Gas migration through a soft granular material involves a strong coupling between the motion of the gas and the deformation of the material. This process is relevant to a variety of natural phenomena, such as gas venting from sediments and gas exsolution from magma. Here, we study this process experimentally by injecting air into a quasi-2D packing of soft particles and measuring the morphology of the air as it invades and then rises due to buoyancy. We systematically increase the confining prestress in the packing by compressing it with a fluid-permeable piston, leading to a gradual transition in migration regime from fluidization to pathway opening to pore invasion. We find that mixed migration regimes emerge at intermediate confinement due to the spontaneous formation of a compaction layer at the top of the flow cell. By connecting these migration mechanisms with macroscopic invasion, trapping, and venting, we show that mixed regimes enable a sharp increase in the average amount of gas trapped within the packing, as well as much larger venting events. Our results suggest that the relationship between invasion, trapping, and venting could be controlled by modulating the confining stress.

A data-driven framework for formulation of closures of the Reynolds-average Navier-Stokes (RANS) equations is presented. In recent years, the scientific community has turned to machine learning techniques to translate data into improved RANS closures. While the body of work in this area has primarily leveraged neural networks (NNs), we alternately leverage a sparse regression framework. This methodology has two important properties: (1) The resultant model is in a closed, algebraic form, allowing for direct physical inferences to be drawn and naive integration into existing computational fluid dynamics solvers, and (2) Galilean invariance can be guaranteed by thoughtful tailoring of the feature space. Our approach is demonstrated for two classes of flows: homogeneous free shear turbulence and turbulent flow over a wavy wall. The model learned based upon the wavy wall configuration is then validated against flow over a backward-facing step. This work demonstrates similar performance to that of modern NNs but with the added benefits of interpretability, increased ease of use and dissemination, and robustness to sparse and noisy training data sets.

The rhythmic motions and wavelike planar oscillations in filamentous soft structures are ubiquitous in biology. Inspired by these, recent work has focused on the creation of synthetic colloid-based active mimics that can be used to move, transport cargo, and generate fluid flows. Underlying the functionality of these mimics is the coupling between elasticity, geometry, dissipation due to the fluid, and active force or moment generated by the system. Here, we use slender-body theory to analyze the linear stability of a subset of these—active elastic filaments, filament arrays and filament carpets—animated by follower forces. Follower forces can be external or internal forces that always act along the filament contour. The application of slender-body theory enables the accurate inclusion of hydrodynamic effects, screening due to boundaries, and interactions between filaments. We first study the stability of fixed and freely suspended sphere-filament assemblies, calculate neutral stability curves separating stable oscillatory states from stable straight states, and quantify the frequency of emergent oscillations. The results from the slender-body theory differ from that obtained using an approximate theory used often in the literature to study dynamics of filaments, referred to as the resistance force theory, in which the tangential and normal components of the fluid traction at a point on the filament are proportional to the tangential and normal components of the velocity of the filament. Next, we examine the onset of instabilities in a small cluster of filaments attached to a wall and examine how the critical force for onset of instability and the frequency of sustained oscillations depend on the number of filaments and the spacing between the filaments. Our results emphasize the role of hydrodynamic interactions in driving the system toward perfectly in-phase or perfectly out-of-phase responses depending on the nature of the instability. Specifically, the first bifurcation corresponds to filaments oscillating in-phase with each other. We then extend our analysis to filamentous (line) array and (square) carpets of filaments and investigate the variation of the critical parameters for the onset of oscillations and the frequency of oscillations on the interfilament spacing. The square carpet also produces a uniform flow at infinity and we determine the ratio of the mean-squared flow at infinity to the energy input by active forces. We conclude by analyzing the bending and buckling instabilities of a straight passive filament attached to a wall and placed in a viscous stagnant flow—a problem related to the growth of biofilms, and also to mechanosensing in passive cilia and microvilli. Taken together, our results provide the foundation for more detailed nonlinear studies on elastohydrodynamical instabilities in active filament systems.

The characteristics of an aqueous drop spreading on a solid surface are the keys to many deposition processes, including coating, printing, enhanced oil production, and surfactant replacement therapies. It is generally believed that the addition of surface-active materials increases the rate of the drop spreading. We report on an unexpected phenomenon whereby the initial spread of surfactant drops is impeded by the Marangoni stresses, resulting in a large increase in the total spreading time. This is demonstrated by an experimental study of the early-time regimes of surfactant-laden drops spreading on a hydrophilic solid surface, submerged in a second immiscible viscous liquid. Remarkably, we find that the surfactants delay the initial fast motion of the three-phase contact lines. The nonuniform distribution of the surfactants at the interface generates the Marangoni stresses before the drop-solid contact that suppresses the film drainage and the expansion of the droplet. Surfactant solutions with 0.1 and 1 critical micelle concentrations wet the surface, with their radius growing according to $r\sim t^{0.5}$ for very short timescales, as opposed to the viscous regime for which $r\sim t$. Our research can provide a guideline for the design of systems with controllable and desirable wetting dynamics.

The dynamics of ligaments retracting under the action of surface tension occurs in a multitude of natural and industrial applications; these include inkjet printing and atomization. We perform direct, fully three-dimensional, two-phase numerical simulations of the retracting process over a range of system parameters that account for surfactant solubility, sorption kinetics, and Marangoni stresses. Our results indicate that the presence of surfactant inhibits the “end-pinching” mechanism and promotes neck reopening through Marangoni-flow; this is induced by the formation of surfactant concentration gradients that drive flow-reversal toward the neck. The vortical structures associated with this flow are also analyzed in detail. We also show that these Marangoni stresses lead to interfacial rigidification, observed through a reduction of the retraction velocity and ligament kinetic energy.

We develop a physical model of the dam-break flow of fine noncohesive particles initially fluidized by a gas. By revisiting previous experiments, we show that the dynamics of such flows involves two uncoupled phenomena. On the one hand, the settling of the particles is the same as that of a nonflowing suspension, so that the mass flux of particles that deposit can be related solely to the properties of the suspension. On the other hand, the flow of the gas-particle mixture is similar to that of an equivalent fluid of constant density and negligible viscosity. The momentum lost by the flowing mixture is equal to the product of the deposited mass flux and the longitudinal velocity. These properties allow us to model the time duration of the flow as the time taken by the particles to settle and the slope of the final deposit as the ratio between the growth rate of the deposit height and the velocity of the front of the dam-break flow. Finally, these findings lead to the formulation of consistent shallow-water equations involving specific terms of mass and momentum transfer at the bottom wall, which can be used to compute the dense lower layer of ash flows generated by a volcanic eruption. They also provide tools for the interpretation of field measurements by geologists.

The article explores a physical phenomenon characteristic of the gas dynamics of microflows. Exhaustion of a supersonic jet of a vibrational exited polyatomic gas $\mathrm{S}{\mathrm{F}}_6$ from convergent nozzles with diameters ranging from 63 to 1000 μm is considered. The influence of vibrational nonequilibrium of the gas on the gas-dynamic structure of supersonic axisymmetric jets is detected in experiments and is numerically confirmed. This influence is manifested as a decrease in the streamwise size of the wave structure cells and reduction of the number of these cells as compared to the equilibrium supersonic flow. It is demonstrated that the maximum effect is observed in jets escaping from nozzles with diameters about 250 μm.

The present work aims to study the evolution of the wake-flow dynamic, including the shear-layers interactions phenomena and the global modes behavior of a square-back Ahmed body with a width to height aspect ratio, $w/h$, of 1.346. Various ground-clearance configurations around the critical case associated with the onset of the lateral bistability and corresponding to a critical ground clearance, $g_c/w=0.1$, are investigated. For this purpose, vertical and transversal planar particle image velocimetry (PIV) and concurrent base pressure and force measurements are performed. Results show that the instantaneous wake-flow interactions between the side- or under-body flow and the wake shear layers depend mainly on the under-body flow rate and that a particular attention is required for the experimental under-body flow conditions. Pressure-velocity correlations and instantaneous filtered PIV snapshots analysis highlight the preferential shear-layer vortex shedding associated with the two selected stable and bistable wake-flow configurations. Present investigations underline the transition process from a stable wake configuration $(g/w<0.1)$ to a bistable state flow configuration $(g/w>0.1)$. The antisymmetric periodic global mode is strongly affected around the critical bistable case at the origin of a substantial drag reduction. The oscillation modes varies between stable and bistable states, and then the corresponding Strouhal numbers for the horizontal (respectively, vertical) evolve from 0.16 (respectively, 0.27) to 0.13 (respectively, 0.18). With regard to the present space-time evolution of the wake-flow features, a dynamical interpretation of the different interactions mechanisms is finally proposed for each case with a particular interest to the low-ground-clearance configurations poorly described in the literature.

Intermittent turbulent-laminar patterns characterize the transition to turbulence in pipe, plane Couette, and plane channel flows. The time evolution of turbulent-laminar bands in plane channel flow is studied via direct numerical simulations using the parallel pseudospectral code ChannelFlow in a narrow computational domain tilted by ${24}^{\circ }$ with respect to the streamwise direction. Mutual interactions between bands are studied through their propagation velocities. Energy profiles show that the flow surrounding isolated turbulent bands returns to the laminar base flow over large distances. Depending on the Reynolds number, a turbulent band can either decay to laminar flow or split into two bands. As with past studies of other wall-bounded shear flows, in most cases survival probabilities are found to be consistent with exponential distributions for both decay and splitting, indicating that the processes are memoryless. Statistically estimated mean lifetimes for decay and splitting are plotted as a function of the Reynolds number and lead to the estimation of a critical Reynolds number ${\mathrm{Re}}_{\text{cross}}\simeq 965$, where decay and splitting lifetimes cross at greater than ${10}^6$ advective time units. The processes of splitting and decay are also examined through analysis of their Fourier spectra. The dynamics of large-scale spectral components seem to statistically follow the same pathway during the splitting of a turbulent band and may be considered as precursors of splitting.

Inspired by the recent multifluid system with thickness down to microscopic scale during thermal drawing for fiber fabrication, we perform the linear analysis of dewetting instability in multilayer planar sheets. The effects of various physical parameters on the dewetting instability have been extensively investigated, including van der Waals forces, viscosities, surface tensions, and thicknesses. As the thickness of the liquid sheet is reduced down to nanoscales, van der Waals forces become more prominent and lead to the dewetting instability. For the three-layer case ($N=3$), the “para-varicose” mode with larger thickness perturbations plays a dominant role. For the four-layer case ($N=4$), there are several more complicated unstable modes, and the maximum growth rate (${\mathrm{\Omega }}_m$) depends on both fluid properties, and the corresponding eigenamplitudes can switch among various modes. Particularly, a slowest growth rate (${\mathrm{\Omega }}_m^{\text{slow}}$) is identified at a critical thickness of the cladding layer ($H_{\text{cr}}$). Additionally, for the relevant applications of fiber drawing, by changing multilayer structure from $N=3$ to 4 through introducing an additional less viscous sheet, the instability can be enhanced, or, by choosing a suitable thickness of a less viscous sheet, the instability can be reduced. These results not only shed light on controlling the dewetting instability by material selection and structure design, but also provide guidance to achieve functional devices with sophisticated nanostructures either in a single fiber or in integrated fabrics for large-scale textiles.

Two new algebraic turbulence models for flows dominated by bubble-induced turbulence (BIT) are presented. They combine different elements of existing models that are considered superior to their alternatives. Both models focus on the core region of a channel flow, where the flow can be assumed to be in local equilibrium and the void fraction is approximately homogeneous. The first model, referred to as the algebraic Reynolds normal stress model, is derived from the differential Reynolds stress model of Ma et al. [J. Fluid Mech. 883, A9 (2020)]. The second model utilizes the original two-equation turbulence model for bubbly flows [Ma et al., Phys. Rev. Fluids 2, 034301 (2017)] to achieve algebraic expressions for $k$ and $\varepsilon$ in BIT-dominated cases. If both models are combined, it results in a purely algebraic (i.e. not involving any differential equations), explicit relation for the Reynolds normal stresses, which depends only on the mean flow parameters, namely, the mean gas void fraction and mean liquid and gas velocities. We find that the model can well predict the Reynolds normal stresses, compared with direct numerical simulation and experimental data.

Universality in compressible turbulence has proven to be elusive as no unifying set of parameters was found to yield universal scaling laws. This severely limits our understanding of these flows and the successful development of theoretically sound models. Using results in specific asymptotic limits of the governing equations in the absence of a mean flow, we show that universal scaling is indeed observed when the set of governing parameters is expanded to include internally generated dilatational scales regardless of driving mechanisms that produce the turbulence. The analysis, though restricted to homogeneous flows, demonstrates why previous scaling laws fail, and it suggests new venues to identify physical processes of interest and aid in the development of more general turbulence models. We support our results with a new massive database of highly resolved direct numerical simulations along with data from the literature comprising isotropic flows with different forcing mechanisms as well as homogeneous shear flows. We also include flows with considerable bulk viscosity. In search of universal features, we postulate the existence of classes that bundle the evolution of flows in the new parameter space. An ultimate asymptotic regime predicted by renormalization-group theories and statistical mechanics is also assessed with available data.

We study the bifurcations of the large-scale jets in the turbulent regime of a forced shear flow using direct numerical simulations of the Navier-Stokes equations. The bifurcations are seen in the probability density function (PDF) of the largest-scale mode with the control parameter being the Reynolds number based on the friction coefficient denoted by Rh. As one increases Rh in the turbulent regime, the PDF of the large-scale mode first bifurcates from a Gaussian to a bimodal behavior, signifying the emergence of reversals of the large-scale flow where the flow fluctuates between two distinct turbulent states. A further increase in Rh leads to a bifurcation from a bimodal to a unimodal PDF, which indicates the disappearance of the reversals of the largest-scale mode. We attribute the latter transition to the long-time memory that the large-scale flow exhibits related to a low-frequency $1/f^{\alpha }$ type of noise with $0<\alpha <2$. We also demonstrate that a minimal model with 15 modes, obtained from the truncated Euler equation, is able to capture the bifurcations of the large-scale jets exhibited by the Navier-Stokes equations.

We present results from a combined experimental and numerical investigation of the fluid-structure interaction of cantilevered porous flexible strips, towed through a fluid bath. We characterize the steady-state deformation of the strips and their associated drag, focusing on the low and moderate Reynolds (Re) number regimes. Our microfabricated strips offer independent control over porosity and permeability, a feature not available in previous studies. We fabricate strips with different levels of permeability, spanning over two orders of magnitude, while fixing their porosity at $50\%$. Then, the vertically clamped porous strips are towed inside a viscous bath. In parallel to the experiments, we model the strip as an elastica that is loaded locally by low (or moderate) Reynolds forces, via local drag coefficients. At low Re, we find that the drag coefficient, which can be obtained from Stokes simulations of rigid strips under perpendicular flow, varies with permeability by less than $10\%$. By contrast, at moderate Re, the drag coefficient depends significantly and nonmonotonically on permeability. Whereas porosity dictates the drag coefficient at low Re, our results demonstrate that a precisely designed permeability plays a major role at moderate Re, enabling large variations of the drag coefficients at a set level of porosity. Since porosity is directly linked to weight via the density of the effective solid, understanding how porous structures of fixed porosity and varying permeability interact with the surrounding fluid is of relevance to flying insects and microdrones.

The statistical properties of species undergoing chemical reactions in a turbulent environment are studied. We focus on the case of reversible multicomponent reactions of second and higher orders, in a condition close to chemical equilibrium sustained by random large-scale reactant sources, while the turbulent flow is highly developed. In such a state a competition exists between the chemical reaction that tends to dump reactant concentration fluctuations and enhance their correlation intensity and the turbulent mixing that on the contrary increases fluctuations and removes relative correlations. We show that a unique control parameter, the Damköhler number (${\text{Da}}_{\theta }$), which can be constructed from the scalar Taylor microscale, the reactant diffusivity, and the reaction rate, characterizes the functional dependence of fluctuations and correlations in a variety of conditions, i.e., at changing the reaction order, and the Reynolds and Schmidt numbers. The larger is such a Damköhler number the more depleted are the scalar fluctuations as compared to the fluctuations of a passive scalar field in the same conditions, and vice versa the more intense are the correlations. A saturation in this behavior is observed beyond ${\text{Da}}_{\theta }\simeq O\left(10\right)$. We provide an analytical prediction for this phenomenon which is in excellent agreement with direct numerical simulation results.

Astrophysical simulations of convection frequently impose different thermal boundary conditions at the top and the bottom of the domain in an effort to more accurately model natural systems. In this work, we study Rayleigh-Bénard convection (RBC) under the Boussinesq approximation. We examine simulations with mixed temperature boundary conditions in which the flux is fixed at the bottom boundary and the temperature is fixed at the top (“FT”). We aim to understand how FT boundaries change the nature of the convective solution compared to the traditional choice of thermal boundaries, in which the temperature is fixed at the top and bottom of the domain (“TT”). We demonstrate that the timescale of thermal relaxation for FT simulations is dependent upon the initial conditions. “Classic” initial conditions that employ a hydrostatically—and thermally—balanced linear temperature profile exhibit a long thermal relaxation. This long relaxation is not seen in FT simulations, which use a TT simulation's nonlinear state as initial conditions (“TT-to-FT”). In the thermally relaxed, statistically stationary state, the mean behavior of an FT simulation corresponds to an equivalent simulation with TT boundaries, and time- and volume-averaged flow statistics like the Nusselt number and the Péclet number are indistinguishable between FT and TT simulations. FT boundaries are fundamentally asymmetric, and we examine the asymmetries that these boundaries produce in the flow. We find that the fixed-flux boundary produces more extreme temperature events than the fixed-temperature boundary. However, these near-boundary asymmetries do not measurably break the symmetry in the convective interior. We briefly explore rotating RBC to demonstrate that our findings with respect to thermal relaxation carry over to this more complex case, and to show the power of TT-to-FT initial conditions.

Levitated liquid droplets are not in contact with containers, and rotating two-lobed droplets are used for measuring the viscosities of molten material. In order to discuss the characteristics of two-lobed droplets, the transient shape variation and the inner flow field of a rotating liquid droplet are simulated numerically in this study. The calculated two-lobed shapes are shown to agree with the existing experimental and calculated results obtained under steady-state conditions. It is also shown that the relation between the maximum deformation and the rotation rate agrees with the experimental results. It is found that two vortices appear in the two-lobed droplet and the countercurrent flow is formed in between two lobes. The relation between the maximum deformation and the rotation rate is affected by the surface tension and the density, and the effect of density becomes small as the deformation increases. In contrast, the relation between the deformation parameter based on the minimum diameter and the aspect ratio is not affected by the droplet properties.

Transonic buffet is an unsteady flow phenomenon that limits the safe flight envelope of modern aircraft. Scale-resolving simulations with span-periodic boundary conditions can provide detailed insight into the flow physics associated with buffet and can help to calibrate simplified models that are needed, for example, to develop more efficient wings based on laminar-flow supercritical sections. However, such simulations are often feasible only for severely restricted spanwise domains. In the current contribution, we analyze an unswept laminar-flow wing section (of Dassault Aviation's V2C profile) at a moderate Reynolds number of $\text{Re}=500000$ and a Mach number of $M=0.7$ with spanwise domains equal to 5% and 100% of the airfoil chord. An implicit large-eddy simulation methodology, using a spectral error estimator to control the action of a high-order filter, is first validated against direct numerical simulations and then used for the domain width study. Quantitative differences, due to domain size, include an increase in amplitude and regularity of the buffet oscillations in the wider domain. Nevertheless, a space-time analysis shows that key physical phenomena such as upstream-propagating shock waves are properly represented in the narrow domain and there is limited sensitivity to the domain size of the aerodynamic coefficients. Even in the very wide domain, which is an order of magnitude wider than the largest turbulent structures measured at the trailing edge, certain features remain two dimensional, including the shock and expansion waves that interact with the boundary layer upstream of transition. The transition mechanism is found to have subtle variations during a typical buffet cycle, with Kelvin-Helmholtz structures prominent during low-lift phases and oblique modes developing behind shock/boundary-layer interactions during high-lift phases. The availability of the wide domain data is used for further study of the buffet mechanism, considering phase-averaged data and instantaneous flow fields to show the global structure of the buffet oscillation.

Using the well-known hydrodynamic theory for dilute suspensions of spheroids, we have previously predicted the destabilization of Taylor-Couette flow due to anisotropic viscous stresses induced by suspended disk-shaped particles [Gillissen and Wilson, Phys. Rev. Fluids 3, 113903 (2018)]. Here we provide experimental evidence for the destabilization mechanism using suspensions of mica flakes. There is good qualitative agreement between the experiment and theory in the mica concentration dependence of the critical speed for instability onset and of the axial wavelength of the corresponding Taylor vortices. Quantitative differences are attributed to hydrodynamic interactions between the disks, which we account for in the theory in an ad hoc fashion using rotary diffusion.

The ability to predict and/or control wall slip is a fundamental problem in the hydrodynamics of yield stress fluids, which is poorly understood to date and has important applications in bio- and microfluidic systems. Systematic measurements of steady flows of a simple yield stress fluid (Carbopol Ultrez 10) in a plane acrylic microchannel are used to establish rigorous scaling laws for the wall velocity gradient and the slip velocity. By means of epifluorescent microscopy combined with a custom-developed digital particle image velocimetry technique, time series of velocity fields were measured within a wide range of flow rates, and three distinct flow regimes were identified: full plug, partial plug, and fully yielded. Corresponding to each flow regime, wall velocity gradients and slip velocities were obtained by extrapolating the velocity profiles using a smoothing spline function. By combining the flow-field measurements with the macro-rheological measurements, scaling laws for the wall velocity gradient and the slip velocity with the wall shear stress were identified and compared with results from the literature. Detailed microscopic measurements of the velocity field enabled an assessment of the effectiveness of a chemical treatment of the channel walls meant to suppress wall slip proposed by Metivier and co-workers [Soft Matter 8, 7365 (2012)].