The surface shear rheology of many insoluble surfactants depends strongly on the surface pressure (or concentration) of that surfactant. Here we highlight the dramatic consequences that surface-pressure-dependent surface viscosities have on interfacially dominant flows, by considering lubrication-style geometries within high Boussinesq (Bo) number flows. As with three-dimensional lubrication, high-Bo surfactant flows through thin gaps give high surface pressures, which in turn increase the local surface viscosity, further amplifying lubrication stresses and surface pressures. Despite their strong nonlinearity, the governing equations are separable, so that results from two-dimensional Newtonian lubrication analyses may be immediately adapted to treat surfactant monolayers with a general functional form of ${\eta }_s\left(\mathrm{\Pi }\right)$. Three paradigmatic systems are analyzed to reveal qualitatively new features: a maximum, self-limiting value for surfactant fluxes and particle migration velocities appears for $\mathrm{\Pi }$-thickening surfactants, and kinematic reversibility is broken for the journal bearing and for suspensions more generally.

We investigate the incompressible turbulent jet formed when buoyant fluid is steadily ejected horizontally from a circular source into an otherwise quiescent uniform environment. As our primary focus, we introduce a horizontal boundary beneath the source. For sufficiently small separations, the jet attaches and clings to the boundary, herein the “clinging jet,” before, farther downstream, the jet is pulled away from the boundary by the buoyancy force. For larger source-boundary separations, the buoyant jet is free to rise under the action of the buoyancy force, herein the “free jet.” Based on measurements of saline jets in freshwater surroundings we deduce the conditions required for a jet to cling. We present a data set that spans a broad range of source conditions for the variation in volume flux (indicative of entrainment), jet perimeter, and jet centerline for both “clinging” and “free” jets. For source Froude numbers ${\text{Fr}}_0\ge 12$ the data collapse when scaled, displaying universal behaviors for both clinging and free jets. Our results for the variation in the volume flux across horizontal planes, $\pi Q_{\mathit{jet}}$, show that within a few jet lengths of the source, $\pi Q_{\mathit{jet}}$ for the clinging jet exceeds that of a free jet with identical source conditions. However, when examined in a coordinate following the jet centerline $\pi Q_{\mathit{jet}}$ for free jets is greater. Finally, we propose a new parametrization for an existing integral model which agrees well with our experimental data as well as with data from other studies. Our findings offer the potential to tailor the dilution of horizontal buoyant jets by altering the distance at which they are released from a boundary.

Turbulent flows laden with inertial particles present multiple open questions and are a subject of great interest in current research. Due to their higher density compared to the carrier fluid, inertial particles tend to form high-concentration regions, i.e., clusters, and low-concentration regions, i.e., voids, due to the interaction with the turbulence. In this work we present an experimental investigation of the clustering phenomenon of heavy sub-Kolmogorov particles in homogeneous isotropic turbulent flows. Three control parameters are varied over significant ranges: ${\text{Re}}_{\lambda }\in [170–450], \text{St}\in [0.1–5]$, and volume fraction ${\varphi }_v\in [(2\times {10}^{-6})–(2\times {10}^{-5})]$. The scaling of clustering characteristics, such as the distribution of Voronoi areas and the dimensions of cluster and void regions, with the three parameters is discussed. In particular, for the polydispersed size distributions considered here, clustering is found to be enhanced strongly (quasilinearly) by ${\text{Re}}_{\lambda }$ and noticeably (with a square-root dependence) with ${\varphi }_v$, while the cluster and void sizes, scaled with the Kolmogorov length scale $\eta$, are driven primarily by ${\text{Re}}_{\lambda }$. Cluster characteristic size $\sqrt{\langle A_c\rangle }$ scales up to $\approx 100\eta$, measured at the highest ${\text{Re}}_{\lambda }$, while void sizes $\sqrt{\langle A_v\rangle }$, scaled also with $\eta$, are typically twice as large as clusters at the same ${\text{Re}}_{\lambda }\left(\approx 200\eta \right)$. The lack of sensitivity of the above characteristics to the Stokes number lends support to the sweep-stick particle accumulation scenario. The non-negligible influence of the volume fraction, however, is not considered by that model and can be connected with collective effects.

An approach to designing passive devices for control of unsteady flows is presented. The method requires only snapshots of the flow to be controlled as inputs. A temporal correlation based on proper orthogonal decomposition of both fluctuating velocity and nonlinear forcing serves to identify the spatial locations in which the forcing drives the different unsteady flow features. The installation of a passive device in these spatial locations inhibits the fluctuating motion. The potential of the methodology is demonstrated via the suppression of vortex shedding in flow past a square cylinder, paving the way to the control of more complex flows using passive devices. Connections in agreement with previous studies targeting the same flow using different passive flow control strategies are provided.

In this paper we consider the effects of adding high-frequency, low-amplitude perturbations to a smooth sinusoidal base input signal for a heaving panel in a closed loop flow tank. Specifically, 0.1 cm amplitude sinusoidal perturbation waves with frequency $f_p$ ranging from 0.5 to 13.0 Hz are added to 1 cm heave sinusoids with base frequencies, $f_b$, ranging from 0.5 to 3.0 Hz. Two thin foils with different flexural stiffness are heaved with the combined input signals in addition to both the high-heave and low-heave signals independently. In all cases, the foils are heaved in a recirculating water channel with an incoming velocity of $V_x=10\text{cm/s}$ and a Reynolds number based on the chord length of $\text{Re}=17300$. Results demonstrate that perturbations increase the net axial force, in the streamwise direction, in most cases tested (with the exception of some poor performing flexible foil cases). Most significantly, for a base frequency of 1 Hz, perturbations at 9 Hz result in a 780.7% increase in net streamwise force production. Generally, the higher the perturbation frequency, $f_p$ the more axial force generated. However, for the stiffer foil, a clear peak in net force exists at $f_p=9\mathrm{Hz}$, regardless of the base frequency. For the stiffer foil, swimming efficiency at a 1 Hz flapping frequency is increased dramatically with the addition of a perturbation, with reduced efficiency increases at higher flapping frequencies. Likewise, for the flexible foil, swimming efficiency gains are greatest at the lower flapping frequencies. Perturbations alter the wake structure by increasing the vorticity magnitude and increasing the vortex shedding frequency; i.e., more, stronger vortices are produced in each flapping cycle.

Back-and-forth oscillations of a container filled with fluid often result in spilling as the gravest mode gets excited, a well-known phenomenon experienced in everyday life and of particular importance in industry. Our understanding of sloshing is largely restricted to linear response, and existing extensions mostly focus on nonlinear coupling between modes. Linear theory is expected to correctly model the dynamics of the system as long as the amplitude of the mode remains small compared to another length scale, so far unknown. Using a fluid in the vicinity of its critical point, we demonstrate that in perfect wetting this length scale is neither the wavelength nor the capillary length but a much shorter one, the thickness of the boundary layer. Above this crossover length scale, the resonance frequency remains roughly constant while dissipation significantly increases. We also show that dynamical wetting is involved in both linear and nonlinear dissipative processes.

Modal and nonmodal growth of three-dimensional perturbations in a shear flow with a free surface are examined for a wide range of Froude numbers. By approximating the mean flow with a piecewise linear profile, the modal instabilities are shown to arise from the interaction of three-dimensional edge waves supported at the interfaces of density discontinuity at the surface and mean vorticity discontinuity at the edges of the shear layer. The mechanism and properties of the instability are explained in terms of the dynamics of the edge-wave interactions. Previously reported modal stability analysis restricted to two-dimensional perturbations in the plane of the flow accurately predicts the fastest growing perturbations but underestimates the range of length scales for the unstable structures. Robust nonmodal transient growth of perturbations within a few advective time units is found. For low Froude numbers or low values of the shear, three-dimensional perturbations with small horizontal scales exhibit the largest growth through a synergy between the Orr and the lift-up mechanisms and produce large streamwise streaks in the shear flow without an effect on the free surface. For large Froude numbers or large values of the shear, planar perturbations with larger horizontal scales exhibit the largest energy growth by effectively instigating the modal instability and excite surface waves at large amplitude.

An analytical expression describing the unsteady pressure evolution of the dispersed phase driven by variations in the carrier phase is presented. In this article, the term “dispersed phase” represents rigid particles, droplets, or bubbles. Letting both the dispersed and continuous phases be inhomogeneous, unsteady, and compressible, the developed pressure equation describes the particle response and its eventual equilibration with that of the carrier fluid. The study involves impingement of a plane traveling wave of a given frequency and subsequent volume-averaged particle pressure calculation due to a single wave. The ambient or continuous fluid's pressure and density-weighted normal velocity are identified as the source terms governing the particle pressure. Analogous to the generalized Faxén theorem, which is applicable to the particle equation of motion, the pressure expression is also written in terms of the surface average of time-varying incoming flow properties. The surface average allows the current formulation to be generalized for any complex incident flow, including situations where the particle size is comparable to that of the incoming flow. Further, the particle pressure is also found to depend on the dispersed-to-continuous fluid density ratio and speed of sound ratio in addition to dynamic viscosities of both fluids. The model is applied to predict the unsteady pressure variation inside an aluminum particle subjected to normal shock waves. The results are compared against numerical simulations and found to be in good agreement. Furthermore, it is shown that, although the analysis is conducted in the limit of negligible flow Reynolds and Mach numbers, it can be used to compute the density and volume of the dispersed phase to reasonable accuracy. Finally, analogous to the pressure evolution expression, an equation describing the time-dependent particle radius is deduced and is shown to reduce to the Rayleigh-Plesset equation in the linear limit.

Heat transfer to fluids at supercritical pressure is different from heat transfer at lower pressures due to strong variations of the thermophysical properties with the temperature. We present and analyze results of direct numerical simulations of heat transfer to turbulent ${\mathrm{CO}}_2$ at 8 MPa in an annulus. Periodic streamwise conditions are imposed so that mean streamwise acceleration due to variations in the density does not occur. The inner wall of the annulus is kept at a temperature of 323 K, while the outer wall is kept at a temperature of 303 K. The pseudocritical temperature $T_{pc}=307.7$ K, which is the temperature where the thermophysical properties vary the most, can be found close to the inner wall. This work is a continuation of an earlier study, in which turbulence attenuation due to the variable thermophysical properties of a fluid at supercritical pressure was studied. In the current work, the direct effects of variations in the specific heat capacity, thermal diffusivity, density, and the molecular Prandtl number on heat transfer are investigated using different techniques. Variations in the specific heat capacity cause significant differences between the mean nondimensionalized temperature and enthalpy profiles. Compared to the enthalpy fluctuations, temperature fluctuations are enhanced in regions with low specific heat capacity and diminished in regions with a large specific heat capacity. The thermal diffusivity causes local changes to the mean enthalpy gradient, which in turn affects molecular conduction of thermal energy. The turbulent heat flux is directly affected by the density, but it is also affected by the mean molecular Prandtl number and attenuated or enhanced turbulent motions. In general, enthalpy fluctuations are enhanced in regions with a large mean molecular Prandtl number, which enhances the turbulent heat flux. While analyzing the Nusselt numbers under different conditions it is found that heat transfer deterioration or enhancement can occur without streamwise acceleration or mixed convection conditions. Finally, through a combination of a relation between the Nusselt number and the radial heat fluxes, a quadrant analysis of the turbulent heat flux, and conditional averaging of the heat flux quadrants, it is shown that heat transfer from a heated surface depends on the density and the molecular Prandtl number of both hot fluid moving away from a heated surface as well as the thermophysical properties of relatively cold fluid moving towards it.

We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of vorticity and velocity increments that are not invariant under mirror symmetry. We also study the scaling properties of high-order structure functions based on the moments of the velocity increments projected on a subset of modes with either positive or negative helicity (chirality). We show that mirror symmetry is recovered at small scales, i.e., chiral terms are subleading and they are well captured by a dimensional argument plus anomalous corrections. These findings are also supported by a high Reynolds numbers study of helical shell models with the same chiral symmetry of Navier-Stokes equations.

Surrounded by a spherically symmetric solute cloud, chemically active homogeneous spheres do not undergo conventional autophoresis when suspended in an unbounded liquid domain. When exposed to external flows, solute advection deforms that cloud, resulting in a generally asymmetric distribution of diffusio-osmotic slip which, in turn, modifies particle motion. Inspired by classical forced-convection analyses [Acrivos and Taylor, Phys. Fluids 5, 387 (1962); Frankel and Acrivos, Phys. Fluids 11, 1913 (1968)] we illustrate this phoretic phenomenon using two prototypic configurations, one where the particle sediments under a uniform force field and one where it is subject to a simple shear flow. In addition to the Péclet number $\mathrm{Pe}$ associated with the imposed flow, the governing nonlinear problem also depends upon $\alpha$, the intrinsic Péclet number associated with the chemical activity of the particle. As in the forced-convection problems, the small-Péclet-number limit is nonuniform, breaking down at large distances away from the particle. Calculation of the leading-order autophoretic effects thus requires use of matched asymptotic expansions, the outer region being at distances that scale inversely with $\mathrm{Pe}$ and ${\mathrm{Pe}}^{1/2}$ in the respective sedimentation and shear problems. In the sedimentation problem we find an effective drag reduction of fractional amount $\alpha /8$; in the shear problem we find that the magnitude of the stresslet is decreased by a fractional amount $\alpha /4$. For a dilute particle suspension the latter result is manifested by a reduction of the effective viscosity.

A one-dimensional numerical simulation is carried out to study the oscillation characteristics of satellite droplets in the beads-on-a-string structure of an Oldroyd-B viscoelastic liquid jet. The oscillation of satellite droplets is compared with the linear oscillation of a single viscoelastic droplet. It is found that, contrary to the predictions of linear theory, the period of oscillation of satellite droplets decreases with time, despite the increase in droplet volume. The mechanism may lie in the existence of the filament, which exerts an extra resistance on droplets. On the other hand, the oscillation of droplets does not influence very much the thinning of the filament. The influence of the axial wave number, viscosity, and elasticity on the oscillation of satellite droplets is examined. Increasing the wave number may result in the decrease in the period and the increase in the decay rate of oscillation, while increasing viscosity may lead to the increase in both the period and the decay rate of oscillation. Elasticity is shown to suppress the oscillation at large wave numbers, but its influence is limited at small wave numbers.

Inspired by the flow processes in the technology of carbon dioxide $\left({\mathrm{CO}}_2\right)$ storage in saline formations, we modeled a homogeneous porous media flow in a Hele-Shaw cell to investigate density-driven convection due to dissolution. We used an analogy of the fluid system to mimic the diffusion and subsequent convection when ${\mathrm{CO}}_2$ dissolves in brine, which generates a heavier solution. By varying the permeability, we examined the onset of convection, the falling dynamics, the wavelengths of fingers, and the rate of dissolution, for the Rayleigh number $\text{Ra}$ (a dimensionless forcing term which is the ratio of buoyancy to diffusivity) in the range of $2.0\times {10}^4\le \text{Ra}\le 8.26\times {10}^5$. Our results reveal that the effect of permeability influences significantly the initial convective speed, as well as the later coarsening dynamics of the heavier fingering plumes. However, the total dissolved mass, characterized by a nondimensional Nusselt number $\text{Nu}$, has an insignificant dependence on $\text{Ra}$. This implies that the total dissolution rate of ${\mathrm{CO}}_2$ is nearly constant in high $\text{Ra}$ geological porous structures.

We demonstrate how to suspend various magnetic and nonmagnetic particles in liquid metals and characterize their properties relevant to magnetohydrodynamics (MHD). The suspending method uses an acid as a flux to eliminate oxidation from both metal particles and liquid, which allows the particles to be wetted and suspended into the liquid if the particles have higher conductivity than the liquid. With this process we were able to suspend a wide range of particle materials and sizes from 40 nm to 500 $\mu \mathrm{m}$ into three different liquid metal bases and volume fractions $\varphi$ up to the liquid-solid transition ${\varphi }_c$. By controlling the volume fraction of iron particles in liquid eGaIn, we increased the magnetic permeability by a factor of 5.0 and the electrical conductivity by 13% over that of the pure liquid metal, which gives these materials the potential to exhibit strong MHD effects on the laboratory scale that are usually only observable in the cores of planets and stars. By adding nonmagnetic zinc particles, we increased the viscosity by a factor of 160 while keeping the magnetic and electrical properties nearly constant, which would allow independent control of MHD effects from turbulence. We show that the suspensions flow like Newtonian fluids up to the volume fraction of the liquid-solid transition ${\varphi }_c$.

The angular dynamics of a very small ellipsoidal particle in a viscous flow decouples from its translational dynamics and the particle angular velocity is given by Jeffery's theory. It is known that cuboid particles share these properties. In the literature a special case is most frequently discussed, namely that of axisymmetric particles with a continuous rotation symmetry. Here we compute the angular dynamics of crystals that possess a discrete rotation symmetry and certain mirror symmetries but do not have a continuous rotation symmetry. We give examples of such particles that nevertheless obey Jeffery's theory. However, there are other examples where the angular dynamics is determined by a more general equation of motion.

Spectra and one-point statistics of velocity and thermodynamic variables in isotropic turbulence of compressible fluid are examined by using numerical simulations with solenoidal forcing at the turbulent Mach number $M_t$ from 0.05 to 1.0 and at the Taylor Reynolds number ${\text{Re}}_{\lambda }$ from 40 to 350. The velocity field is decomposed into a solenoidal component and a compressible component in terms of the Helmholtz decomposition, and the compressible velocity component is further decomposed into a pseudosound component, namely, the hydrodynamic component associated with the incompressible field and an acoustic component associated with sound waves. It is found that the acoustic mode dominates over the pseudosound mode at turbulent Mach numbers $M_t\ge 0.4$ in our numerical simulations. At turbulent Mach numbers $M_t\le 0.4$, there exists a critical wave number $k_c$ beyond which the pseudosound mode dominates while the acoustic mode dominates at small wave numbers $k<k_c$. In the pseudosound-mode-dominated region, the compressible velocity is fully enslaved to the solenoidal velocity, and its spectrum scales as $M_t^4{k}^{-3}$ in the inertial range. It is also found that in the inertial range, the spectra of pressure, density, and temperature exhibit a $k^{-7/3}$ scaling for $M_t\le 0.3$ and a $k^{-5/3}$ scaling for $M_t\ge 0.5$.

We report about an intriguing boiling regime occurring for small heaters embedded on the boundary in subcooled water. The microheater is realized by focusing a continuous wave laser beam to about $10\mu \mathrm{m}$ in diameter onto a 165-nm-thick layer of gold, which is submerged in water. After an initial vaporous explosion a single bubble oscillates continuously and repeatedly at several $100\mathrm{kHz}$ albeit with constant laser power input. The microbubble's oscillations are accompanied with bubble pinch-off, leading to a stream of gaseous bubbles in the subcooled water. The self-driven bubble oscillation is explained with a thermally kicked oscillator caused by surface attachment and by the nonspherical collapses. Additionally, Marangoni stresses induce a recirculating streaming flow which transports cold liquid towards the microheater, reducing diffusion of heat along the substrate and therefore stabilizing the phenomenon to many million cycles. We speculate that this oscillate boiling regime may overcome the heat transfer thresholds observed during the nucleate boiling crisis and offers a new pathway for heat transfer under microgravity conditions.

We present numerical simulations of ideal magnetohydrodynamics showing suppression of the Richtmyer-Meshkov instability in spherical implosions in the presence of an octahedrally symmetric magnetic field. This field configuration is of interest owing to its high degree of spherical symmetry in comparison with previously considered dihedrally symmetric fields. The simulations indicate that the octahedral field suppresses the instability comparably to the other previously considered candidate fields for light-heavy interface accelerations while retaining a highly symmetric underlying flow even at high field strengths. With this field, there is a reduction in the root-mean-square perturbation amplitude of up to approximately $50\%$ at representative time under the strongest field tested while maintaining a homogeneous suppression pattern compared to the other candidate fields.