Despite important progresses in recent continuum modeling, most nonlocal rheologies remain exclusive to dry granular flows. Indeed, popular theories such as nonlocal granular fluidity (NGF) are only valid for dry materials and extensions for wetted particles have yet to be proposed. To address such shortcomings, a detailed analysis of the split-bottom geometry subject to capillary forces is presented. The principal features of such flow are explained and highlighted using a coarse-graining procedure. In particular, the granular fluidity field from the NGF theory is examined and its relationship with the cohesiveness of the material is explored through the dimensionless Bond number. By limiting the scope to critical-state areas and using normalizations based on the granular temperature, exponential-type cohesive constitutive laws have been obtained. This work deepens the current understanding of cohesive granular flows, brings the construction of a cohesive nonlocal rheology one step closer, and leads the way toward a unification of both NGF and kinetic theory frameworks.

The motion of small spherical particles in unsteady fluid flow can be predicted using the Boussinesq-Basset-Oseen equation, which is an integrodifferential equation balancing the particle inertia with the unsteady hydrodynamic force on a particle. For rigid spherical particles on whose surface the no-slip condition is obeyed, the Basset history force has been shown to significantly alter the statistical behavior of ensembles of particles in unsteady flows [Daitche and Tél, Phys. Rev. Lett. 107, 244501 (2011)]. Here, we determine the effect of hydrodynamic slip at the surface of the particle on the statistical behavior of an ensemble of spherical particles in a two-dimensional von Kármán flow in the wake of a cylinder. We compute the dynamics of a large quantity of spherical particles (on the order of a million) in this flow, and therefrom calculate escape rates, invariant manifold locations, and the uncertainty dimension of scattering trajectories for two cases: no-slip spheres and perfectly slipping spheres. We compare individual particle trajectories, locations of invariant manifolds, and residence time distributions for the two cases. We find that the presence of slip on a particle can lead to significant differences in escape rates, more initial positions that lead to vortex trapping at long times, and a greater uncertainty in scattering predictions. Thus, our paper shows that hydrodynamic slip significantly affects particle trajectories in unsteady flows.

The bubble size distribution below a breaking wave is of paramount interest when quantifying mass exchanges between the atmosphere and oceans. Mass fluxes at the interface are driven by bubbles that are small compared with the Hinze scale $d_h$, the critical size below which bubbles are stable, even though individually these are negligible in volume. Combining experimental and numerical approaches, we report a power-law scaling $d^{-3/2}$ for the small bubble size distribution, for sufficiently large separation of scales between the injection size and the Hinze scale. From an analysis of individual bubble breakups, we show that small bubbles are generated by capillary effects, and that their breakup time scales as $d^{3/2}$, which physically explains the sub-Hinze scaling observed.

Unsteady shock wave propagation and generation mechanisms in aviation fuel cavitation are experimentally characterized in a planar converging-diverging nozzle geometry via high-speed digital imaging and a signal processing technique that we denote as enhanced gradient shadowgraphy. Two fuels, JP-5, and JP-8, in two different flow cavitation regimes were studied: (1) aerated cavitating flow, where air microbubbles are injected into the flow at the nozzle inlet, and (2) nonaerated cavitating flow, where the flow evolved into the two-phase cavitating flow without bubble injection. For a sufficiently low range of imposed nozzle pressure ratios, gaseous cavitation led to choked flow for each working fluid. Two independent sustained mechanisms responsible for shock wave generation in the diverging section of the nozzle have been observed and characterized in the choked flow regime. The first mechanism exists only in the aerated case due to the injected bubbles. The second mechanism exists in both aerated and nonaerated cases and resulted in weaker shock waves than in the first case. This is related to the shed cavity clouds from a sheet cavity attached to nozzle sidewalls. More violent collapse events and stronger shock wave emissions were observed for aerated JP-5 than JP-8 due to the first mechanism. Detailed quantitative data are obtained to characterize shock wave intensity and velocity in aerated flow regimes under different bubble injection rates, nozzle back pressures, and void fractions. A strong similarity is obtained between shock speeds from our experimental data and the nonlinear solutions of the governing equations for nonbarotropic homogeneous flow. Results from the study shed some light on the complex physics of unsteady fuel cavitation phenomena and may lead to improved design of fuel system components, which suffer from system performance degradation due to the damaging impact of these shock waves.

A fluid-structure interaction study on free-stream flow across a NACA0012 hydrofoil, with a traveling wave-based surface undulation, is numerically studied at a constant wave number $K=10$ of the traveling wave and phase difference of ${180}^{\text{o}}$ between the top and bottom surface undulations. Effect of phase speed $c^{*}$ (1–10) of the wave, local amplitude-thickness ratio $A_L$ (0.05–0.25), and Reynolds number Re on the near-wake flow characteristics and propulsive performance are investigated. For the various values of the nondimensional governing parameters, the present results revealed two types of vortex patterns: an almost steady vortex sheet and periodic vortex street. Further, forward and reverse types of both vortex sheets and vortex streets are found behind the hydrofoil. A novel two-pair of reverse vortex streets and reverse vortex sheets are found at larger values of $c^{*}$, $A_L$, and Re. Surface undulations cause a high-pressure and high-velocity zone near the troughs of the wave. Consequently, a pressure-suction mechanism in the leeward and forward side of each wavy section produces a spatially varying thrust. The spatial variation of the thrust is attributed to the variation of wave amplitude along the foil. A threshold value of $c^{*}$, Re, and $A_L$ exists to produce thrust. A scaling analysis is presented with a power-law scaling for the mean thrust coefficient $\langle C_T\rangle$ as a function of $K$, $c^{*}$, $A_L$, with 3, 2, and 3 as the respective exponents. The proposed scaling is found to be consistent with the computations. The present biomimetic fish-inspired study can lead to design and development of a need-based autonomous underwater vehicle or energy harvesting device.

Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the elastic and viscous stresses. Perhaps more surprisingly, the instabilities produce flows with many of the hallmarks of turbulence—even though the effective Reynolds numbers may be $O\left(1\right)$ or smaller. We provide perspectives on viscoelastic flow instabilities by integrating the input from speakers at a recent international workshop: historical remarks, characterization of fluids and flows, discussion of experimental and simulation tools, and modern questions and puzzles that motivate further studies of this fascinating subject. The materials here will be useful for researchers and educators alike, especially as the subject continues to evolve in both fundamental understanding and applications in engineering and the sciences.

We experimentally investigate the speed of fragments produced by ligament breakup in the laser-induced deformation of tin microdroplets into axisymmetric sheets. The experiments were carried out covering a wide range of droplet diameters and laser-pulse energies. In addition to fragments produced by end-pinching, we also observe fragments shed via Rayleigh-Plateau breakup of long ligaments at late times. A double-frame backlit camera was used to obtain the speeds of the fragments $u_f$ and the time of their detachment $t_d$. We show that by normalizing $u_f$ to the initial expansion speed of the sheet ${\dot{R}}_0$, all data collapse onto a single, universal curve that is a function of the dimensionless time $t_d/{\tau }_c$ only, where ${\tau }_c$ is the capillary time. This universal curve is explicitly independent of the droplet's Weber number. The collapse of $u_f$ is supported by energy conservation arguments. Our findings enable the prediction of the instantaneous speed and position of the fragments shed from liquid tin targets used in state-of-the-art extreme ultraviolet nanolithography, facilitating the design of effective mitigation strategies against microparticulate debris.

Liquid-infused solids (LISs) are textured materials infused by oil, which makes them highly slippery for drops of another nonmiscible liquid. In this article, we discuss what happens when a water drop contacts and spreads on such LISs. Focusing on the influence of the oil layer trapped in the texture, we report that, despite lubrication, spreading on a LIS is slower than on a bare solid, even at short times. Yet the dynamics unexpectedly preserves its scaling, which we explain by considering the friction in the film, showing that the slippery nature of LISs can be accompanied by a significant dissipation.

Dynamic organization of the cytoskeletal filaments and rodlike proteins in the cell membrane and other biological interfaces occurs in many cellular processes, including cell division, membrane transport, and morphogenesis. The filament dynamics are determined, in part, by their membrane-mediated hydrodynamic interactions. Previous modeling studies have considered the dynamics of a single rod on fluid planar membranes. We extend these studies to the more physiologically relevant case of a single filament moving in a spherical membrane. Specifically, we use a slender-body formulation to compute the translational and rotational resistance of a single filament of length $L$ moving in a membrane of radius $R$ and 2D viscosity ${\eta }_m$, and surrounded on its interior and exterior with Newtonian fluids of viscosities ${\eta }^{-}$ and ${\eta }^{+}$. We first discuss the case where the filament's curvature is at its minimum $\kappa =1/R$. We show that the boundedness of spherical geometry gives rise to flow confinement effects that increase in strength with increasing the ratio of filament's length to membrane radius $L/R$. These confinement flows result only in a mild increase in filament's resistance along its axis, ${\xi }_{\parallel }$, and its rotational resistance, ${\xi }_{\mathrm{\Omega }}$. As a result, our predictions of ${\xi }_{\parallel }$ and ${\xi }_{\mathrm{\Omega }}$ can be quantitatively mapped to the results on a planar membrane, when the momentum transfer length scale is modified from ${\ell }_0=({\eta }^{+}+{\eta }^{-})/{\eta }_m$ in planar membranes to ${\ell }^{★}={({\ell }_0^{-1}+R^{-1})}^{-1}$. In contrast, we find that the drag in the perpendicular direction, ${\xi }_{\perp }$, increases superlinearly with the filament's length when $L/R>1$ and ultimately ${\xi }_{\perp }\to \infty$ as $L/R\to \pi$. Next, we consider the effect of the filament's curvature, $\kappa$, on its parallel motion, while fixing the membrane's radius. We show that the flow around the filament becomes increasingly more asymmetric with increasing its curvature. These flow asymmetries induce a net torque on the filament, coupling its parallel and rotational dynamics. This coupling becomes stronger with increasing $L/R$ and $\kappa$.

A comparative experimental study is conducted on the effect of the incoming boundary layer state on the near-wake of a surface-mounted square cylinder with a height-to-width aspect ratio ($h/d$) of 4. Two cases are considered: (i) an incoming laminar boundary layer (LBL) with relative thickness $\delta /h=0.053$ at a nominal Reynolds number (Re) of 10 500, and (ii) an incoming turbulent boundary layer (TBL) with $\delta /h=0.18$ at $\text{Re}=12000$. Planar particle image velocimetry synchronized with surface pressure measurements enable a phase-averaged characterization of the wake dynamics. The mean field description is complemented using oil-film visualizations of the surface flow patterns. For the TBL case, the obstacle-wall-junction region is characterized by the interaction of the von Kármán vortices with a junction vortex, which results in distinctive mean surface flow patterns not observed for the LBL case. The mean wake structure for both cases shows a dipole consisting of a counter-rotating pair of streamwise vortices extending from the recirculation region. However, the LBL wake contains an additional vortex pair descending from the dipole. The descending vortices coincide with the locus of points along which successive von Kármán vortices of opposite sign connect via vortical strands. These connection sites are associated with regions of high Reynolds stresses and turbulence production. The higher fluctuation levels and reconnection process observed in the LBL wake can be related to the strength of the connector strands enhancing the energy transfer between coherent and incoherent fluctuating fields.

Finite-size effects can lead neutrally buoyant particles to exhibit different dynamics than tracer particles, and can alter their transport properties in fluid flows. Here we investigate the effect of the particle's shape on their dispersion in two-dimensional complex flows. Combining numerical simulations with laboratory experiments, we show that particles with isotropic and anisotropic shapes exhibit different Lagrangian coherent structures, resulting in distinct dispersion phenomena within a given flow field. Experiments with rod-shaped particles show a focusing effect in the vicinity of vortex cores. We present a simple model that describes the dynamics of neutrally buoyant ellipsoidal particles in two-dimensional flow and show that particle aspect ratio and orientation-dependent forces can generate clustering phenomena in vortices.

Conventional empirical turbulence modeling is progressive: one begins by modeling simple flows and progressively works towards more complex ones. The outcome is a series of nested models, with the next, more complex model accounting for some additional physics relative to the previous, less complex model. The above, however, is not the philosophy of data-enabled turbulence modeling. Data-enabled modeling is one stop: one trains against a group of data, which contains simple and complex flows. The resulting model is the best fit of the training data but does not closely reproduce any particular flow. The differences between the two modeling approaches have left data-enabled models open to criticism: machine learned models do not fully preserve, e.g., the law of the wall (among other empirical facts), and they do not generalize to, e.g., high Reynolds numbers (among other conditions). The purpose of this paper is to respond to and resolve some of these criticisms: we intend to show that the conventional progressive modeling is compatible with data-enabled modeling. The paper hinges on the extrapolation theorem and the neutral neural network theorem. The extrapolation theorem allows us to control a network's behavior when extrapolating and the neutral neural network theorem allows us to augment a network without “catastrophic forgetting.” For demonstration purposes, we successively model the flow in the constant stress layer, which is simple; the flow in a channel and a boundary layer, which is more complex; and wall-bounded flow with system rotation, which is even more complex. We show that the more complex models respect the less complex models, and that the models preserve the known empiricism.

Flow oscillations in the near-wake region of a two-dimensional circular cylinder are experimentally investigated at Mach 6 over the Reynolds number range $2.3\times {10}^5$ to $5\times {10}^5$. The oscillation frequency is obtained by spectral proper orthogonal decomposition of high-speed schlieren data. The Strouhal number based on the length of the near-wake shear layers is found to exhibit universal behavior. This corroborates experimental findings at Mach 4 from recent literature, and furthermore, the universal behavior is also seen to hold with respect to Mach number. Time-resolved pressure measurements at the flow separation points on the cylinder aft surface show that coherent oscillatory activity occurs with a phase difference of $\pi$ radians between the two statistically symmetric halves of the flow. This aspect of the flow dynamics at high speeds is in common with its low-speed counterpart, i.e., the canonical problem of the cylinder wake in an incompressible flow.

We derive low-dimensional, data-driven models for transitions among exact coherent states in one of the most studied canonical shear flows, the plane Couette flow. These one- or two-dimensional nonlinear models represent the leading-order reduced dynamics on attracting spectral submanifolds (SSMs), which we construct using the recently developed SSMLearn algorithm from a small number of simulated transitions. We find that the energy input and dissipation rates provide efficient parametrizations for the most important SSMs. By restricting the dynamics to these SSMs, we obtain reduced-order models that also reliably predict nearby, off-SSM transitions that were not used in their training.

Droplet microfluidics, in which microdroplets serve as individual reactors, has enabled a wide range of high-throughput biochemical processes. Unlike solid wells typically used in current biochemical assays, droplets are subject to instability and can undergo breakup, especially under fast flow conditions. Although the physics of single drops has been studied extensively, the flow of crowded drops or concentrated emulsions—where droplet volume fraction exceeds $\sim 80\%$—is relatively unexplored in microfluidics. In this paper and the related invited lecture from the 74th Annual Meeting of the American Physical Society's Division of Fluid Dynamics, we describe the collective behavior of drops in a concentrated emulsion by tracking the dynamics and the fate of individual drops within the emulsion. At the slow flow limit of the concentrated emulsion, we observe an unexpected order, where the velocity of individual drops in the emulsion exhibits spatiotemporal periodicity. This periodicity is surprising from both fluid and solid mechanics points of view. We show the phenomenon can be explained by treating the emulsion as a soft crystal undergoing plasticity, in a nanoscale system comprising thousands of atoms as modeled by droplets. Our results represent a type of collective order which can have practical use in on-chip droplet manipulation. As the flow rate increases, the emulsion transitions from a solidlike to a liquidlike material, and the spatiotemporal order in the flow is lost. At the fast flow limit, droplet breakup starts to occur. We show that droplet breakup within the emulsion follows a probability distribution, in stark contrast to the deterministic behavior in classical single-drop studies. In addition to capillary number and viscosity ratio, breakup probability is governed by a confinement factor that measures drop size relative to a characteristic channel length. The breakup probability arises from the time-varying packing configuration of the drops. Replacing surfactant with nanoparticles as droplet stabilizers suppresses breakup and increases the throughput of droplet processing by $>300\%$. Strategic placement of an obstacle suppresses breakup by $>{10}^3$-fold. Finally, we discuss recent progress in computation methods for recapitulating the flow of concentrated emulsions.

It is well known that the fluid-particle acceleration is intimately related to the dissipation rate of turbulence, in line with the Kolmogorov assumptions. However, various experimental and numerical works have reported as well its dependence on the kinetic energy, which is generally attributed to intermittency and nonindependence of the small-scale dynamics from large-scale ones. The analyses given in this paper focus on statistics of the fluid-particle acceleration conditioned on both the local dissipation rate and the kinetic energy. It is shown that this quantity presents an exponential dependence on the kinetic energy with a growth rate independent of the Reynolds number, in addition to the expected power-law behavior with the dissipation rate. The exponential growth, which clearly departs from the previous propositions, reflects additional kinematic effects of the flow structures on the acceleration. Regarding intermittency, to account for the persistence of the effect of the large scales on the dissipation rate, it is further proposed scaling laws for the Reynolds number dependence of the conditional and unconditional acceleration variance using Barenblatt's incomplete similarity framework. It is then shown that both these intermittency and kinematic effects can be combined in a multiplicative cascade process for the acceleration depending on the kinetic energy and the dissipation rate. On the basis of these observations, we introduce a vectorial stochastic model for the dynamics of a tracer in turbulent flows. This model incorporates a fractional log-normal process for the dissipation rate recently proposed, as well as an additional hypothesis regarding nondiagonal terms in the diffusion tensor which naturally leads to the decomposition between tangential and centripetal acceleration. This model is shown to be in good agreement with direct numerical simulations and presents the essential characteristics of the Lagrangian turbulence highlighted in recent years, namely (i) non-Gaussian acceleration, (ii) scale separation between the norm of the acceleration and its components, (iii) anomalous scaling law for the Lagrangian velocity spectra, and (iv) negative skewness of the increments of the mechanical power, reflecting the temporal irreversibility of the dynamics.

In the logarithmic layer of boundary-layer turbulence, velocity structure functions scale as power and logarithmic functions of displacement at small and large scales, respectively. The small-scale scaling can be explained as a near-isotropy behavior, while the mechanism behind the logarithmic behavior is debatable. By rescaling the horizontal displacement by the distance to the wall, using the attached eddy hypothesis to the Kármán-Howarth-Monin (KHM) equation results in the logarithmic behavior. Also, from the picture of energy cascade, i.e., introducing a characteristic scale $u_{\tau }^3/\epsilon$ with $u_{\tau }$ and $\epsilon$ the friction velocity and energy dissipation rate, respectively, the logarithmic profile of the third-order structure function can also be obtained. These two explanations suggest a dependence of the third-order structure function on the difference between local production and dissipation. By analyzing data measured from the Qingtu Lake Observation Array built on a dry flatbed of Qingtu Lake in Minqin (China) with ${\mathrm{Re}}_{\tau }=O\left({10}^6\right)$, we provide evidence for the scaling behaviors and justify the underlying balances in the range with large displacements. And we study the robustness of the structure function theory using clear-air and sand-containing data: sands modify key statistical quantities of the boundary-layer turbulence, such as the height dependence of the Reynolds stress, but the behavior of the third-order structure function remains unchanged. Considering that the shear production captures the strength of anisotropic perturbation-mean interaction in the KHM equation, the ratio of production and dissipation controls the relative extensions of the power and logarithmic ranges, and a stronger production leads to a relatively wider logarithmic range, which is justified by measured data.

When the interface between a dielectric and a conducting liquid is excited by an oscillatory electric field, electrostatic Faraday waves can be induced. Here, we study the response of the interface to an ac electric field, which is superposed by either a second ac field of different frequency, or by a dc field. An algorithm based on light refraction at the fluidic interface is used to obtain the spatiotemporal response of the Faraday waves, and the critical voltage corresponding to onset of instability, the interfacial oscillation frequency, and the dominant wavelengths are determined. The influence of the mixing ratio, which denotes the relative amplitudes of the different components of the driving signal, is analyzed, and the experimental results are compared with theoretical predictions. For ac/ac driving, gradual variations of the mixing ratio can induce a jump of the pattern wavelength, which is a result of the transition from harmonic to a subharmonic oscillation. For ac/dc driving, the interface oscillates either harmonically or subharmonically, and the response wavelength can be tuned continuously by adjusting the admixture of the dc component. For both driving modes, the experiments show good agreement with theory.

We present predictions of the energy spectrum of forced two-dimensional turbulence obtained by employing a structure-preserving integrator. In particular, we construct a finite-mode approximation of the Navier-Stokes equations on the unit sphere, which, in the limit of vanishing viscosity, preserves the Lie-Poisson structure. As a result, integrated powers of vorticity are conserved in the inviscid limit. We obtain robust evidence for the existence of the double energy cascade, including the formation of the $-3$ scaling of the inertial range of the direct cascade. We show that this can be achieved at modest resolutions compared to those required by traditional numerical methods.