Most bubbles contain a mixture of vapor and incondensible gases. While the limit cases of pure vapor and pure gas bubbles are well studied, much less is known about the more realistic case of a mixture. The bubble contents continuously change due to the combined effects of evaporation and condensation and of gas diffusion in the liquid and in the bubble. This paper presents a model for this situation and illustrates by means of examples several physical processes that can occur: a bubble undergoing a temporary pressure reduction, which makes the liquid temporarily superheated; a bubble subjected to a burst of sound; and a bubble continuously growing by rectified diffusion of heat in the presence of an incondensible gas.

A rarefied gas is considered in a channel consisting of two infinite parallel plates between which an evenly spaced array of smaller plates is arranged normal to the channel direction. Each of these smaller plates is assumed to possess one ideally specularly reflective and one ideally diffusively reflective side. When the temperature of the small plates differs from the temperature of the sidewalls of the channel, these boundary conditions result in a temperature profile around the edges of each small plate that breaks the reflection symmetry along the channel direction. This in turn results in a force on each plate and a net gas flow along the channel. The situation is analyzed numerically using the direct simulation Monte Carlo method and compared with analytical results where available. The influence of the ideally specularly reflective wall is assessed by comparing with simulations using a finite accommodation coefficient at the corresponding wall. The configuration bears some similarity to a Crookes radiometer, where a nonsymmetric temperature profile at the radiometer vanes is generated by different temperatures on each side of the vane, resulting in a motion of the rotor. The described principle may find applications in pumping gas on small scales driven by temperature gradients.

Previous studies have shown that intermediate magnitude of surface tension has a counterintuitive destabilizing effect on two-phase planar jets. In the present study, the transition process in confined two-dimensional jets of two fluids with varying viscosity ratio is investigated using direct numerical simulations (DNSs). The outer fluid coflow velocity is $17\%$ of that of the central jet. Neutral curves for the appearance of persistent oscillations are found by recording the norm of the velocity residuals in DNS for over 1000 nondimensional time units or until the signal has reached a constant level in a logarithmic scale, either a converged steady state or a “statistically steady” oscillatory state. Oscillatory final states are found for all viscosity ratios ranging from ${10}^{-1}$ to 10. For uniform viscosity $\left(m=1\right)$, the first bifurcation is through a surface-tension-driven global instability. On the other hand, for low viscosity of the outer fluid, there is a mode competition between a steady asymmetric Coanda-type attachment mode and the surface-tension-induced mode. At moderate surface tension, the first bifurcation is through the Coanda-type attachment, which eventually triggers time-dependent convective bursts. At high surface tension, the first bifurcation is through the surface-tension-dominated mode. For high viscosity of the outer fluid, persistent oscillations appear due to a strong convective instability, although it is shown that absolute instability may be possible at even higher viscosity ratios. Finally, we show that the jet is still convectively and absolutely unstable far from the inlet when the shear profile is nearly constant. Comparing this situation to a parallel Couette flow (without inflection points), we show that in both flows, a hidden interfacial mode brought out by surface tension becomes temporally and absolutely unstable in an intermediate Weber and Reynolds regime. By an energy analysis of the Couette flow case, we show that surface tension, although dissipative, can induce a velocity field near the interface that extracts energy from the flow through a viscous mechanism. This study highlights the rich dynamics of immiscible planar uniform-density jets, where different self-sustained and convective mechanisms compete and the nature of the instability depends on the exact parameter values.

The presence of bubbles and voids inside nozzles has a large effect on the morphology and atomization of sprays. In this investigation the voids formed by microbubbles entering the nozzle are investigated using transparent glass nozzles, pressure transducers, and high-speed diffuse backlight imaging. A correlation is found between the magnitude of pressure pulses inside the nozzle and the size of the bubbles causing these pulses. This relation allows the prediction of cavity formation also in nontransparent nozzles, which allow more realistic conditions of operation. Subsequently, the direct measurements of dispersion derived from the spread of glowing fluid showed no significant increase of the dispersion compared to cavitation-free conditions. This indicates that, while the spray angle may increase, the turbulence (in both liquid and gas phase) that governs the dispersion remains the same and the cavitation bubble events do not have a significant impact on this process.

The dynamics of a three-dimensional (3D) bimodal turbulent wake downstream of a square-back Ahmed body are experimentally studied in a wind tunnel through high-frequency wall-pressure probes mapping the rear of the model and a horizontal two-dimensional (2D) velocity field. The barycenters of the pressure distribution over the rear part of the model and the intensity recirculation are found highly correlated. Both described the most energetic large-scale structures dynamics, confirming the relation between the large-scale recirculation bubble and its wall-pressure footprint. Focusing on the pressure, its barycenter trajectory has a stochastic behavior but its low-frequency dynamics exhibit the same characteristics as a weak strange chaotic attractor system, with two well-defined attractors. The low-frequency dynamics associated to the large-scale structures are then analyzed. The largest Lyapunov exponent is first estimated, leading to a low positive value characteristic of strange attractors and weak chaotic systems. Afterwards, analyzing the autocorrelation function of the timeseries, we compute the correlation dimension, larger than two. The signal is finally transformed and analyzed as a telegraph signal, showing that its dynamics correspond to a quasirandom telegraph signal. This is the first demonstration that the low-frequency dynamics of a turbulent 3D wake are not a purely stochastic process but rather a weak chaotic process exhibiting strange attractors. From the flow control point of view, it also opens the path to more simple closed-loop flow-control strategies aiming at the stabilization of the wake and the control of the dynamics of the wake barycenter.

Among different devices developed quite recently to quantify the resistance to erosion of natural soil within the broader context of dyke safety, the most commonly used is probably the jet erosion test in which a scouring crater is induced by impingement of an immersed water jet. A comprehensive experimental investigation on the jet erosion in the specific situation of a cohesionless granular material is presented here. The tests were performed by combining special optical techniques allowing for an accurate measurement of the scouring onset and evolution inside an artificially translucent granular sample. The impinging jet hydrodynamics are also analyzed, empirically validating the use of a self-similar theoretical framework for the laminar round jet. The critical conditions at the onset of erosion appear to be best described by a dimensionless Shields number based on the inertial drag force created by the fluid flow on the eroded particles rather than on the pressure gradients around them. To conclude, a tentative empirical model for the maximal flow velocity initiating erosion at the bottom of the scoured crater is put forward and discussed in the light of some preliminary results.

Turbulence modeling is a critical component in numerical simulations of industrial flows based on Reynolds-averaged Navier-Stokes (RANS) equations. However, after decades of efforts in the turbulence modeling community, universally applicable RANS models with predictive capabilities are still lacking. Large discrepancies in the RANS-modeled Reynolds stresses are the main source that limits the predictive accuracy of RANS models. Identifying these discrepancies is of significance to possibly improve the RANS modeling. In this work, we propose a data-driven, physics-informed machine learning approach for reconstructing discrepancies in RANS modeled Reynolds stresses. The discrepancies are formulated as functions of the mean flow features. By using a modern machine learning technique based on random forests, the discrepancy functions are trained by existing direct numerical simulation (DNS) databases and then used to predict Reynolds stress discrepancies in different flows where data are not available. The proposed method is evaluated by two classes of flows: (1) fully developed turbulent flows in a square duct at various Reynolds numbers and (2) flows with massive separations. In separated flows, two training flow scenarios of increasing difficulties are considered: (1) the flow in the same periodic hills geometry yet at a lower Reynolds number and (2) the flow in a different hill geometry with a similar recirculation zone. Excellent predictive performances were observed in both scenarios, demonstrating the merits of the proposed method.

In recent work, Renaud, Venaille, and Bouchet (RVB) [Renaud et al., J. Stat. Phys. 163, 784 (2016)] revisit the equilibrium statistical mechanics theory of the shallow water equations, within a microcanonical approach, focusing on a more careful treatment of the energy partition between inertial gravity wave and eddy motions in the equilibrium state and deriving joint probability distributions for the corresponding dynamical degrees of freedom. The authors derive a Liouville theorem that determines the underlying phase space statistical measure, but then, through some physical arguments, actually compute the equilibrium statistics using a measure that violates this theorem, choosing equal volume vs equal area fluid parcels. Here, using a more convenient, but essentially equivalent, grand canonical approach, the full statistical theory consistent with the Liouville theorem is derived. The results reveal several significant differences from the previous results (1) The microscale wave motions lead to a strongly fluctuating thermodynamics, including long-range correlations, in contrast to the mean-field-like behavior found by RVB. The final effective model is equivalent to that of an elastic membrane with a nonlinear wave-renormalized surface tension. (2) Even when a mean-field approximation is made, a rather more complex joint probability distribution is revealed. Alternative physical arguments fully support the consistency of the results. Of course, the true fluid final steady state relies on dissipative processes not included in the shallow water equations, such as wave breaking and viscous effects, but it is argued that the current theory provides a more mathematically consistent starting point for future work aimed at assessing their impacts.

Non-Newtonian fluids are susceptible to flow instabilities such as shear banding, in which the fluid may exhibit a markedly discontinuous viscosity at a critical stress. Here we report the characteristics and causes of a jetting flow instability of shear banding wormlike micelle solutions in microfluidic channels with rectangular cross sections over an intermediate volumetric flow regime. Particle-tracking methods are used to measure the three-dimensional flow field in channels of differing aspect ratios, sizes, and wall materials. When jetting occurs, it is self-contained within a portion of the channel where the flow velocity is greater than the surroundings. We observe that the instability forms in channels with aspect ratio greater than 5, and that the location of the high-velocity jet appears to be sensitive to stress localizations. Jetting is not observed in a lower concentration solution without shear banding. Simulations using the Johnson-Segalman viscoelastic model show a qualitatively similar behavior to the experimental observations and indicate that compressive normal stresses in the cross-stream directions support the development of the jetting flow. Our results show that nonuniform flow of shear thinning fluids can develop across the wide dimension in rectangular microfluidic channels, with implications for microfluidic rheometry.

A cornstarch suspension is the quintessential particulate system that exhibits shear thickening. By adding large non-Brownian spheres to a cornstarch suspension, we show that shear thickening can be significantly enhanced. More precisely, the shear-thickening transition is found to be increasingly shifted to lower critical shear rates. This influence of the large particles on the discontinuous shear-thickening transition is shown to be more dramatic than that on the viscosity or the yield stress of the suspension.

This study considers the linear stability of Poiseuille-Rayleigh-Bénard flows subjected to a transverse magnetic field, to understand the instabilities that arise from the complex interaction between the effects of shear, thermal stratification, and magnetic damping. This fundamental study is motivated in part by the desire to enhance heat transfer in the blanket ducts of nuclear fusion reactors. In pure magnetohydrodynamic flows, the imposed transverse magnetic field causes the flow to become quasi-two-dimensional and exhibit disturbances that are localized to the horizontal walls. However, the vertical temperature stratification in Rayleigh-Bénard flows feature convection cells that occupy the interior region, and therefore the addition of this aspect provides an interesting point for investigation. The linearized governing equations are described by the quasi-two-dimensional model proposed by Sommeria and Moreau [J. Fluid Mech. 118, 507 (1982)], which incorporates a Hartmann friction term, and the base flows are considered fully developed and one-dimensional. The neutral stability curves for critical Reynolds and Rayleigh numbers, ${\mathrm{Re}}_c$ and ${\mathrm{Ra}}_c$, respectively, as functions of Hartmann friction parameter $H$ have been obtained over ${10}^{-2}\le H\le {10}^4$. Asymptotic trends are observed as $H\to \infty$ following ${\mathrm{Re}}_c\propto H^{1/2}$ and ${\mathrm{Ra}}_c\propto H$. The linear stability analysis reveals multiple instabilities which alter the flow both within the Shercliff boundary layers and the interior flow, with structures consistent with features from plane Poiseuille and Rayleigh-Bénard flows.

The majority of investigations characterizing the motion of single or multiple particles in fluid flows consider canonical body shapes, such as spheres, cylinders, discs, etc. However, protrusions on bodies—either surface imperfections or appendages that serve a function—are ubiquitous in both nature and applications. In this work, we characterize how the dynamics of a sphere with an axis-symmetric wake is modified in the presence of thin three-dimensional elliptic-shaped protrusions. By investigating a wide range of three-dimensional appendages with different aspect ratios and lengths, we clearly show that the sphere with an appendage may robustly undergo an inverted-pendulum-like (IPL) instability. This means that the position of the appendage placed behind the sphere and aligned with the free-stream direction is unstable, similar to how an inverted pendulum is unstable under gravity. Due to this instability, nontrivial forces are generated on the body, leading to turn and drift, if the body is free to fall under gravity. Moreover, we identify the aspect ratio and length of the appendage that induces the largest side force on the sphere, and therefore also the largest drift for a freely falling body. Finally, we explain the physical mechanisms behind these observations in the context of the IPL instability, i.e., the balance between surface area of the appendage exposed to reversed flow in the wake and the surface area of the appendage exposed to fast free-stream flow.

Pinning and depinning of a windswept droplet on a surface is familiar yet deceptively complex for it depends on the interaction of the contact line with the microscopic features of the solid substrate. This physical picture is further compounded when wind of the Reynolds number greater than 100 blows over pinned drops, leading to the boundary layer separation and wake generation. In this Rapid Communication, we incorporate the well-developed ideas of the classical boundary layer to study partially wetting droplets in a wake created by a leader object. Depending on its distance from the leader, the droplet is observed to exhibit drafting, upstream motion, and splitting, due to the wake-induced hydrodynamic coupling that is analogous to drafting of moving bodies. We successfully rationalize the onset of the upstream motion regime using a reduced model that computes the droplet shape governed by the pressure field inside the wake.

Using results from previous direct numerical simulations and experiments in the outer region of spatially evolving turbulent boundary layers, we compute the streamwise evolution and the wall-normal variation of the dissipation parameter $C_{\varepsilon }$, namely, the turbulent kinetic energy dissipation rate, normalized by appropriate powers of the local turbulent kinetic energy and integral length scale. For ${\mathrm{Re}}_{\theta }\gtrsim 10000$ (${\mathrm{Re}}_{\theta }$ is a Reynolds number on the freestream velocity and the local momentum thickness), $C_{\varepsilon }$ is essentially constant in the streamwise direction, but varies by up to 50% in the wall-normal direction. For ${\mathrm{Re}}_{\theta }<10000$, $C_{\varepsilon }$ is additionally found to vary in the streamwise direction and is inversely proportional to the local turbulence Reynolds number ${\mathrm{Re}}_{\lambda }$.

Experimental results reveal that the asymmetric flow of shear-thinning fluid through a cylindrical pipe, which was previously associated with the laminar-turbulent transition process, appears to have the characteristics of a nonhysteretic, supercritical instability of the laminar base state. Contrary to what was previously believed, classical transition is found to be responsible for returning symmetry to the flow. An absence of evidence of the instability in simulations (either linear or nonlinear) suggests that an element of physics is lacking in the commonly used rheological model for inelastic shear-thinning fluids. These unexpected discoveries raise new questions regarding the stability of these practically important fluids and how they can be successfully modeled.

Intermittency of low-drag pointwise wall shear stress measurements within Newtonian turbulent channel flow at transitional Reynolds numbers (friction Reynolds numbers 70 – 130) is characterized using experiments and simulations. Conditional mean velocity profiles during low-drag events closely approach that of a recently discovered nonlinear traveling wave solution; both profiles are near the so-called maximum drag reduction profile, a general feature of turbulent flow of liquids containing polymer additives (despite the fact that all results presented are for Newtonian fluids only). Similarities between temporal intermittency in small domains and spatiotemporal intermittency in large domains is thereby found.

Properly resolved large-eddy simulations of wall-bounded high Reynolds number flows using standard subgrid-scale (SGS) models requires high spatial and temporal resolution. We have shown that a more elaborate SGS model taking into account the SGS Reynolds stress anisotropies can relax the requirement for the number of grid points by at least an order of magnitude for the same accuracy. This was shown by applying the recently developed explicit algebraic subgrid-scale model (EAM) [Marstorp et al., J. Fluid Mech. 639, 403 (2009)] to fully developed high Reynolds number channel flows with friction Reynolds numbers of 550, 2000, and 5200. The near-wall region is fully resolved, i.e., no explicit wall modeling or wall functions are applied. A dynamic procedure adjusts the model at the wall for both low and high Reynolds numbers. The resolution is reduced, from the typically recommended 50 and 15 wall units in the stream- and spanwise directions respectively, by up to a factor of 5 in each direction. It was shown by comparison with direct numerical simulations that the EAM is much less sensitive to reduced resolution than the dynamic Smagorinsky model. Skin friction coefficients, mean flow profiles, and Reynolds stresses are better predicted by the EAM for a given resolution. Even the notorious overprediction of the streamwise fluctuation intensity typically seen in poorly resolved LES is significantly reduced when EAM is used on coarse grids. The improved prediction is due to the capability of the EAM to capture the SGS anisotropy, which becomes significant close to the wall.

Phoretic swimmers provide new avenues to study nonequilibrium statistical physics and are also hailed as a promising technology for bioengineering at the cellular scale. Exact solutions for the locomotion of such swimmers have been restricted so far to spheroidal shapes. In this paper we solve for the flow induced by the canonical nonsimply connected shape, namely an axisymmetric phoretic torus. The analytical solution takes the form of an infinite series solution, which we validate against boundary element computations. For a torus of uniform chemical activity, confinement effects in the hole allow the torus to act as a pump, which we optimize subject to fixed particle surface area. Under the same constraint, we next characterize the fastest swimming Janus torus for a variety of assumptions on the surface chemistry. Perhaps surprisingly, none of the optimal tori occur in the limit where the central hole vanishes.

Budgets of the turbulent kinetic energy from direct numerical simulations (DNSs) of disperse bubbly channel flows are used to develop a model for bubble-induced turbulence in the Euler-Euler Reynolds-averaged framework. First, an appropriate time scale is selected. Second, links between the unclosed terms in the transport equations of the turbulence quantities and the DNS data for small bubbles are established. Third, a suitably chosen iterative procedure employing the full Reynolds-averaged model provides suitable coefficients for the closure of the terms resulting from bubble-induced turbulence while largely removing the influence of others. At the same time these results validate the closure, exhibiting very good agreement with the DNS and better performance than the standard closures. The model is now ready for use and can be employed in practical Euler-Euler simulations.

Recent experiments and simulations have shown that unsteady turbulent flows display a universal behavior at short and intermediate times, different from classical scaling relations. The origin of these observations is explained using a nonequilibrium correction to Kolmogorov's energy spectrum, and the exact form of the observed universal scaling is derived.