The structure of the flow induced by the van der Waals destabilization of a nonwetting liquid film placed on a solid substrate is studied by means of theory and numerical simulations of the Stokes equations. Our analysis reveals that lubrication theory, which yields $h_{\text{min}}\propto {\tau }^{1/5}$, where $h_{\text{min}}$ is the minimum film thickness and $\tau$ is the time until breakup, cannot be used to describe the local flow close to rupture. Instead, the slender lubrication solution is shown to experience a crossover to a universal self-similar solution of the Stokes equations that yields $h_{\text{min}}\propto {\tau }^{1/3}$, with an opening angle of ${37}^{\circ }$ off the solid.

Small-scale turbulence is the most promising place to establish proper turbulence theory. An understanding of the relationships between the two descriptors of small-scale turbulence, namely, enstrophy and dissipation, is one of the longstanding research topics. Meanwhile, current knowledge on this point is controversial because past observations are inconsistent with the existing theoretical arguments. We present a different approach to investigate this problem by enhancing small-scale fluctuations with finite-size particles. In this particle-augmented turbulent flow, several common observations about small-scale turbulence are obtained with recent high-Reynolds-number studies, though the operating conditions are quite different. Specifically, it is found that the discrepancy between the intermittency of enstrophy and dissipation is reduced when small-scale motions become intense. In addition, the spatial distributions of intense enstrophy and dissipation are found to be correlated. Lastly, a quantitative relationship for enstrophy and dissipation is observed in these intense events. The similarity of enstrophy and dissipation in all of these aspects does not occur in low-Reynolds-number turbulence, and the current common findings could imply potential universality for intense small-scale turbulence. The conditional probability density functions of pressure Laplacian and velocity derivatives are also analyzed to further understand why dissipation and enstrophy become similar when small-scale motions become strong.

Wind-forced near-inertial waves form a high-energy wave component in the upper ocean. The weakly dispersive nature of these large horizontal and small vertical scale waves make them suitable candidates for energetic interactions with mesoscale balanced flows. We take advantage of an idealized two-vertical-mode system obtained by projecting the hydrostatic Boussinesq equations onto the barotropic and a single high baroclinic mode to examine wave-balanced flow interactions. Our detailed analysis using results of freely evolving numerical simulations demonstrate how the well established two-mode quasigeostrophic turbulence phenomenology changes in the presence of high-energy near-inertial waves. In the absence of waves, the barotropic flow, which contains most of the balanced energy, undergoes an inverse energy cascade resulting in the formation of large-scale coherent vortices. In contrast, high-energy near-inertial waves transfer energy to the barotropic flow, facilitating a forward energy cascade of the balanced flow. The balanced flow in turn assists in the forward energy cascade of the wave field, which transforms the wave field from low-frequency near-inertial waves to high-frequency inertia-gravity waves. Given that the idealized model we employ is two-dimensional, the forward energy cascade of wave and balanced flow is an unexpected and intriguing feature.

Flows induced by Quincke rotation in particle suspensions are considered. Nonlinear boundary problems for the suspension velocity and particle angular velocity fields in rectangular capillaries are formulated and solved for both no-slip and free boundary conditions. Linear stability analysis shows that the critical electric field strength necessary for the development of macroscopic flow is smaller than the field strength at which spontaneous Quincke rotation of a single particle occurs. This decrease is caused by hydrodynamic synchronization of the particle rotations. In the case of free boundaries interesting intermittent behavior is observed: as the parameters governing the problem pass degenerate eigenmodes revealed by the stability analysis, the nature of the induced flow changes qualitatively.

Settling inertial aerosols dispersed at high enough concentration modulate the structure of the suspending turbulent flow. The present study addresses this modulation in a canonical flow, which is homogeneously sheared turbulence (HST). Eulerian-Eulerian (EE) and Eulerian-Lagrangian (EL) simulations are conducted in the semidilute regime, i.e., such that the particulate phase is sufficiently dilute to neglect particle-particle interaction but sufficiently concentrated to be strongly coupled with the carrier flow. Four cases are considered for which the Stokes number based on the Kolmogorov timescale is ${\mathrm{St}}_{\eta }=0.06$ or 0.19 and mass loading is $M=0.125$ or 0.5. Turbulence is initialized with a Taylor microscale Reynolds number ${\mathrm{Re}}_{{\lambda }_{,}0}=29$ and is strongly sheared, resulting in a shear number $S_0^{*}=27$. Simulations of the suspension with ${\mathrm{St}}_{\eta }=0.06$ and $M=0.125$ show no turbulence modification compared with single-phase HST. However, when the mass loading is increased to $M=0.5$ the aerosols cluster, despite their small inertia, and measurably modify the carrier flow. These aerosols enhance turbulence in the carrier phase, causing an increase of the growth rates of the turbulent kinetic energy (TKE) and dissipation rate among other effects. The opposite behavior emerges when the Stokes number is ${\mathrm{St}}_{\eta }=0.19$. These aerosols cause the attenuation of turbulence by reducing the growth rates of the TKE and dissipation rate in HST. This attenuation is weaker for the larger mass loading case $M=0.5$ due to stronger forcing by the particles on the gas in the gravity direction. Turbulence modulation in the EE simulation is verified to hold excellent agreement with EL simulations. In the former approach, simulating a few integral lengths of turbulence leads to a large number of Lagrangian particles, up to $1.7\times {10}^9$ particles in the present work. Eulerian-Eulerian simulations are performed with a positivity-preserving kinetic-based formulation that assumes an anisotropic-Maxwellian distribution of the subgrid particle velocity probability distribution function. The excellent agreement with EL simulations shows that this EE simulation strategy is a robust and predictive method in the semidilute regime.

Numerical studies of passive scalars in three-dimensional (3D) periodic box turbulence have often used arbitrary scalar forcing schemes to sustain the variance. These existing methods represent certain flow configurations, but they have not been derived using specific velocity and scalar profiles. In this work, a forcing technique is devised to generate centerline scalar mixing of round jets in a triply periodic box. It is derived from the scalar transport equation using a Reynolds-like decomposition of the scalar field. The equation is closed by applying the known mean velocity and scalar profiles of axisymmetric jets. The result is a combination of a mean gradient term and a linear scalar term. Direct numerical simulations at different ${\text{Re}}_{\lambda }$ have been performed with these source terms for unity Schmidt numbers. Scalar flux values and scaling exponents of energy spectra from simulations are comparable to experimental values. In addition, a dimensional analysis shows that the normalized scalar statistics, such as variance, flux, and dissipation rate, should only be a function of Reynolds number; indeed, such quantities computed from our simulations approach constant values as the Reynolds number increases. The effects of velocity forcing on scalar fields are also investigated; changing velocity forcing terms may result in unstable scalar fields even under the same scalar forcing. It may indicate that an appropriate relation between the velocity and scalar forcing schemes can help producing a proper scalar mixing environment.

Real liquids exhibit a viscoelastic response when excited mechanically to deform at sufficiently high frequency. We use classical nonequilibrium molecular dynamics simulations to calculate the linear viscoelastic response of extended simple point charge (SPC/E) water under both shear and elongation, for frequencies between 50 GHz and 10 THz and temperatures spanning the liquid phase of water at atmospheric pressure. These simulations are validated using equilibrium simulations that make use of Green-Kubo relations. Data up to and including 2 THz is fit to a single relaxation time linear Maxwell model, to facilitate comparison with reported experiments. We find that the resulting elastic moduli agree well with measurement, but this is not the case for the viscous moduli. This data also obeys a generalized Cauchy relation, implying that the elastic response of SPC/E water is dominated by central forces. This opens a pathway toward development of a simplified, molecular elastic water model for viscoelastic flows at high frequency. Furthermore, both elastic and loss moduli obey the time temperature superposition principle for frequencies up to 2 THz; an anomaly is observed above 2 THz, pointing to different physics. This behavior remains to be observed experimentally.

The dynamics of vesicles in simple shear or extensional flows has been extensively studied, but the conditions where vesicles experience more complex flow types, such as those seen in microfluidic devices or industrial processing conditions, warrant greater investigation. In this study, we use the boundary element method to investigate the shape stability of deflated vesicles in a general linear flow, i.e., linear combinations of extensional and rotational flows. We model the vesicles as a droplet with an incompressible interface with a bending resistance. We simulate a range of flow types from purely shear to extensional at viscosity ratios ranging from 0.01 to 5.0 and reduced volumes from 0.60 to 0.70. The vesicle's viscosity ratio appears to play a minimal role in describing its shape and stability for many mixed flows, even in cases when significant flows are present in the vesicle interior. We find in these cases that the critical capillary number for shape instabilities collapses onto similar values if the capillary number is scaled by an effective extensional rate. These results contrast with droplet studies where both viscosity ratio and flow type have significant effects on breakup. Our simulations suggest that if the flow type is not close to pure shear flow, one can accurately quantify the shape and stability of vesicles using the results from an equiviscous vesicle in pure extension. When the flow type is nearly shear flow, we start to see deviations in the observations discussed above. In this situation, the vesicle's stationary shape develops asymmetric cusps, which introduces a stabilizing effect and makes the critical capillary number depend on the viscosity ratio.

The shape and the stability of a static liquid bridge under either pressure control or volume control can be derived by knowing only the shape of a master liquid bridge. No perturbation problems need be solved.

We investigate the stability of a one-parameter family of periodic solutions of the four-vortex problem known as “leapfrogging” orbits. These solutions, which consist of two pairs of identical yet oppositely signed vortices, were known to W. Gröbli [Ph.D. thesis, Georg-August-Universität Göttingen, 1877] and A. E. H. Love [Proc. London Math. Soc. 1, 185 (1883)] and can be parameterized by a dimensionless parameter $\alpha$ related to the geometry of the initial configuration. Simulations by Acheson [Eur. J. Phys. 21, 269 (2000)] and numerical Floquet analysis by Tophøj and Aref [Phys. Fluids 25, 014107 (2013)] both indicate, to many digits, that the bifurcation occurs when $1/\alpha ={\varphi }^2$, where $\varphi$ is the golden ratio. This study aims to explain the origin of this remarkable value. Using a trick from the gravitational two-body problem, we change variables to render the Floquet problem in an explicit form that is more amenable to analysis. We then implement G. W. Hill's [Acta Math. 8, 1 (1886)] method of harmonic balance to high order using computer algebra to construct a rapidly converging sequence of asymptotic approximations to the bifurcation value, confirming the value found earlier.

We investigate the coupling between a premixed flame freely propagating inside a Hele-Shaw burner and the mechanical vibrations of the burner structure. The combustion chamber deformations are not only able to damp the classical thermo-acoustic instabilities but they can also trigger a new oscillating combustion instability. We demonstrate that the flow oscillations induced by the burner vibrations can be used to control the shape of the flame surface, by damping the Darrieus-Landau dynamics, or by triggering Faraday-like waves.

The initiation of contact between liquid and a dry solid is of great fundamental and practical importance. We experimentally probe the dynamics of wetting that occur when an impacting drop first contacts a dry surface. We show that, initially, wetting is mediated by the formation and growth of nanoscale liquid bridges, binding the liquid to the solid across a thin film of air. As the liquid bridge expands, air accumulates and deforms the liquid-air interface, and a capillary wave forms ahead of the advancing wetting front. This capillary wave regularizes the pressure at the advancing wetting front and explains the anomalously low wetting velocities observed. As the liquid viscosity increases, the wetting front velocity decreases; we propose a phenomenological scaling for the observed decrease of the wetting velocity with liquid viscosity.

Phoretic particles exploit local self-generated physico-chemical gradients to achieve self-propulsion at the micron scale. The collective dynamics of a large number of such particles is currently the focus of intense research efforts, both from a physical perspective to understand the precise mechanisms of the interactions and their respective roles, as well as from an experimental point of view to explain the observations of complex dynamics as well as formation of coherent large-scale structures. However, an exact modeling of such multiparticle problems is difficult, and most efforts so far rely on the superposition of far-field approximations for each particle's signature, which are only valid asymptotically in the dilute suspension limit. A systematic and unified analytical framework based on the classical Method of Reflections (MoR) is developed here for both the Laplace and Stokes' problems to obtain the higher-order interactions and the resulting velocities of multiple phoretic particles, up to any order of accuracy in the radius-to-distance ratio $\varepsilon$ of the particles. Beyond simple pairwise chemical or hydrodynamic interactions, this model allows us to account for the generic chemo-hydrodynamic couplings as well as $N$-particle interactions ($N\ge 3$). The ${\varepsilon }^5$-accurate interaction velocities are then explicitly obtained, and the resulting implementation of this MoR model is discussed and validated quantitatively against exact solutions of a few canonical problems.

Direct numerical simulations of cross-flow over a circular cylinder are performed for $\text{Re}=100$, 220, 300, 800, and 1575, spanning laminar-to-turbulent transition and progressively capturing the initial two-dimensional global instability, three-dimensional mode $A^{*}$ and mode $B$ instabilities, a distinct $B+$ instability, and Kelvin-Helmholtz instability, respectively. For $\text{Re}\ge 800$, vortex topology and snapshot proper orthogonal decomposition (sPOD) analyses of the three-dimensional flow fields reveal significant alterations in the dynamics of secondary vortices preceding shear layer transition, denoted $B+$ instability. The defining instantaneous characteristic of $B+$ instability is hairpin vortex formations straddling mode $B$ structures. An iterative scheme for three-dimensional vortex tracking is employed and the probability density functions of secondary vortex statistics show a marked broadening for $\text{Re}\ge 800$, associated with the increased variability in the wake vortex dynamics. The significant broadening of the modal energy spectrum of the sPOD serves as a marker for the topological change to $B+$ instability, reflecting the increased complexity of the dynamics. Integral effects on the primary shedding instability due to the increase in secondary vortex formation are deduced through a decomposition of the vorticity transport in the wake. An increase in streamwise and transverse reorientation of spanwise vorticity is identified for increasing Re, leading to a decrease of up to $20\%$ in the advected spanwise vorticity of the primary vortices. Therefore, the reorientation of spanwise vorticity may be identified as a subsidiary mechanism for the attenuation of fluctuating structural loads in the basic cylinder wake.

Laboratory experiments on the collapse of a liquid-saturated granular column on a horizontal plane are reported. The trigger and the resulting dynamics of the collapse when occurring, as well as the shape of the final deposit, are characterized and analyzed in light of some dimensionless parameters, namely, the “column” Bond number Bo, the grain diameter to capillary length ratio $d/l_c$, the initial aspect ratio $a$, the Stokes number St, and the initial volume fraction $\varphi$, by varying the properties of the interstitial fluid and of the grains, the geometry, and the compaction of the initial granular column. The main contribution of this study is to: (i) provide a diagram of the different regimes of collapse shown to be mostly controlled by capillary effect, (ii) develop simple criteria that capture the transitions between each regime in terms of critical values of the Bond number and the ratio of the grain diameter to the capillary length, (iii) extend a predictive model of the runout for dry collapses to the more general case of liquid-saturated granular collapses, and (iv) quantify the influence of $a$, St, and $\varphi$ on the collapse dynamics and the shape of the final deposit in the capillary-free regime. A perspective description of the role of the interstitial fluid on the spreading of the granular medium, and more particularly of the driving role of the fluid, is discussed and argued on the basis of the present set of experiments.

Spherical particles in dilute suspension flows through a square duct are known to focus at certain points in the downstream cross-section. When the blockage ratio of a particle diameter to the duct width equals approximately 0.1, previous experimental and numerical studies showed three types of particle equilibrium points: channel-face equilibrium positions located at the center of the duct faces, channel-corner equilibrium positions near the corners on diagonals, and intermediate equilibrium positions located at intermediate positions symmetric with respect to the diagonals. Several patterns of the particle focusing over the duct cross-section were observed according to the appearance or disappearance of these equilibrium points depending on the Reynolds number. In the present study, we numerically investigate the inertial focusing patterns of a neutrally buoyant spherical particle suspended in square duct flows. We describe the transitions between the particle focusing patterns in terms of bifurcation of the particle equilibrium positions. Saddle-node bifurcations occur at two different critical Reynolds numbers corresponding to the appearance and disappearance of the intermediate equilibrium positions, respectively. Pitchfork bifurcation occurs at another Reynolds number where stability of the channel-corner equilibrium positions changes from saddle to stable. Channel-face equilibrium positions are always stable for all the investigated Reynolds numbers at this blockage ratio.

We derive a system of equations for the statistical moments of a passive scalar dispersed in a turbulent flow from the transport equation of the probability density function. We solve the system through a Green's function and we obtain a formally exact solution for the statistical moments of the passive scalar concentration. We use this solution to achieve an analytical relationship for the second moment of a passive scalar released from a point source. Comparison with wind-tunnel experiments shows that the relationship is valid also in a neutral turbulent boundary layer if the reflection onto the ground and an appropriate model for the mixing timescale are considered. This approach, combined with a suitable model for the distribution of the concentration, allows the statistics of the passive scalar to be obtained in the whole domain in a closed and ready-to-use form.

Thermal convection driven by internal heat sources and sinks was recently shown experimentally to exhibit the mixing-length or “ultimate” scaling-regime: The Nusselt number $\mathrm{Nu}$ (dimensionless heat flux) increases as the square-root of the Rayleigh-number $\mathrm{Ra}$ (dimensionless internal temperature difference). While for standard Rayleigh-Bénard convection this scaling regime was proven to be a rigorous upper bound on the Nusselt number, we show that this is not so for convection driven by internal sources and sinks. To wit, we introduce an asymptotic expansion to derive steady nonlinear solutions in the limit of large ${\mathrm{Ra}}_{\mathrm{Q}}$, the Rayleigh-number based on the strength of the heat source. We illustrate this procedure for a simple sinusoidal heat source and show that it achieves heat transport enhancement beyond the mixing-length scaling regime: $\mathrm{Nu}$ increases linearly with $\mathrm{Ra}$ over this branch of solutions. Using rigorous upper bound theory, we prove that the scaling regime $\mathrm{Nu}\sim \mathrm{Ra}$ of the asymptotic solution corresponds to a maximization of the heat flux subject to simple dynamical constraints, up to a dimensionless prefactor. Not only do two-dimensional numerical simulations confirm the analytical solution for the sinusoidal source, but, more surprisingly, they indicate that it is stable and indeed achieved by the system up to the highest ${\mathrm{Ra}}_{\mathrm{Q}}$ investigated numerically, with a heat transport efficiency orders of magnitude higher than the standard mixing-length estimate.

An elastic sheet that deforms near a solid substrate in a viscous fluid is a situation relevant to various dynamical processes in biology, geophysics, and engineering. Here, we study the relaxation dynamics of an elastic plate resting on a thin viscous film that is supported by a solid substrate. By combining scaling analysis, numerical simulations, and experiments, we identify asymptotic regimes for the elastohydrodynamic leveling of a surface perturbation of the form of a bump, when the flow is driven by either the elastic bending of the plate or thermal fluctuations. In both cases, two distinct regimes are identified when the bump height is either much larger or much smaller than the thickness of the prewetted viscous film. Our analysis reveals a distinct crossover between the similarity exponents with the ratio of the perturbation height to the film height.

The evolution of a finite liquid ligament into either a single drop or several droplets is driven by the competition of two simultaneous processes: the recoil and the pinch-off. Scalings providing the kinetics of each process can be compared to predict the breakup of cylindrical symmetric ligaments. Here, asymmetric ligaments formed by a main drop connected to a cylindrical tail and commonly produced by inkjet printing are considered. Using two print heads, 16 inks, and various printing parameters, we show the limits of commonly admitted scalings for asymmetric ligaments. The recoil is governed by a modified Taylor-Culick velocity and a complex drainage, possibly leading to pinch-off, develops at the junction of the ligament with the main drop. The ligament aspect ratio affects this process for which two regimes must be accounted for. Finally, the ratio between the recoil and pinch-off timescales successfully predicts asymmetric ligament breakup.