This work deals with the fluidization and sedimentation of fine solid particles, of random shape and size, similar to those commonly involved in geophysical mass flows, such as pyroclastic flows. While heated to avoid the effect of moisture and the formation of clusters, particles were first uniformly fluidized by a hot gas flow, up to a high expansion rate, and then sedimented after stopping the gas supply. Three different materials are explored, involving contrasted geometries, each characterized by a specific particle volume fraction at packing ${\mathrm{\Phi }}_{\mathrm{pack}}$. Within the range of values of the solid volume fraction ${\mathrm{\Phi }}_s/{\mathrm{\Phi }}_{\mathrm{pack}}$ studied here, the dense suspension forms a fully fluidized homogeneous mixture, with no segregation, for which the fluidization and sedimentation velocities are equal. Despite a significant discrepancy between the intrinsic properties of the different materials used, all measured velocities are observed to collapse into a single master curve $f({\mathrm{\Phi }}_s/{\mathrm{\Phi }}_{\mathrm{pack}})$ provided that they are normalized by the relevant scaling. Regarding the sedimentation velocity, ${\mathrm{\Phi }}_{\mathrm{pack}}$ turns out to be sufficient to characterize the material made with a random distribution in particle shape and size.

In this work we present experimental results of the gravity-driven discharge of poppy seeds from three-dimensionally (3D) printed silos. The velocity fields of the flowing poppy seeds are measured using magnetic resonance imaging (MRI) velocimetry techniques. Crucially, this approach allows the velocity field to be determined throughout the flow domain, unlike visual techniques such as particle image velocimetry and related methods where only the flow at or near the wall is accessible. We perform the experiment three times; with 3D-printed silos of cone half angles ${30}^{\circ }$ and ${50}^{\circ }$, respectively, and then repeat the ${30}^{\circ }$ silo experiment but with a layer of poppy seeds glued to the silo wall to create a “rough wall” condition. In our experiments, we observe and quantify velocity fields for three well-known granular flow regimes; mass flow, funnel flow, and rat-holing. The results of the experiments are compared to equivalent output of numerical simulations. In this mathematical model, the well-known $\mu \left(I\right)$ friction law is used to define an effective granular viscosity, and the flow is solved using a standard Navier-Stokes type solver. While the results are generally encouraging, it is noted that some aspects of the model are lacking and should be improved; in particular, the rat-holing effect observed in one of the MRI experiments was not predicted by the model, nor was the exact volumetric flow rate from any of the silos. Suggestions for model improvement are discussed.

In Rayleigh–Bénard convection (RBC) for fluids with Prandtl number $\text{Pr}\gtrsim 1$, rotation beyond a critical (small) rotation rate is known to cause a sudden enhancement of heat transfer, which can be explained by a change in the character of the boundary layer (BL) dynamics near the top and bottom plates of the convection cell. Namely, with increasing rotation rate, the BL signature suddenly changes from Prandtl–Blasius type to Ekman type. The transition from a constant heat transfer to an almost linearly increasing heat transfer with increasing rotation rate is known to be sharp and the critical Rossby number ${\text{Ro}}_c$ occurs typically in the range $2.3\lesssim {\text{Ro}}_c\lesssim 2.9$ (for Rayleigh number $\text{Ra}=1.3\times {10}^9$, $\text{Pr}=6.7$, and a convection cell with aspect ratio $\mathrm{\Gamma }=\frac{D}{H}=1$, with $D$ the diameter and $H$ the height of the cell). The explanation of the sharp transition in the heat transfer points to the change in the dominant flow structure. At $1/\text{Ro}\lesssim 1/{\text{Ro}}_c$ (slow rotation), the well-known large-scale circulation (LSC) is found: a single domain-filling convection roll made up of many individual thermal plumes. At $1/\text{Ro}\gtrsim 1/{\text{Ro}}_c$ (rapid rotation), the LSC vanishes and is replaced with a collection of swirling plumes that align with the rotation axis. In this paper, by numerically studying Lagrangian acceleration statistics, related to the small-scale properties of the flow structures, we reveal that this transition between these different dominant flow structures happens at a second critical Rossby number, ${\text{Ro}}_{c_2}\approx 2.25$ (different from ${\text{Ro}}_{c_1}\approx 2.7$ for the sharp transition in the Nusselt number Nu; both values for the parameter settings of our present numerical study). When statistical data of Lagrangian tracers near the top plate are collected, it is found that the root-mean-square values and the kurtosis of the horizontal acceleration of these tracers show a sudden increase at ${\text{Ro}}_{c_2}$. To better understand the nature of this transition we compute joint statistics of the Lagrangian velocity and acceleration of fluid particles and vertical vorticity near the top plate. It is found that for $\text{Ro}\gtrsim 2.25$ there is hardly any correlation between the vertical vorticity and extreme acceleration events of fluid particles. For $\text{Ro}\lesssim 2.25$, however, vortical regions are much more prominent and extreme horizontal acceleration events are now correlated to large values of positive (cyclonic) vorticity. This suggests that the observed sudden transition in the acceleration statistics is related to thermal plumes with cyclonic vorticity developing in the Ekman BL and subsequently becoming mature and entering the bulk of the flow for $\text{Ro}\lesssim 2.25$.

Under statically stable conditions in wall-bounded flows, turbulence is generated by shear and dissipated by buoyancy and viscosity. Most studies have focused on the steady-state balance of this budget, but the time evolution of the turbulence when the stabilizing buoyancy flux is first imposed is as important in many geophysical applications. In this paper, we utilize a new paradigm on the critical role of shear production damping by buoyancy to develop a quantitative model for the rate of decay of turbulent kinetic energy (TKE), at early and intermediate times, after buoyancy is abruptly imposed on a steady neutrally stratified Ekman boundary-layer flow. Scaling analyses and reduced models are developed to obtain an expression for this rate of decay, which is then validated using results from direct numerical simulation. We further show that the TKE production term persists as a parameter outside of the classic stability parameter term (the flux Richardson number) under unsteady conditions, and is therefore needed to describe the dynamics of evolving stable boundary layers. The long-time steady dissipation-production-buoyancy balance is also analyzed using the same modeling framework and confirms that the damping of shear TKE production by buoyancy is the main agent for the reduction in TKE, while the direct role of buoyancy destruction is secondary.

We consider axisymmetric rotating convection in a cylindrical domain, focusing on the eye that can form at the center of a cyclonic vortex. Upon increasing the thermal forcing we observe that the system undergoes a Hopf bifurcation from a state with a steady eye to one in which the eye oscillates. For an aspect ratio, Ekman number, and Prandtl number of 0.1 we find that the critical Reynolds number at which this transition occurs is 398.

We examine the nature of the oscillations and propose that the behavior results from an inertial wave trapped in the eye, with the frequencies falling within the expected range for inertial waves, and the oscillations displaying clear similarities to a standing inertial wave in a cylinder. We also examine the effect of Ekman number on the oscillation, finding that there is an upper limit beyond which oscillations do not occur.

The nonlinear dynamics of waves at the sea surface is believed to be ruled by the weak-turbulence framework. In order to investigate the nonlinear coupling among gravity surface waves, we developed an experiment in the Coriolis facility, which is a 13-m-diam circular tank. An isotropic and statistically stationary wave turbulence of average steepness of 10% is maintained by two wedge wave makers. The space- and time-resolved wave elevation is measured using a stereoscopic technique. Wave-wave interactions are analyzed through third- and fourth-order correlations. We investigate specifically the role of bound waves generated by nonresonant three-wave coupling. Specifically, we implement a space-time filter to separate the dynamics of free waves (i.e., following the dispersion relation) from the bound waves. We observe that the free-wave dynamics causes weakly resonant four-wave correlations. A weak level of correlation is actually the basis of the weak-turbulence theory. Thus our observations support the use of the weak turbulence to model gravity wave turbulence as is currently being done in the operational models of wave forecasting. Although in the theory bound waves are not supposed to contribute to the energy cascade, our observation raises the question of the impact of bound waves on dissipation and thus on energy transfers as well.

The study and control of flow instabilities is a key problem in aerodynamics. Aircrafts are designed not only to generate the lift force needed to balance their weight but, more importantly, to be stable and reasonably steady when in cruise conditions. Similar flow stability properties are naturally achieved by biological flying objects such as the dandelion seeds that are transported by the wind owing to a disklike structure called a pappus. The pappus creates a parachute flow configuration and is a remarkable prototype of how the wake, which would be unsteady if the pappus was completely impermeable, can be stabilized by changing the body structure so as to allow the flow to pass through. We approach the problem using the approximation of an anisotropic and nonhomogeneous rigid porous disk, combined with the linear stability analysis technique. The results show the presence of a mean porosity threshold beyond which the flow is always characterized by a separated, steady, and axisymmetric recirculating vortex ring. We compare our results with those of real dandelion pappi. The threshold is very close to the experimentally observed values of porosity, explaining why the morphology of the pappus promotes a steady wake regime.

Taking different diffusivities into account, the effect of irreversible A+B →C reaction on the growth of a buoyancy-driven instability in a Hele-Shaw cell is analyzed theoretically. For the limiting cases of infinitely fast reaction, an asymptotic stability analysis is conducted based on base density profile. To confirm the asymptotic stability analysis, under the linear stability theory, new linear stability equations are derived and solved numerically. In addition, fully nonlinear numerical simulations are conducted using the Fourier spectral method. The present asymptotic and linear stability analyses and nonlinear numerical simulations are in good agreement, and they modify the previous general classification of stability. For some cases where a stable barrier is sandwiched by two unstable regions, we also conducted linear and nonlinear analyses. It is interesting that for a certain case, instabilities with different wavelengths are possible below and above a central stable barrier.

We investigate the radial oscillations of small gas bubbles trapped in yield-stress fluids and driven by an acoustic pressure field. We model the rheological behavior of the yield-stress fluid using the recently developed elastoviscoplastic constitutive equation that takes into account the elastic and viscoplastic deformations of the material [Saramito, J. Non-Newton. Fluid Mech. 158, 154 (2009)]. Assuming that the bubble remains spherical during the pressure driving, we reduce the problem to a set of ordinary differential equations and an integrodifferential equation, which we solve numerically for the case of two yield-stress fluids, i.e., a soft Carbopol gel and a stiffer kaolin suspension. We find that depending on the amplitude and frequency of the pressure field, the radial oscillations of the bubble produce elastic stresses that may or may not suffice to yield the surrounding material. We evaluate the critical amplitude of the acoustic pressure required to achieve yielding and we find a good agreement between numerical simulations and an analytical formula derived under the assumption of linear deformations. Finally, we examine the bubble oscillation amplitude for a very wide range of applied pressures both below and above the critical value to assess the impact of yielding on the bubble dynamics. This analysis could be used to identify a signature of yielding in experiments where the radial dynamics of a bubble is measured. More generally, these results can be used to rationalize the optimal conditions for pressure-induced bubble release from yield-stress fluids, which is relevant to various biomedical and industrial applications, including the oil industry and food processing.

Dissolution-driven density instability (DI) occurs when a species $A$ dissolves into a host fluid and introduces a buoyantly unstable stratification. Such an instability has positive effects in related applications and may be affected if species $A$ reacts with solute $B$ in the host fluid. In this paper, the lattice Boltzmann (LB) method is employed to simulate the dynamics of such an instability coupled with reaction $A+B\to C$ in porous media at the pore scale. Numerical simulations in homogeneous media have demonstrated that six types of dissolution-driven DI can be classified based on the Rayleigh numbers of three chemical species ${\text{Ra}}_r$ (ratio of buoyancy to viscous forces), and reaction can accelerate, delay or even trigger the development of DI. Then, a parametric study has indicated that, increasing $\mathrm{\Delta }{\text{Ra}}_{CB}$ (${\text{Ra}}_C-{\text{Ra}}_B$) can intensify density instability and reaction, promote the diffusion of species $A$, and also introduce either stabilizing or destabilizing effects of reaction. Besides, the increase of initial reactant concentration or/and Damköhler number $\text{Da}$ (ratio of flow time to chemical time) can enhance the influence of chemistry. Finally, simulations are carried out in three types of heterogeneous media HE1–HE3, and six groups of fingering scenarios can also be observed in each medium. However, compared with the homogeneous case, heterogeneous media HE1 with randomly distributed solid grains can introduce deeper advancing position and rougher density fingering, and media HE2 and HE3 with vertical variations of pore spaces can affect the developing speed of fingering obviously. In terms of the storage of species $A$ in the host fluid, medium HE2 with large pore size in the top layer is favorable. The present study is of significant importance for applications such as carbon capture and storage.

The Richtmyer-Meshkov instability (RMI) occurs when a shock impulsively accelerates an interface between two different fluids, and it is important in many technological applications such as inertial confinement fusion (ICF) and astrophysical phenomena such as supernova. Here, we present incompressible models of an impulsively accelerated interface separating conducting fluids of different densities in cylindrical geometry. The present study complements earlier investigations on linear and nonlinear simulations of RMI. We investigate the influence of a normal or an azimuthal magnetic field on the growth rate of the interface. This is accomplished by solving the linearized initial value problem using numerical inverse Laplace transform. For a finite normal magnetic field, although the initial growth rate of the interface is unaffected by the presence of the magnetic field, at late-time the growth rate of the interface decays. This occurs by transporting the vorticity by two Alfvén fronts which propagate away from the interface. For the azimuthal magnetic field configuration, the suppression mechanism is associated with the interference of two waves propagating parallel and antiparallel to the interface that transport vorticity and cause the growth rate to oscillate in time with nearly a zero mean value. Comparing the results of the incompressible models with linear compressible MHD simulations show reasonable agreement at early time of simulations.

We investigate the impact of liquid drops on millimeter-scale hairy surfaces. By varying the speed of the drop, the spacing of the hairs, and the viscosity of the liquid, we observe a variety of behaviors. In some cases, the liquid drop can remain on top of the hair after impact, similar to a Cassie-Baxter superhydrophobic state. If the drop penetrates the hairy surface, the hairs can resist droplet spreading. Using this scenario as a reference case, we rationalize the role of the hairs in dissipating the kinetic energy of the impacting drop through a balance of inertia, viscosity, and surface tension. The various observed behaviors are classified according to scenarios in which kinetic energy is insufficient or in excess of this reference scenario, an argument that allows us to build and rationalize a phase diagram.

Using the observation that slip in simple fluids at low and moderate shear rates is a thermally activated process driven by the shear stress in the fluid close to the solid boundary, we develop a molecular-kinetic model for simple fluid slip at solid boundaries. The proposed model, which is in the form of a universal scaling relation that connects slip and shear rate, reduces to the well-known Navier slip condition under low shear conditions, providing a direct connection between molecular parameters and the slip length. Molecular-dynamics simulations are in very good agreement with the predicted dependence of slip on system parameters, including the temperature and fluid-solid interaction strength. Connections between our model and previous work, as well as simulation and experimental results, are explored and discussed.

Oscillations of flagella and cilia play an important role in biology, which motivates the idea of functional mimicry as part of bioinspired applications. Nevertheless, it still remains challenging to drive their artificial counterparts to oscillate via a steady, homogeneous stimulus. Combining theory and simulations, we demonstrate a strategy to achieve this goal by using an elastoelectrohydrodynamic instability (based on the Quincke rotation instability). In particular, we show that applying a uniform dc electric field can produce self-oscillatory motion of a microrobot composed of a dielectric particle and an elastic filament. Upon tuning the electric field and filament elasticity, the microrobot exhibits three distinct behaviors: a stationary state, undulatory swimming, and steady spinning, where the swimming behavior stems from an instability emerging through a Hopf bifurcation. Our results imply the feasibility of engineering self-oscillations by leveraging the elastoviscous response to control the type of bifurcation and the form of instability. We anticipate that our strategy will be useful in a broad range of applications imitating self-oscillatory natural phenomena and biological processes.

The linear stability and nonlinear dynamics of viscoelastic liquid films flowing down inclined surfaces with sinusoidal topography are investigated. The Oldroyd-B constitutive model is used and numerical solutions of a long-wave nonlinear evolution equation for the film thickness, introduced by Dávalos-Orozco [L. A. Dávalos-Orozco, Stability of thin viscoelastic films falling down wavy walls, Interfacial Phenom. Heat Transfer 1, 301 (2013)], provide insight into the influence of elasticity and wall topography on the nonlinear film dynamics, while Floquet analysis of the linearized evolution equation is used to study the onset of linear instability. Focusing initially on inertialess films (with zero Reynolds number), linear stability results are organized into three regimes based on the wall wavelength. For sufficiently short and sufficiently long wall wavelengths, the onset of instability is not tangibly affected by the topography. There is however an intermediate range of wavelengths where, as the wall wavelength is increased, the critical Deborah number for the onset of instability first decreases (topography is destabilizing) and then increases sufficiently for topography to be stabilizing (relative to the flat wall). Solutions to a perturbation amplitude equation indicate that the character of the instability changes substantially within this intermediate range; topography induces streamwise variations in the base-state velocity at the free surface which couple with perturbations and substantially influence the instability growth rate. Very similar trends are observed for Newtonian films and variations in the critical Reynolds number. Simulations of the full nonlinear evolution equation produce a broad range of nonlinear states including traveling waves, time-periodic waves, and chaos. Perturbations to the film generally saturate at higher amplitudes for cases with larger linear growth rates, e.g., with increasing Deborah number or for a destabilizing wall wavelength, and topography introduces finer temporal scales in the dynamics. The qualitative influences of inclination and inertia on the nonlinear dynamics are shown to be simply related to the influence of elasticity using analytical linear stability results for the flat-wall case.

This paper reports the results of a theoretical modeling of the fully developed electroosmotic flow in a rectangular microchannel with a high-density polyelectrolyte layer (PEL) attached to the walls. At these conditions, the ions are partitioned between the PEL and the fluid outside the PEL owing to the difference between the permittivities of the two media. It is taken into account that the dynamic viscosity is higher within the PEL because of hydration effects. Solutions are obtained for the electric potential and velocity distributions as well as the mean velocity by making use of a variational approach, applied to the linearized form of the governing equations, which treats the whole area under consideration as a single domain with variable physical properties. The resulting equations are solved using a spectral method. Closed-form analytical expressions are obtained for a slit geometry, representing the case of high aspect ratios. The solutions obtained are validated by comparing to finite-element simulations of the full nonlinear equations. It is shown that the electric potential drop inside the channel increases due to the depletion of the counterions within the PEL caused by the ion partitioning effect. This effect, surprisingly, magnifies the electroosmotic flow rate because of the increase of the space charge outside the PEL. As expected, the hydration effects reduce the flow rate, especially for thick PELs.

We study suspensions of rigid particles in a plane Couette flow with deformable elastic walls. We find that, in the limit of vanishing inertia, the elastic walls induce shear thinning of the suspension flow such that the effective viscosity decreases as the wall deformability increases. This shear-thinning behavior originates from the interactions between rigid particles, soft walls, and carrier fluids; an asymmetric wall deformation induces a net lift force acting on the particles which therefore migrate towards the bulk of the channel. Based on our observations, we provide a closure for the suspension viscosity which can be used to model the rheology of suspensions with arbitrary volume fraction in elastic channels.

Dense particulate suspensions can not only increase their viscosity and shear thicken under external forcing, but also jam into a solidlike state that is fully reversible when the force is removed. An impact on the surface of a dense suspension can trigger this jamming process by generating a shear front that propagates into the bulk of the system. Tracking and visualizing such a front are difficult because suspensions are optically opaque and the front can propagate as fast as several meters per second. Recently, high-speed ultrasound imaging has been used to overcome this problem and extract two-dimensional sections of the flow field associated with jamming front propagation. Here we extend this method to reconstruct the three-dimensional flow field. This enables us to investigate the evolution of jamming fronts for which axisymmetry cannot be assumed, such as impact at angles tilted away from the normal to the free surface of the suspension. We find that sufficiently far from solid boundaries, the resulting flow field is approximately identical to that generated by normal impact, but rotated and aligned with the angle of impact. However, once the front approaches the solid boundary at the bottom of the container, it generates a squeeze flow that deforms the front profile and causes jamming to proceed in a nonaxisymmetric manner.

We consider the long-standing problem of Rayleigh-Taylor instability with variable acceleration, and focus on the early-time scale-dependent dynamics of an interface separating incompressible ideal fluids of different densities subject to an acceleration being a power-law function of time for a spatially extended three-dimensional flow periodic in the plane normal to the acceleration with symmetry group p6mm. By employing group theory and scaling analysis, we discover two distinct subregimes of the early-time dynamics depending on the exponent of the acceleration power-law. The time scale and the early-time dynamics are set by the acceleration for exponents greater than (-2), and by the initial growth-rate (due to, e.g., initial conditions) for exponents smaller than (-2). At the exponent value (-2) a transition occurs from one subregime to the other with varying acceleration strength. For a broad range of the acceleration parameters, the instability growth rate is explicitly found, the dependence of the dynamics on the initial conditions is investigated, and theory benchmarks are elaborated.

The aeroelastic response and energy harvesting performance of an elastically mounted hydrofoil subject to a prescribed pitching motion are experimentally studied using a cyber-physical force-feedback control system in a uniform flow. By taking advantage of this cyber-physical system, we systematically sweep through the parameter space of the elastic support (stiffness, damping, and mass) for various frequencies of the prescribed pitching motion. It is found that the flow-induced heave amplitude and the energy harvesting performance are both strongly affected by the frequency ratio between the prescribed pitching frequency and the natural frequency of the system and the damping coefficient. In particular, for a fixed damping coefficient, the maximum flow-induced heave amplitude is achieved at the resonant condition (frequency ratio of 1), which also gives rise to the highest energy harvesting performance. At this resonance condition, though a smaller damping produces a larger heave amplitude, the optimal energy harvesting performance is obtained consistently at an intermediate damping coefficient of 1.5. In addition, at the resonance condition, the heave amplitude, or Strouhal number, and the hydrodynamic forces on the foil are both found to collapse well for different reduced frequencies, suggesting a similarity in the vortex dynamics generated by the elastically mounted system. A low-order model based on classical vibration theory is formulated to reproduce the power coefficient using the damping coefficient and Strouhal number, and we find that the power coefficient predicted by the model agrees well with that measured in the experiment over the range of reduced frequency explored.