The wake bifurcations behind two circular disks in tandem arrangement are investigated through numerical simulations. The separation distance between the disks, $S/d$, is chosen at 1, 2, 4, and 6, and the Reynolds number, $\mathrm{Re}$, lies in the range of $100\le \mathrm{Re}\le 500$. The wake dynamics are examined in terms of the flow structures as well as drag and lift coefficient characteristics. Seven main wake regimes are observed in the considered ($\mathrm{Re},S/d$) space: steady state (SS), Zig-zig (Zz) mode, standing wave mode, periodic state with reflectional symmetry breaking (RSB), periodic state with double-helical (DH) structures shedding, periodic state with double-hairpin-loop (DHL) shedding, and weakly chaotic state. Among these bifurcations, the DH and DHL wake modes are reported in the tandem disk wakes, which are not observed in a single disk wake. Compared with the single disk wake, the first bifurcation leading to the SS mode is always delayed in tandem configuration, which is especially evident for the case of $S/d=1$. For the second bifurcation leading to an unsteady state, some differences lie in the wake mode for different tandem configurations. The second bifurcation leads to the Zz wake mode for the cases $S/d=1$, 2, and 4, and the RSB mode for $S/d=6$. In the scenario of $S/d=1$, the bifurcations are similar to those of a thick disk, suggesting that a shorter separation distance in this configuration has equivalent effects as increasing the thickness in the case of a single disk. In the scenario of $S/d=2$, the bifurcations are complex and quite different from those in a single disk wake, indicating that the interaction between two disks in tandem arrangement is stronger when the trailing disk is located close to the end of the recirculation region of the leading one. In the scenario of $S/d=6$, the bifurcations resemble those of a single disk wake, except for an observed DHL wake mode. In addition, the variations of the vortex shedding frequency for the unsteady states are investigated and presented.

The well-mixed assumption has been widely used in predicting the spread of infectious diseases in indoor spaces. It is to be expected that a perfect well-mixed state will not be achieved in an indoor space at any reasonable level of ventilation. This work evaluates the well-mixed assumption by comparing the theory with results from large eddy simulations. The robustness of the well-mixed theory is established by comparing at four different levels. The comparison also points out systematic departures in pathogen concentration which can be accurately accounted for with an easily implementable correction factor to quantities such as cumulative exposure time. With the well-mixed model as the baseline, the correction factor can be used to account for additional important problem-specific details. We demonstrate that more accurately accounting for variability in pathogen concentration can help obtain improved estimates for enhanced guidelines of indoor airborne transmission. We further demonstrate that at source-sink separation distances smaller than 5 m, the well-mixed theory on average underestimates the risk of contagion, while for distances larger than about 5 m, the well-mixed theory's prediction, on average, is overly restrictive.

We present laboratory experiments that investigate the structure and flow characteristics of gravity currents traveling through an array of roughness elements. The roughness elements are of comparable height to the gravity current such that the current flows through the roughness array rather than over it. The frontal velocity and density structure are measured as the current transitions from flowing along a smooth bed to flowing through the roughness array and then back to a smooth bed. We find that, upon entering the roughness array, the gravity current decelerates and the density structure changes from the head-and-tail structure typical of smooth bed gravity currents to a wedge shape. A model is presented that explains the deceleration and change in shape based on a dynamic balance between a pressure gradient within the current tail and a drag force associated with individual roughness elements. This model accurately predicts the deceleration of the gravity current, supporting the proposed dynamic balance.

In this paper, we study the coagulation rate of like-charged Brownian spherical particles dispersed in a gaseous medium. Most previous calculations of the Brownian-induced coagulation rate have considered that the particle pairs interact through continuum hydrodynamics, and at a close approach, van der Waals attraction forces allow the collision and subsequent coagulation. However, the continuum approximation of the hydrodynamic interactions is no longer valid when the gap thickness between the surface is less than the mean free path of the surrounding fluid medium and the noncontinuum lubrication interactions lead to surface-to-surface contact in a finite time. We report the Brownian coagulation rate in the presence of noncontinuum lubrication resistances for a range of pair size ratios. At small separations, like-charged conducting particles almost always attract each other. Thus we also incorporate the attractive electrostatic interactions between like-charged conducting spheres in our calculation and report the effects of van der Waals and electrostatic forces on the coagulation rate of conducting spheres interacting with each other through noncontinuum hydrodynamics for a range of size and charge ratios.

The current theories on the mechanism for polymer drag reduction (DR) are generally applicable for long-chain flexible polymers that form viscoelastic solutions. Rigid polymer solutions that generate DR seemingly lack prevalent viscoelastic characteristics. They do however demonstrate higher viscosities and a noticeable shear-thinning trend, approximated by generalized Newtonian models. The following experimental investigation scrutinizes the flow statistics of an aqueous xanthan gum solution in a turbulent channel flow, with friction Reynolds numbers ${\text{Re}}_{\tau }$ between 170 and 700. The amount of DR varies insignificantly between 27% and 33%. The velocity field is measured using planar particle image velocimetry and the steady shear rheology is measured using a torsional rheometer. The results are used to characterize the flow statistics of the polymer drag-reduced flows at different ${\text{Re}}_{\tau }$ and with negligible changes in DR, a parametric study only previously considered by numerical simulations. Changes to the mean velocity and Reynolds stress profiles with increasing ${\text{Re}}_{\tau }$ are similar to the modifications observed in Newtonian turbulence. Specifically, the inner-normalized mean velocity profiles overlap for different ${\text{Re}}_{\tau }$ and the Reynolds stresses monotonically grow in magnitude with increasing ${\text{Re}}_{\tau }$. Profiles of mean viscosity with respect to the wall-normal position demonstrate a thin layer that consists of a low-viscosity fluid in the immediate vicinity of the wall. Fluid outside this thin layer has a significantly higher viscosity. We surmise that the demarcation in the mean shear viscosity between the inner lubricating layer and the outer layer cultivates fluid slippage in the buffer layer and an upward shift in the logarithmic layer, a hypothesis akin to DR using wall lubrication and superhydrophobic surfaces.

Previous experiments and analyses have demonstrated that elastic boundaries reduce the speed of sound and alter the acoustic waves in fluid-filled tubes. Similar effects will occur in any configuration with deformable boundaries and fluid-fluid interfaces. In this work, we study the propagation of nonlinear acoustic waves in 1D liquid-filled tubes with superhydrophobic longitudinal grooved boundaries. Recently, grooved channels have attracted significant interest because of their reduced friction to flow, but such configurations also allow for a new kind of sound wave behavior due to the dependence of the pressure on the triple-phase contact line. We derive a model which contains an interplay between the pressure and the shape of the liquid-gas interface, subject to the hysteresis of the contact line, which is a dominant mechanism for energy dissipation. Our results present front propagation, showing an order of magnitude reduction in the speed of sound, as well as oscillation patterns in which the liquid is pinned in one part of the channel yet oscillating in the rest of the channel.

We performed experiments on a large particle segregating upward in turbulent bedload transport. The experiment was conducted in a narrow flume, fed with small glass beads and water. The large particle, called the intruder, was a glass bead plunged into the bed of smaller glass beads. Its ascent was tracked using image analysis methods. We performed 11 configurations using two Shields numbers and eight size ratios ranging from 1 to 5.3. For each configuration, the experiment was repeated from five to seven times in order to evaluate its repeatability. We found that the temporal ascent of the intruder exhibited two stages. At first, the intruder rose slowly with an intermittent motion. Then, a second stage was observed in which the intruder accelerated suddenly until it reached the top of the bed. While the kinematics of the second stage was found to be repeatable for a given configuration, it was not the case for the first stage. A transition in the size ratio was also observed. For size ratio close to unity, the ascent was much more intermittent than above a size ratio $r=1.7$. Above the same value, the trajectory of the intruder (vertical displacement as a function of the streamwise displacement) became linear with a constant slope, independent of the Shields number and the size ratio. Based on observations, we proposed a segregation mechanism that could explain this linear trajectory.

We studied experimentally and numerically the effect of an imposed gas pressure on the discharge flow of granular media from a cylindrical silo. This study is motivated by a nuclear safety related phenomenology of fuel fragments displaced from a fuel rod under several accidental conditions, the flow being potentially driven by pressurized fission gases within the rod. We imposed a moderate constant air pressure at the top of the granular column ($\approx 3000$ Pa) and we varied the size and type of the particles and the surrounding fluid where the discharge occurs, using air and water to test the role of the coolant fluid in the nuclear safety problem. The measured parameters are the particle mass flow rate, the volumetric flow rate of air, and the pressure along the silo. The particle and air flow rates are found to be nonsteady and to increase with time. To model these behaviors, we use a two-phase continuum model with a frictional rheology to describe particle-particle interactions, and we propose a simple quasisteady analytical model considering the air-pressure gradient at the orifice as an additional driving force to the gravity. We implemented numerically the two-phase continuum model in an axisymmetric configuration which reproduces the experimental results.

In this paper, we study the linear stability and the subsequent formation of nonlinear waves in a colloidal, gravity-driven falling film flow. We first investigate the system's stability by performing a linear stability analysis and observe that the presence of colloidal particles stabilizes both the long-wave surface and the short-wave shear instability modes. The stabilization is attributed to Brownian diffusion equilibrating the leading order particle volume fraction, causing a uniform increase in viscosity. With the particle evolution equation decoupled from the momentum equation in the linear limit, we analytically study the damped yet intricate evolution of perturbations to the particle concentration field. The particle mode decays via three different asymptotic routes: Brownian diffusion, anomalous diffusion, and Taylor dispersion. To study the nonlinear waves, we then derive nonlinear models in the framework of long-wave theory using Benney's gradient expansion approach and the integral-boundary-layer approach. Subsequently, we use a central-manifold approach to derive a depth-averaged equation for the particle volume fraction evolution, incorporating Brownian diffusion and Taylor dispersion. Comparisons of the linear predictions of the nonlinear models with the linear stability calculations show good agreement in the limit of small wave numbers.

We investigate by direct numerical simulation Rayleigh-Bénard convection in a rotating rectangular cell with rotation vector and gravity perpendicular to each other. The flow is two-dimensional near the onset of convection with convection rolls aligned parallel to the rotation axis of the boundaries. At a sufficiently large Rayleigh number, the flow becomes unstable to three-dimensional disturbances which changes the scaling of heat transport and kinetic energy with Rayleigh number. The mechanism leading to the instability is identified as an elliptical instability. At the transition, the Reynolds and Rossby numbers $\mathrm{Re}$ and $\mathrm{Ro}$ based on the kinetic energy of the flow are related by $\mathrm{Re}\propto {\mathrm{Ro}}^{-2}$ at small $\mathrm{Ro}$ with a geometry-dependent prefactor.

The dynamics of microbubbles under the action of external acoustic forces has become particularly important in several applications. In this work, we are particularly interested in studying the transport of surfactant molecules to the surface of an oscillating microbubble, considering the impact that the dynamic surface tension and temporal evolution of the radius of the microbubble has when an acoustic pressure as a driving force is used to promote the nonlinear oscillations. The resulting governing equations to predict the radius of the microbubble and the evolution of the surfactant at the surface are written in dimensionless form. For these equations, we identify two fundamental dimensionless parameters: the Gibbs elasticity $E$, and the cohesive (or repulsive) parameter $K$. Using the physical domain $0\le E\le 10$ and $-13.2\le K\le 13.2$, and considering that the diffusive Péclet number is large, as occurs in some applications, the surfactant concentration equation is solvable by using a similarity transformation, whereas the Rayleigh-Plesset-type equation that includes the influence of the previous parameters $E$ and $K$ is solved by the fourth-order Runge-Kutta method. When the numerical predictions are compared with the well-known cases $E=K=0$, strong deviations reveal that the oscillation mechanisms can be significantly altered.

The lifetime $\tau$ of an isothermal and purely diffusively dissolving droplet in a host liquid scales as $\tau \sim R_0^2$ with its initial radius $R_0$ [Langmuir, Phys. Rev. 12, 368 (1918)]. For a droplet dissolving due to natural convection driven by density differences, its lifetime scales as $\tau \sim R_0^{5/4}$ [Dietrich et al., J. Fluid Mech. 794, 45 (2016)]. In this paper we experimentally find and theoretically derive yet another droplet dissolution behavior, resulting in $\tau \sim R_0^4$. It occurs when the dissolution dynamics is controlled by local heating of the liquid, leading to a modified solubility and a thermal Marangoni flow around the droplet. The thermal gradient is achieved by plasmonic heating of a gold nanoparticle decorated sample surface, on which a sessile water droplet immersed in water-saturated 1-butanol solution is sitting. The resulting off-wall thermal Marangoni flow and the temperature dependence of the solubility determine the droplet dissolution rate, resulting in a shrinkage $R\left(t\right)\sim {(\tau -t)}^{1/4}$ of the droplet radius and thus in $\tau \sim R_0^4$.

We numerically investigate a two-time Lagrangian velocity correlation function (TTLVCF) for particle pairs in two-dimensional energy inverse-cascade turbulence. We consider self-similarity of the correlation function by means of incomplete similarity. In this framework, we propose a self-similar form of the correlation function, whose scaling exponents cannot be determined by only using the dimensional analysis based on the Kolmogorov's phenomenology. As a result, the scaling laws of the correlation function can depend on the initial separation. This initial-separation dependency is frequently observed in laboratory experiments and direct numerical simulations of the relative dispersion, which is directly related to the correlation function, at moderate Reynolds numbers. We numerically verify the self-similar form by direct numerical simulations of two-dimensional energy inverse-cascade turbulence. The involved scaling exponents and the dependencies on finite Reynolds-number effects are determined empirically. Then, we consider implication of the scaling laws of the correlation function on the relative dispersion, i.e., the Richardson-Obukhov $t^3$ law. Our results suggest a possibility not to recover the Richardson-Obukhov $t^3$ law at infinite Reynolds number.

Flows over two side-by-side circular cylinders exhibit fascinating flow physics due to complex interactions between the coupled wakes. However, their mutual interference effects have not been elucidated in a quantitative manner thus far. In this paper, we create a mismatch between the two wakes by introducing a size difference in the cylinder pair, such that the effects of one wake on the other can be distinguished. Depending on the size and gap ratios between the two cylinders, the coupled wake exhibits distinct dynamical features including the single bluff-body flows, chaotic flows, quasi-periodic flows, and synchronized flows. As with the cases of two identical cylinders, the chaotic flows are featured by the flip-flop phenomenon (random switching of the gap flow direction) even for cases with large size difference. The quasiperiodic flows are mainly composed of two primary frequencies associated with vortex shedding in the near wakes of the two cylinders. Both wakes impose their own frequencies on the other, resulting in the beating phenomenon in the lift coefficients. The phase lag associated with each of the primary frequencies between the two cylinders modulates the combined lift forces. The triad interactions between the two wakes generate the sideband frequencies, which are associated with modal structures that are mostly active in the far wake. The transition from quasiperiodicity to synchronization is dominated by the vortex shedding behind the larger cylinder, to which the wake of the smaller cylinder locks in. These results reveal new insights on the coupled wakes of two cylinders, and are pivotal for understanding more general wake interaction problems.

An antibubble is an uncommon fluid object with a unique structure: a liquid globule is wrapped by a thin air film, with the whole being immersed in a liquid bath. In short, the antibubble is the opposite of a soap bubble. The antibubble has been regarded as a promising candidate for various industrial applications since two components can be separated only by an air layer before mixing. However, the use of the antibubble is limited by the short lifetime $(\approx 1 \min )$ and the broad distribution of the lifetimes. We demonstrate a simple and efficient method to extend the lifetime of the antibubbles. The proposed system consists of a liquid surface covered by a layer of bubbles under which antibubbles are generated. The liquid is then vertically shaken. Above a given acceleration threshold that depends on the frequency, the lifetime of the antibubbles is significantly increased. Under vibrations, antibubbles were kept alive up to 13 h. As soon as the vibration is stopped, the antibubble collapses immediately. The antibubble popping can therefore be programmed. A model based on the dynamical air drainage in the air shell of the antibubble is proposed to account for these observations.

We define and characterize multitime Lagrangian structure functions using data stemming from two swirling flows with mean flow and turbulent fluctuations: a Taylor-Green numerical flow and a von Kármán laboratory experiment. Data is obtained from numerical integration of tracers in the former case and from three-dimensional particle tracking velocimetry measurements in the latter. Multitime statistics are shown to decrease the contamination of large scales in the inertial range scaling. A timescale at which contamination from the mean flow becomes dominant is identified, with this scale separating two different Lagrangian scaling ranges. The results from the multitime structure functions also indicate that Lagrangian intermittency is not a result of large-scale flow effects. The multitime Lagrangian structure functions can be used without prior knowledge of the forcing mechanisms or boundary conditions, allowing their application in different flow geometries.

The present paper explores the effect of asymmetric and helical excitation of the flow about the exit plane of a jet injected perpendicularly into crossflow. Both acetone planar laser-induced fluorescence and stereo particle image velocimetry were used to quantify transverse jet response at relatively high jet-to-crossflow momentum flux ratios ($J=61$ and 41), which in the absence of external excitation produced a highly penetrating jet with a naturally convectively unstable upstream shear layer (USL) and asymmetric cross-sectional shape. For various excitation conditions, in some cases involving complete clockwise or clockwise perturbations and, in other cases, localized perturbations, alterations in the spectral character of the USL were observed, including lock-in to the applied frequency and quasiperiodicity involving applied and natural frequencies. For forcing frequencies and amplitudes producing lock-in, asymmetric excitation was found to accelerate USL vorticity roll-up and improved mean symmetry in the jet cross section. With these alterations in jet structure, molecular mixing between jet and crossflow fluid was improved in both center plane and cross-sectional planes of the transverse jet. Proper orthogonal decomposition analysis applied to the images revealed 2D and 3D mode coefficient plots with interesting topological features. In many cases, these phase diagrams revealed attractor like shapes, especially when excitation frequencies and amplitudes produced lock-in of the USL, suggesting that with further study, such topologies could be used as characteristic signatures for mixing optimization and low-order model development.

The phenomenon of unidirectional solidification of binary solutions leads to various flow patterns such as solute fingers, plumes, and double-diffusive layers (DDLs) due to density variations arising out of the coupled effects of thermal and solutal gradients. The present work reports experiments to elucidate the transport phenomena responsible for the formation of DDLs during unidirectional solidification of aqueous ${\mathrm{NH}}_4\mathrm{Cl}$ solution in a narrow solidification chamber. The spatiotemporally resolved flow and transported properties associated with the phenomenon have been determined through a combination of nonintrusive techniques. Dual-wavelength interferometry has been used for simultaneous measurement of temperature and salt concentration distributions. Various subprocesses such as convection transients, plume formation, and evolution of DDLs that result in the formation of the stepped structure of solutal-thermal gradients have been mapped through rainbow-schlieren deflectometry. Flow velocities have been quantified using PIV. Based on the whole-field measurements, plausible mechanisms responsible for the development and further evolution of DDLs have been identified. Direct experimental observations revealed the existence of counter-rotating rolls near the chamber sidewalls. Interaction of these convective rolls with the plumes originating from the mushy zone results in a downward inclination of DDLs (towards plume locations), thus giving DDLs a slanted shape instead of their horizontal orientations. The alternate sense of rotation of convective rolls in the adjacent DDLs has been explained through observations made using different experimental techniques. Experimental results are additionally supported with analytical scales of flow parameters such as plume velocity, diameter, the height of DDLs, the downward velocity of DDLs, etc.

Steady dipole-flow through a porous medium, and disturbed by a circular inclusion ${\mathrm{\Omega }}_0$ of conductivity different from the background, is solved analytically. The solution is achieved by means of the circle theorem, which is reformulated to account for the entry/leave of mass and energy through the boundary $\partial {\mathrm{\Omega }}_0$. It is shown that the governing potential is that which one would consider in absence of the disturbance supplemented with an ad hoc (fictitious) dipole laying inside ${\mathrm{\Omega }}_0$. Besides the theoretical interest, the analytical solution is used to compute the effective conductivity ${\mathrm{K}}^{\mathrm{eff}}$, by means of the self-consistent approximation. Overall, ${\mathrm{K}}^{\mathrm{eff}}$ is found to depend upon the flow configuration, and therefore it cannot be sought as a medium's property (nonlocality). In particular, ${\mathrm{K}}^{\mathrm{eff}}$ depends upon the joint probability density function $f$ of the conductivity and the distribution/size of the inclusions. Results, analyzed for a fairly general model of $f$, demonstrate that the coefficient of correlation $\rho$ between the involved random fields is the key parameter characterizing the structure of ${\mathrm{K}}^{\mathrm{eff}}$. Indeed, the latter results larger or smaller than that of the background, depending on whether $\rho$ is negative or positive, respectively. For $\rho =0$, the effective conductivity is a local property and, in this case, one can apply the superposition principle with the homogeneous conductivity replaced by the geometric mean.

Interfacial tension gradients drive flow along fluid-fluid interfaces in a process known as the Marangoni effect. Such gradients can be caused by surfactants, as extensively studied in the literature. Less is known of its nanoscale behavior, where molecular interfaces exhibit specific properties such as interfacial viscosity. In this work we study the solutal Marangoni effect at a model fluid-fluid interface using molecular dynamics simulations. We show that molecular interfacial effects are important and should be accounted for in nanofluidic regimes. Hydrodynamic models can be extended with effective terms that include them.