help in probing the various states of lubrication of the viscous central stream in the bulging, tubing, and threading regimes at various capillary and Péclet numbers. A range of intriguing flow phenomena is revealed using a dual approach based on thread and droplet mutual behaviors, including droplet breakup, formation of low-viscosity currents, thread splitting, viscous fingering, and viscous buckling instabilities. The thread-forming ability of miscible fluids having large viscosity contrasts is discussed in conjunction with mixing applications where a thinner or a viscosifier is continuously added to a viscosity-differing fluid in confined microsystems.

Recently, it was observed that in nonequilibrium turbulent flows the normalized dissipation rate depends in a fairly universal way on the Reynolds number of the flow. To assess theoretical explanations of this observation, we consider here the nonequilibrium properties of freely decaying turbulence from initial conditions where the velocity field is reversed in every point in space. This test-case allows us to manipulate a turbulent flow differently from the usual way, where nonequilibrium is induced by modification of large-scale forcing mechanisms. It is shown that it is possible to obtain a different Reynolds-dependent scaling of the dissipation rate, which can be derived directly as a perturbation around the equilibrium state.

The equilibrium contact angle and the receding contact angle of water droplets suspended on surfaces comprising arrays of equidistant, uniformly sized square micropillars has been measured with goniometry. Surfaces with distinct pillar size and spacing were fabricated via photolithography and deep reactive-ion etching prior to hydrophobization via the molecular vapor deposition of perflourodecyltrichlorosilane (FDTS). The surfaces exhibited superhydrophobic properties and the measured equilibrium contact angle was compared with the prediction of the Cassie equation based on the measured contact angle on a flat FDTS surface and the surface morphology. A poor agreement between the experimental data and the data predicted by the Cassie equation was found when the spacing between structures was less than the width of the pillars. For more closely spaced structures, the deviation between the measured and predicted values increased. In this roughness region, the measured angle is unchanged by the spacing but the receding angle continues to be dependent on the surface structure. A microscopic examination of the interface between the surface and the droplet revealed that the liquid-gas portion of the contact line was distorted at the pillar edges. The extent of the distortion could not be accurately quantified but it was shown that if the capillary region was assumed to be semicircular and extending half of the width of a pillar in to the liquid-gas region of the contact line, that the contact angle could be predicted well. Moreover, a good prediction of the experimental data of a prior study of droplets on closely spaced circular polydimethylsiloxane micropillar arrays is presented.

‘‘Rinsing” liquids and their dynamics are interesting both fundamentally in the interaction of several classic modes of spreading, and industrially in a variety of cleaning applications, such as in the manufacturing of silicon wafers. In this paper, we investigate the time-dependent spreading behavior of a rinsing liquid across a horizontal, rotating substrate; the rinsing liquid is applied to the center of the rotating substrate as an orthogonal impinging jet of constant volumetric flow. We present experimental findings on the azimuthally averaged outer radius of the spreading liquid, in which we observed four distinct growth behaviors in time. We use lubrication theory to explain these phenomena and to define boundaries within the explored parameter space where each was observed. In the absence of rotation, capillarity dominates and the spreading radius grows as $t^{4/10}$. When centrifugal forces dominate the spreading process, several time dependencies of the spreading radius are possible, with lubrication theory predicting exponential growth as well as power laws of $t^{3/4}$ and $t^{3/2}$.

We present results from an experimental investigation of a viscous fluid driven through and around porous disks at low and moderate Reynolds number conditions: $\mathrm{Re}=O({10}^{-4}–{10}^{-3})$ and $\mathrm{Re}=O(1–10)$. Specifically, we quantify the hydrodynamic drag that these thin circular disks exhibit as a function of their size and the shape of their voids, while keeping their porosity fixed (void fraction, $\varphi =0.69\pm 0.02$). We characterize the hydrodynamic loading using the drag ratio, which compares the magnitudes of drag experienced by a porous disk versus that of an impermeable, but otherwise equivalent, reference disk. We find that this drag ratio depends on the effective void radius, but not on the thickness of the disk. During this analysis, great attention has been dedicated to properly account for the effect of the wall confinement on the experimental data. Through scaling analysis, we rationalize our results by comparing them to an existing analytical solution for flow through and around porous disks. In particular, we find that an existing model based on Darcy flow within the porous disk and on Stokes flow outside the disk can be used in conjunction with a permeability model based on aperture flow to predict the forces that porous disks experience, even though the disks have finite thickness. Ultimately, we are able to combine these existing models to successfully predict the dependence of our experimentally measured drag ratio as a function of the Brinkman parameter of the perforated disks, at a fixed level of porosity. In contrast to the sedimentation experiments that are typically employed to evaluate the geometrical effects on the drag forces experienced by objects at low Re, our experiments were displacement controlled.

Kolmogorov [A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 299 (1941)] formulated a theory of small-scale turbulence (K41), valid at extremely large Reynolds numbers, based on two similarity hypotheses and on an exact result derived from the transport equation for the second-order structure function, known as the 4/5 law. Although K41 was praised for its simplicity and elegance, Kolmogorov [A. N. Kolmogorov, J. Fluid Mech. 13, 82 (1962).] proposed a new refined similarity hypothesis (K62) mainly to account for the effect of the large scales on the small scales. It has been widely interpreted in the literature as a correction to K41 arising from the intermittency of the instantaneous energy dissipation rate $\epsilon$. In this paper we argue that since K62 retains the 4/5 law, it must satisfy the same constraints as K41, viz., extremely large Reynolds number and flow stationarity. The retention of the 4/5 law is not however consistent with the presence of nonstationarity due to the effect of the large scales, as postulated by K62. A relatively extensive survey of published data shows that, indeed, the 4/5 law has not yet been observed in either experiments or simulations due to the Reynolds number not being sufficiently large. The use of the transport equation for the second-order structure function, together with an empirical model for the Kolmogorov-normalized second-order velocity structure function, confirms that the 4/5 law is established only after this structure function becomes independent of the Reynolds number.

In the present work, dynamic detonation stabilization in expanding channels is numerically investigated by injecting a hot jet into a hydrogen-oxygen combustible mixture flowing at supersonic speed. The two-dimensional reactive Navier-Stokes equations and one-step two-species reaction model are solved using a hybrid sixth-order Weighted Essentially-Centered Difference scheme based on the Structured Adaptive Mesh Refinement framework. The results show that the highly unstable shear layer interactions with the unburned jet resulting from the Prandtl-Meyer expansion fan result in numerous large-scale vortices, which contribute significantly to rapid turbulent mixing and diffusion effects. This can further facilitate the consumption of the unburned jet and its subsequent heat release to support the dynamically stationary propagation of detonation. Meanwhile, detonation attenuation in the supersonic flow can be also effectively suppressed because of the formation of a hydrodynamic channel associated with a corresponding hydrodynamic throat. It is indicated that the shear layer interactions with the unburned jet and the generation of hydrodynamic channel can both play important roles in dynamically stationary propagation of detonation in supersonic expanding channels after the shutdown of the hot jet. With the increase of the expansion angle, the enlarged unburned jet is gradually extended out of the sonic line, and the deficit of heat release cannot contribute to stationary propagation of detonation, thus eventually leading to detonation failure. It is indicated that there might exist a critical angle ${\theta }_{\mathrm{CT}}$. Dynamic stabilization of detonation can be realized in expanding channels when the angle is smaller than the ${\theta }_{\mathrm{CT}}$, while the detonation propagates below the CJ velocity and finally fails when the angle is larger than the ${\theta }_{\mathrm{CT}}$. Through the control of the moving boundary by dynamically changing the expansion angle, the continuous detonation attenuation can be effectively suppressed and finally turned to forward propagation successfully, indicating that dynamically stationary propagation of detonation can be realized through the dynamic control of the moving boundary.

We present a systematic experimental investigation of the onset of instability in the flow of concentrated, shear-thinning, polyethylene oxide (PEO) solutions through rigid microtubes (diameters $\sim 500\mu \mathrm{m}$ and $2840\mu \mathrm{m}$). Micro-PIV measurements are performed for the flow of PEO solutions ($\sim 2000–6000\mathrm{ppm}$ in water) in the $500\mu \mathrm{m}$ tube to obtain the magnitude of normalized velocity fluctuations, which show a jump at Reynolds number ${\text{Re}}_s$ as low as $\sim 10$, indicative of an instability of the laminar flow, where ${\text{Re}}_s=\left(DV\rho \right)/{\eta }_s$ is the Reynolds number based on the viscosity ${\eta }_s$ evaluated at the maximum shear rate prevailing in the flow, $D$ is the tube diameter, $V$ is the cross-sectional average velocity, and $\rho$ is the fluid density. However, the ratio of peak to center-line velocity does not show any significant shift from the laminar value. Experiments are also carried out to obtain friction factor data for the flow of $2000–4000\mathrm{ppm}$ PEO solutions through a $2.84\mathrm{mm}$ glass tube. Here the transition is inferred from the deviation of the experimental data from the friction factor associated with the laminar flow obtained by fitting the shear-thinning rheology of the polymer solution using the Carreau model. The data for transition Reynolds number ${\text{Re}}_{s,t}$ inferred from micro-PIV and friction factor measurements, for polymer solutions of varying concentrations and for two different tube diameters, collapse reasonably well to yield a scaling law ${\text{Re}}_{s,t}\sim {\left[E_s(1-\beta )\right]}^{-3/4}$, where $E_s=4{\lambda }_s{\eta }_s/\rho D^2$ is the elasticity number based on the fluid relaxation time ${\lambda }_s$ estimated at the maximum shear rate of the flow, and $\beta$ is the ratio of solvent to (shear-rate dependent) total viscosity of the polymer solution. The scaling exponent of $-3/4$ inferred from the present experiments for concentrated polymer solutions is very different from the $-1/2$ exponent reported in previous studies for relatively dilute solutions concerning the onset of elastoinertial turbulence. This suggests that the instability observed in this study for concentrated polymer solutions is qualitatively different from the instability leading to elastoinertial turbulence in relatively dilute solutions. Our study further shows that even rectilinear laminar flows of concentrated polymer solutions become unstable at a relatively low ${\text{Re}}_s\sim 10$, provided the fluid is both sufficiently shear thinning and elastic.

We study the linear stability of plane Poiseuille flow of a Bingham fluid through a deformable neo-Hookean channel. The analysis reveals the existence of a finite-wave instability in the creeping-flow limit, which is absent for Newtonian fluid flow in the same geometry. Indeed, the instability in plane Poiseuille flow of a Bingham fluid closely resembles the finite-wave instability exhibited by plane Couette flow of a Newtonian fluid past a deformable solid. The motion of the unyielded region near the channel centerline effectively results in a Couette-like drag flow of the fluid in the yielded region, albeit with a parabolic base flow velocity profile. More importantly, the boundary conditions at the interface between yielded and unyielded zones is found to be crucial for the existence of the finite-wave instability. This is in stark contrast to Newtonian channel flow where the conditions at the channel centerline are dictated by the symmetry or antisymmetry of the velocity perturbations. The continuation of the predicted instability in the creeping-flow limit is also shown to determine the stability of the flow of a Bingham fluid at higher Reynolds number. In addition to treating the plug as a rigid solid, we also consider the plug to be an elastic solid and show that the elastic nature of the plug does not have any effect on the predicted finite-wave instability. We further argue, using the elastic plug scenario, that some of the regularized models can introduce model-dependent instabilities which are specific to the parameters used in the models.

It was recently claimed by Bhagat et al. [J. Fluid Mech. 851, R5 (2018)] that the scientific literature on the circular hydraulic jump in a thin liquid film is flawed by improper treatment and severe underestimation of the influence of surface tension. Bhagat et al. use an energy equation with a new surface energy term that is introduced without reference, and they conclude that the location of the hydraulic jump is determined by surface tension alone. We show that this approach is incorrect, and we derive a corrected energy equation. Proper treatment of surface tension in thin film flows is of general interest beyond hydraulic jumps, and we show that the effect of surface tension is fully contained in the Laplace pressure due to the curvature of the surface. Following the same approach as Bhagat et al., i.e., keeping only the first derivative of the surface velocity, the influence of surface tension is, for thin films, much smaller than claimed by them. We further describe the influence of viscosity in thin film flows, and we conclude by discussing the distinction between time-dependent and stationary hydraulic jumps.

It is well known that the circulation of the velocity field of a fluid along a closed material curve is conserved for any solution of the Euler equation. We offer a slightly more explicit proof of that fact than that generally found in the literature. We then rewrite that property in terms of the rescaled variables and functions leading to the Euler-Leray equations and that are appropriate for studying self-similar solutions. We end up by discussing the implications of the conservation of circulation on the existence of such solutions.

The steady flow over a rotating cone is investigated theoretically and numerically in order to improve the traditional von Kármán solution by proposing a self-similar correction which is an explicit function of the cone angle. The effect of the correction on the linear stability analysis of the rotating-cone flow is successively investigated through a weakly divergent approach. Both the base flow correction and the results of the stability analysis are validated against dedicated numerical simulations. As for the base flow, the comparison shows a clear improvement obtained by using the proposed correction in comparison with the classical von Kármán solution. As for the stability properties of the flow, the com- parison against the reference simulations shows a good agreement among all the approaches for large azimuthal wave numbers, but a better performance is obtained with the weakly divergent approach for lower wave numbers. The latter approach provides a lower critical Reynolds number than that predicted by parallel theory and, most importantly, changes the interplay between modes I and II with respect to what predicted by the parallel stability calculations. Finally, it is observed that the proposed correction of base flow has a slight effect on the stability analysis of the considered cases, but it may have important effects for low cone angles. Thus, while the classical Kármán solution is appropriate for large cone angles, the proposed correction is recommended for future stability analyses of slender cones.