We examine the process of particle capture by large deformable drops in turbulent channel flow. We simulate the solid-liquid-liquid three-phase flow with an Eulerian-Lagrangian method based on direct numerical simulation of turbulence coupled with a phase-field model, to capture the interface dynamics, and Lagrangian tracking of small (sub-Kolmogorov) particles. Drops have the same density and viscosity of the carrier liquid, and neutrally buoyant, quasi-inertialess, solid particles are one-way coupled with the other phases. Our results show that particles are transported towards the interface by jetlike turbulent motions and, once close enough, are captured by interfacial forces in regions of positive surface velocity divergence. These regions appear to be well correlated with high-enstrophy flow topologies that contribute to enstrophy production via vortex compression or stretching. Examining the turbulent mechanisms that bring particles to the interface, we have been able to derive a simple transport model for particle capture. The model is based on a single turbulent transport equation in which the only parameter scales with the turbulent kinetic energy of the fluid measured in the vicinity of the drop interface, and its predictions of the overall capture efficiency agree remarkably well with numerical results.

We demonstrate a method for direct numerical simulations (DNS) of incompressible, flat-plate, zero pressure gradient, turbulent boundary layers, without the use of auxiliary simulations or fringe regions, in a streamwise periodic domain via the homogenized Navier-Stokes equations. This approach is inspired by Spalart's original (1987) method, but improves upon his drawbacks while simplifying the implementation. Most simulations of flat-plate boundary layers require long streamwise domains owing to the slow boundary layer growth and inflow generation techniques. Instead, we use anticipated self-similarity to solve the equations in a normalized coordinate system to allow for streamwise periodicity, similar to Spalart's original method. The resulting integral values, the skin friction coefficient and shape factor, $H_{12}$ and $C_f$, are within $\pm 1\%$ and $\pm 3\%$ of the empirical fits. The mean profiles show good agreement with spatially developing DNS and experimental results for a wide range of Reynolds numbers from ${\text{Re}}_{{\delta }^{*}}=1460$ to 5650. The method manages to reduce computational costs by an estimated one to two orders of magnitude.

In the present work, we theoretically analyze the influence of the slippage phenomenon on the atomization via surface acoustic waves of a millimeter-order water drop deposited over a hydrophilic substrate. The analysis is conducted by considering, in the first place, a standing surface acoustic wave acting at the free surface of the parent drop. Subsequently, the lubrication theory is applied to the flow field governing equations to derive an evolution equation of the air-liquid interface in terms of the acoustic capillary number and the Navier-slip coefficient. Such an equation's numerical solution leads to a simplified drop model, depicting the spatiotemporal deformation of the free surface under the influence of slippage phenomenon and predicts the atomization threshold once the instability length at the induced capillary waves is achieved. Our numerical simulations show that the high-frequency acoustic excitation under consideration leads to the development of a standing wave at the free surface, which oscillates at a viscous-capillary resonance frequency on order ${10}^4$ Hz. Moreover, a spreading phenomenon on the fluid drop is induced, strongly linked to the magnitude of the acoustic capillary number. In this scenario, the slippage under hydrophilic conditions has a noticeable impact on the free surface dynamics, causing smaller aerosol characteristic diameters in comparison with the no-slip case. In this context, the present study provides an analytical expression that calculates the droplet diameter in terms of the slip coefficient. In the process, we postulate the slippage phenomenon as a valuable means to control the parent drop's deformation mechanism and, therefore, the aerosol characteristic diameter.

Here we study viscous oscillatory nanoflows generated in a fluid by mechanical oscillations of miniaturized resonators. In particular, we focus on the limits of two-dimensional cylinder theory, which approximates a slender nanoresonator, such as an atomic force microscopy microcantilever or a nanobeam resonator, as a cylinder oscillating in a fluid. The cylinder theory is the mainstay in the micro- and nanoelectromechanical systems literature, but is only accurate in certain regimes. We observe and explain two distinct routes to the breakdown of the cylinder theory. First, when a substrate is present, squeeze film effects become significant and the cylinder theory underpredicts the fluid force applied to the resonator. Second, the cylinder theory overpredicts the fluid force when axial flow becomes relatively large. This occurs at higher bending modes where the spatial gradients along the beam are larger. A dimensionless squeeze number and axial flow number are introduced to facilitate in-depth investigations into the limitations of the two-dimensional cylinder theory. Results from experiments and three-dimensional finite-element models are presented in order to illustrate where two-dimensional flow models break down.

This experimental study investigates the evolution of mean flow and turbulence in the near field of an immiscible buoyant oil jet injected into water at a low Reynolds number $(\mathrm{Re}=1230)$. Refractive index matching of the liquid pair using silicone oil and sugar water enables simultaneous applications of particle image velocimetry and planar laser induced fluorescence. The results include flow visualizations, ensemble-averaged phase and velocity distributions, and Reynolds normal and shear stresses for each phase and combined. Trends are compared to those of a single-phase jet. Close to the nozzle, the surrounding water gains momentum when thin layers are entrained into the jet. Also, as oil ligaments begin to extend outward, water-containing vortices form around their tips. Further downstream, as the oil breaks up into blobs and then to smaller droplets, the spreading rate of the oil volume fraction and the decrease in its centerline concentration are lower than those of the axial momentum and centerline velocity. Universal profiles of either the phase distribution or the axial momentum scaled with the half widths and centerline values develop after six diameters, the latter occurring earlier than the single-phase jet. As expected, the mean velocity in the oil is higher than that in the water, and after thirteen diameters, the difference between them is consistent with the buoyant rise velocity of oil droplets with the same Sauter mean diameter in turbulent flows. Initially, the normal and shear Reynolds stress components in the oil jet are higher than those in the single-phase jet, but the differences between them decrease with axial distance. Phase-conditioned statistics in the oil jet reveal significant spatially varying discrepancies between the turbulence level in the oil and water phases. The peripheral turbulence in the water is higher near the jet exit, but lower after six diameters. The latter trend is attributed to the intermittency and lower peripheral shear-dominated turbulence production rate in the entrained water. In contrast, near the jet centerline, the turbulence production rate, hence the turbulent kinetic energy, is higher in the water. Here, while the axial contraction increases the turbulence in both phases, the radial extension in the spreading oil, as opposed to the radial contraction in the entrained water, causes a discrepancy in the production rates. After thirteen diameters, the differences between oil and water turbulence levels diminish. Still, the axial velocity fluctuations are substantially higher than the radial ones. The oil blob size distribution in this region still has a Sauter mean diameter that is five times larger than that measured after thirty diameters, indicating that fragmentation of the oil persists well beyond the range examined in this paper.

How anisotropic particles rotate and orient in a flow depends on the hydrodynamic torque they experience. Here we compute the torque acting on a small spheroid in a uniform flow by numerically solving the Navier-Stokes equations. Particle shape is varied from oblate (aspect ratio $\lambda =1/6$) to prolate $(\lambda =6)$, and we consider low and moderate particle Reynolds numbers $(\mathrm{Re}\le 50)$. We demonstrate that the angular dependence of the torque, predicted theoretically for small particle Reynolds numbers, remains qualitatively correct for Reynolds numbers up to $\mathrm{Re}\sim 10$. The amplitude of the torque, however, is smaller than the theoretical prediction, the more so as $\mathrm{Re}$ increases. For Re larger than 10, the flow past oblate spheroids acquires a more complicated structure, resulting in systematic deviations from the theoretical predictions. Overall, our numerical results provide a justification of recent theories for the orientation statistics of ice crystals settling in a turbulent flow.

The fragmentation of solid objects in turbulence is of paramount importance in a large number of situations, especially for marine plastic pollution where small plastic debris are formed by the fragmentation of plastic litter under hydrodynamic forces. Up to now, investigations have focused on the fragmentation of particle aggregates in turbulent flows. Here we study the fragmentation of a single deformable object that behaves elastically up to breakage, in the inertial range of turbulence. Using laboratory experiments with glass fibers as a model system, complemented by numerical simulations and theoretical analyses, we exhibit a comprehensive fragmentation scenario, further modeled by an evolution equation. Our results demonstrate that the fragmentation process is limited at small scales by a physical cutoff length originating from the fluid-structure interactions between the objects and the turbulence, and therefore independent of the brittleness of the fibers. This scenario leads to the accumulation of fragments with a typical length slightly longer than the cutoff scale, as smaller fragments are too short to be deformed and broken by the turbulence.

Flapping wing propulsion offers unrivaled maneuverability and efficiency at low flight speeds and in hover. These advantages are attributed to the leading edge vortex developing on an unsteady wing, which induces additional lift. We propose and validate a manipulation hypothesis that allows prolongation of the leading edge vortex growth phase, by delaying its detachment with the aid of flow control. This approach targets an overall lift increase on unsteady airfoils. A dielectric barrier discharge plasma actuator is successfully used to compress secondary structures upstream of the main vortex on a pitching and plunging flat plate. To determine flow control timing and location, the tangential velocity on the airfoil surface is used, which is also used to quantify topological effects of flow control. This flow control is then tested for different motion kinematics on a NACA 0012 airfoil. An increase of the peak circulation of the leading edge vortex of about 20% for all cases with flow control indicates that this approach is applicable for various kinematics, dynamics, and airfoil types.

Improving the ability to control viscous fingering instabilities plays an essential role in a wide variety of scientific and engineering fields. Based on linear stability analysis, we present an energy model characterized by the viscous dissipation rate, which can reflect the evolution process of the fluid-fluid interface, and predictions of control schemes are obtained from the model. One type of scheme is to control the morphological patterns of instability through initial disturbances. Another series of schemes is to control whether the viscous fingering instability is suppressed or continues to develop by different scaling laws of injection rate versus time based on the variational method. Furthermore, a stable and continual forward movement of the interface is achieved by a periodic suppression scheme, which is significant in practical applications. The effectiveness of the energy model and all control schemes are well verified by experiments.

Ionic liquids have remarkable properties and are commonly harnessed for green chemistry, lubrication, and energy applications. In this paper, we study a thermoresponsive ionic liquid (IL) solution which has the property of phase separating above a critical temperature, an interesting feature for the recovery of the IL-rich phase. For this purpose, we generate a temperature gradient in a microfluidic cavity where the confinement strengthens wetting effects and enhances the demixing. We show that the phase separation is performed by the joint effects of sedimentation and thermocapillary actuation giving rise to a three-dimensional flow structure, which is quantitatively captured by our model. Altogether those mechanisms lead to the accumulation of the wetting phase near the heating source. We believe this work will find applications in the recycling of ionic liquids.

The flow around an inclined tangent ogive-cylindrical body of a finite length with a blunt elliptical base, placed in a wind tunnel and allowed to yaw in the x-y plane, is studied computationally. The flow is three-dimensional, compressible, and laminar with a Reynolds number of 30 000 based on the body diameter and a Mach number of 0.2. The study covers the range of angles of attack from 0° to 65°, both for fixed and yaw-restrained configurations where solutions are determined after removal of initial disturbances. The flow around the fixed body, for α > 52° and after disturbance removal, is nonstationary with large amplitude oscillations; for 0°< α < 52° the flow is almost steady with small nonstationary amplitude oscillations possibly due to the body's blunt end nonstationary wake. We identify a transition region between 45° < α < 52° where the attached wake behind the body end becomes detached. The resulting yaw response exhibits an intricate bifurcation structure that includes bistable periodic (finite amplitude) and nonstationary (small amplitude) limit cycles for moderate angles of attack, and nonstationary (finite amplitude) oscillations for high angles of attack. Investigation of the restraint torsion stiffness reveals a resonant periodic lock-in phenomena for low angles of attack which becomes quasiperiodic for a 40° angle of attack.

We study how the complex interplay between channel roughness, inertia, and diffusion controls tracer transport in rough channel flows. We first simulate flow and tracer transport over wide ranges of channel roughness, Reynolds number (Re), and Péclet number (Pe) observable in nature. Pe exerts a first-order control on first-passage time distributions, and the effect of roughness on the tracer transport becomes evident as Re increases. The interplay between the roughness and Re causes recirculating flows, which intensify or suppress anomalous transport depending on Pe. At infinite Pe, the late-time scaling follows a universal power-law scaling, which is explained by conducting a scaling analysis. With extensive numerical simulations and stochastic modeling, we show that the roughness, inertia, and diffusion effects are encoded in Lagrangian velocity statistics represented by velocity distribution and velocity correlation. We successfully reproduce anomalous transport using an upscaled stochastic model that honors the key Lagrangian velocity statistics.

The aim of the present work is to study the interaction between an oscillating bubble and a free surface. We perform a series of experiments and numerical simulations and attempt to characterize both early and late stages of the interaction. The focus is on providing insight into the mechanisms of bubble-induced atomization. For this reason, we are particularly interested in characterizing the patterns and dynamics of the liquid jets that are formed at the free surface. Observations regarding the evolution of the free surface are presented by measuring the jet's surface area and volume. Finally, based on these quantities, we introduce a metric that may be used to characterize the liquid jetting and predict whether late-time atomization of the interface will occur.

In this experimental study, we report on the mixing properties of interfacial colloidal floaters (glass bubbles) by chemical and hydrodynamical currents generated by self-propelled camphor disks swimming at the air-water interface. Despite reaching a statistically stationary state for the glass bubbles distribution, those floaters always remain only partially mixed. This intermediate state results from a competition between (i) the mixing induced by the disordered motion of many camphor swimmers and (ii) the unmixing promoted by the chemical cloud attached to each individual self-propelled disk. Mixing/unmixing is characterized globally using the standard deviation of concentration and spectra, but also more locally by averaging the concentration field around a swimmer. Besides the demixing process, the system develops a “turbulentlike” concentration spectra, with a large-scale region, an inertial regime, and a Batchelor region. We show that unmixing is due to the Marangoni flow around the camphor swimmers, and is associated to compressible effects.

We investigate the collective behavior of active suspensions of microswimmers immersed in a viscous fluid through numerical studies. We consider the two kind of organisms generally studied in experimental and theoretical studies, namely the pullers and the pushers, which differ in the way they are able to swim. We model them such that the body shape and the flagella used to swim are mathematical described. We tackle the problem using a new numerical approach, based on fictitious domains, which allows to fully solve the fluid-structure interaction and therefore exactly captures both the far- and near-field interactions between swimmers. Considering a two-dimensional domain for simplicity, we first investigate the state of bacterial turbulence in an unbounded domain, analyzing also their dynamical properties in terms of chaos. Then we analyze the rheological properties of the suspension by varying the different parameters. Our main findings are the following: (i) At variance with some previous studies, we show that pullers are able to trigger bacterial turbulence, although there is an asymmetry between ellipsoidal puller and pusher swimmers when elongated. (ii) Moreover, spherical pullers and pushers are found to be indistinguishable from a macroscopic point of view. (iii) We show that the complex dynamics, in particular the difference between pushers and pullers in collective properties, is related to a spontaneous breaking of the time-reversal symmetry. The key ingredients for breaking the symmetry are the concentration of the suspension and the shape of the organisms. (iv) The suspensions are chaotic in all cases, but that plays no role with regard to the macroscopic properties of the suspension. (v) Rheological signatures, already known in experiments, are analyzed and explained within this framework. We unambiguously show that our results are due to hydrodynamic interactions, whereas collisions or contacts do not play a role. The present results should be taken into account for the proposition of simplified models.

Electrothermohydrodynamic convection driven by strong unipolar charge injection in the presence of a stabilizing inverse thermal gradient between two parallel electrodes is investigated by a linear stability analysis and a numerical simulation. The generalized Schur decomposition is used to solve for the eigenvalues of the linearized system revealing the critical parameters. The two relaxation time lattice Boltzmann method coupled to a fast Poisson solver is used to resolve the nonlinear system for the spatiotemporal distribution of flow field, electric field, charge density, and temperature. With strong charge injection and high electric Rayleigh number, the system exhibits electrothermoconvective vortices. The interactions between the stabilizing buoyancy force and the destabilizing electric force lead to overstability, where the flow constantly oscillates when instability evolves. A two-stage bifurcation is observed for overstability near the threshold Rayleigh number with a significant change in phase and amplitude. The effects of ion mobility and thermal diffusivity are characterized by the ratio of the counteracting forces.

The phase of the bispectrum of a turbulent velocity signal is presented as a unified tool to relate the geometry and energetics of interactions between large- and small-scale motions in wall-bounded turbulence. The normalized bispectrum naturally describes nonlinear triadic interactions and thus is ideally suited for measuring the magnitude of coupling between the different scales of turbulence without the use of filtering procedures. In this study, the corresponding biphase is shown to represent the delay between large and small scales imposed by convective interactions and simultaneously to describe the direction of the turbulent streamwise energy cascade. The bispectrum and biphase are measured from a direct numerical simulation of a high-Reynolds-number channel flow and used to illustrate the relationship between the relative geometry of the interacting scales, the interaction delay, and the cascade of energy between them, offering an integrated perspective on scale interactions in turbulence through a single statistic.

Natural convection over a roof-shaped triangular surface is investigated using direct numerical simulations. The Rayleigh number (Ra) was varied from 1 to $5\times {10}^6$ with air as working fluid (Prandtl number of 0.71) at a fixed geometrical aspect ratio of 0.1, defined as the ratio of roof height to half-width. The transition route from a steady flow to a chaotic flow on the surface is characterized by the topological method with the increase of Ra. A weak flow, dominated by conduction, occurs when Ra was relatively small. As Ra increases, the convective flow becomes stronger and a sequence of bifurcations is found. Between $\mathrm{Ra}={10}^2$ and ${10}^3$, a primary pitchfork bifurcation occurs. Secondary and tertiary pitchfork bifurcations are observed in the range $\mathrm{Ra}=\left[{10}^3,{10}^4\right]$ and $\left[{10}^4,{10}^5\right]$, respectively. After another pitchfork bifurcation at $\mathrm{Ra}=\left[1.4,1.5\right]\times {10}^6$, which makes the plume tilt to either side of the roof top edge, a Hopf bifurcation is observed in $\mathrm{Ra}=\left[1.9,2\right]\times {10}^6$, after which both the slope flow and plume become periodic. This is followed by further bifurcations including a period doubling bifurcation at $\mathrm{Ra}\approx 3\times {10}^6$ and a quasiperiodic bifurcation firstly arising at $\mathrm{Ra}\approx 3.4\times {10}^6$. Finally, the flow becomes chaotic for $\mathrm{Ra}>3.7\times {10}^6$. The state space, the maximum Lyapunov exponent, the fractal dimension, and the power spectral density are presented to analyze the flows in the transition to chaos. This work is a comprehensive description of the flow transition from steady state to chaos on surface of a section-triangular roof that is pertinent to various settings where fluid flow develops.

Existing studies of bubble-structure interaction mainly focus on the interaction between a bubble and a movable rigid body or deformable linear elastic structure. The strong nonlinear interaction of a bubble with an elastic-plastic plate has rarely been studied while the inherent dynamic behavior is not clear. In this paper, we develop a three-dimensional fully coupled model to investigate the interaction between a bubble and an elastic-plastic thin-walled plate, which can consider the fluid disturbance on both sides of the thin-walled plate. In this developed model, the dynamic behaviors of the bubble are obtained by the boundary integral method based on the potential flow theory, and the nonlinear elastic-plastic responses of the structure are resolved by the explicit finite element method on the basis of the Mindlin-Reissner plate theory. The structural nonlinear responses are incorporated into the fluid boundary integral equation (BIE), and the extra relation between the ${\varphi }_t$ (time derivative of velocity potential) jump across the two sides of the thin-walled plate and its normal derivative ${\varphi }_{tn}$ is derived, which can describe the hydrodynamic balance on both sides of the submerged plate. The derived relation is added to the BIE about ${\varphi }_t$, so that the bubble loading acting on the plate can be accurately calculated. The established coupled model is validated by comparing with experimental results. Using this numerical model, the influence of the standoff distance and plate thickness on the bubble-plate interaction is discussed. Subjected to the violent loading from the bubble, the oscillation characteristics and elastic-plastic deformation of the plate are analyzed. Due to the elastic-plastic effects of the plate, the bubble can display different interesting featured patterns, including attractive motion, repulsive motion, or splitting.

The amplitude equations governing the temporal evolution of internal waves forming a resonant triad in a two-dimensional inviscid stably stratified uniform shear flow, bounded between two infinite horizontal parallel plates, are derived in the absence of diffusive effects. The density is considered to be a linear function of the vertical coordinate. The interaction of two vertically confined and horizontally propagating primary internal waves having the same frequency is considered. Specifically, for different local Richardson numbers, we show the existence and stability of the resonant triad formed by three different internal waves having the wave vector and frequency pairs as $({\vec{k}}_m,\omega )$, $({\vec{k}}_n,\omega )$, and $({\vec{k}}_m+{\vec{k}}_n,2\omega )$. For each resonant triad, we solve the amplitude equations numerically as an initial value problem. The equilibrium solutions of the amplitude equations are obtained analytically. Furthermore, the linear stability analysis of the resonant triads, around the equilibrium solutions, is carried out for various interaction cases. The triads containing a wave with the lowest mode number are found to be linearly unstable. The exact solutions of the amplitude equations are presented under the pump-wave approximation, in which the amplitude of one of the waves in the triad is larger than the amplitudes of the other two waves initially. From the exact solutions, the amplitudes of the waves forming a resonant triad are found to be unbounded when the wave with the mode number 1 acts as the pump wave. The present study helps one to have a better understanding of the stability of resonant triads of internal waves formed in a stratified shear flow.