# Latest papers in fluid mechanics

### Analytic derivation of the inertial range of compressible turbulence

An analytic model for steady state turbulence is employed to obtain the inertial range power spectrum of compressible turbulence. We assume that for homogeneous turbulence, the timescales controlling the energy injected at a given wavenumber from all smaller wavenumbers are equal for each spatial component. However, the longitudinal component energy is diverted into compression, so the rate controlling the energy that is transferred to all larger wavenumbers by the turbulent viscosity is reduced. The resulting inertial range is a power law with an index of −2. Indeed, such power spectra were observed in various astrophysical settings and also in numerical simulations.

### Effect of the liquid–gas interface curvature for a superhydrophobic surface with longitudinal grooves in turbulent flows

A superhydrophobic (SH) surface has shown great potential in reducing flow resistance and saving energy in hydrodynamic applications. In this paper, we have tried to investigate the effects of liquid–gas interface curvature of a SH wall in turbulent flows with the wall-resolved large eddy simulation (LES). The LES is first validated against direct numerical simulation results before the curvature shape is parameterized and examined at various Reynolds numbers (Reτ = 180, 395, and 590). The parametric study shows that a positive curvature angle leads to a higher flow rate, while the effect of a negative curvature angle on the flow resistance is minimal. In addition, the effect of the interface curvature on the flow rate is weakly dependent on the Reynolds number. Analysis shows that larger flow rate can be obtained by reducing the spanwise momentum exchange. A positively curved interface bows into the liquid and shifts the transverse flow circulation (in the cross-sectional plane) away from the solid wall, which helps to reduce spanwise momentum exchange and thus the flow resistance significantly. In contrast, a negatively curved interface does not change the location of the transverse circulation but deforms its shape, which hardly affects the spanwise momentum exchange or the flow rate. The near-wall streak patterns above the SH wall distribute with roughly the same spacing of the surface texture. In addition, the absolute distance plays a more important role than the viscous distance in the variation of the streaks with the distance from the SH wall.

### Linear global stability of a downward flow of liquid metal in a vertical duct under strong wall heating and transverse magnetic field

Author(s): Jun Hu

A three-dimensional unstable oscillatory instability is found for a downward flow of liquid metal in a vertical duct under strong wall heating and a transverse magnetic field. The unstable oscillatory mode first occurs at the specific flow structure which has an upward reverse flow near the heating wall and a downward flow near the opposite wall. The existence of an inflection point is the key instability mechanism of the three-dimensional oscillatory mode which may be regarded as an alternative physical explanation of the high-amplitude, low-frequency pulsations of temperature in experiments and related numerical simulations.

[Phys. Rev. Fluids 6, 073502] Published Wed Jul 21, 2021

### Lagrangian and Eulerian accelerations in turbulent stratified shear flows

Author(s): Frank G. Jacobitz and Kai Schneider

The Lagrangian and Eulerian acceleration (LA and EA) properties of fluid particles in homogeneous turbulence with uniform shear and uniform stable stratification are studied with direct numerical simulations. A wavelet-based scale-dependent decomposition of LA and EA is performed. Joint probability density functions of LA and EA show a trend of stronger correlation with increasing stratification strength and at larger turbulent scales. From the Navier–Stokes equation, LA is dominated by the pressure-gradient term, and EA by the nonlinear convection term. From geometrical statistics, the magnitude of EA is larger than LA due to mutual cancellation of the Eulerian and convective acceleration.

[Phys. Rev. Fluids 6, 074609] Published Wed Jul 21, 2021

### Stability of an oscillatory Taylor–Couette flow in an upper convected Maxwell fluid

The stability of pulsed bi-dimensional flow between two co-oscillating cylinders in a linear Maxwell fluid was studied by Riahi et al. [J. Soc. Rheol. 42, 321–327 (2014)]. In the present paper, we revisit this flow configuration with emphasis on the effect of the non-linear terms in the constitutive equation of the model, measured by the Weissenberg number, on the dynamics of the system. Under these assumptions and using the upper convected Maxwell derivative, we examine this model to large amplitude oscillatory shear giving rise to the appearance, in comparison to the linear Maxwell model, of the azimuthal normal stress in the basic state. Using the spectral method and the Floquet theory for the spatiotemporal resolution of the obtained eigenvalue problem, numerical results exhibit numerous classes of Taylor vortex flows depending on the order of magnitude of the fluid elasticity. The resulting stability diagram consists of several branches intersecting at specific frequencies where two different Taylor vortex flows simultaneously branch off from the basic state. This feature is accompanied by the occurrence of several co-dimension two bifurcation points besides jumps/drops in the corresponding critical wave number. In addition, it turns out that the elasticity produces strong destabilizing and stabilizing effects in the limit of high and low frequency regimes, respectively, attributed solely to the non-linearities considered by the rheological model.

### Active control of transport through nanopores

The passive particle transport through narrow channels is well studied, while for an active particle system, it is not well understood. Here, we demonstrate the active control of the transport through a nanopore via mean-field analysis and molecular dynamics simulations. We prove that the active force enhances the transport efficiency with an effective diffusion coefficient [math], where Dt is the translational diffusion coefficient and Pe is the Péclet number that determines the strength of the active force. For the number of particles inside the channel, it experiences subdiffusion at short times and then turns to normal at longer times. Finally, we extend our research for several sinusoidal shapes of the channel surface. More particles are trapped in the channel if the roughness of the channel surface is increased, resulting in fewer particles are transported from one side of the channel to the other.

### A rheological analog for Brownian motion with hydrodynamic memory

When the density of the fluid surrounding suspended Brownian particles is appreciable, in addition to the forces appearing in the traditional Ornstein and Uhlenbeck theory of Brownian motion, additional forces emerge as the displaced fluid in the vicinity of the randomly moving Brownian particle acts back on the particle giving rise to long-range force correlations which manifest as a “long-time tail” in the decay of the velocity autocorrelation function known as hydrodynamic memory. In this paper, after recognizing that for Brownian particles immersed in a Newtonian, viscous fluid, the hydrodynamic memory term in the generalized Langevin equation is essentially the 1/2 fractional derivative of the velocity of the Brownian particle, we present a rheological analog for Brownian motion with hydrodynamic memory which consists of a linear dashpot of a fractional Scott Blair element and an inerter. The synthesis of the proposed mechanical network that is suggested from the structure of the generalized Langevin equation simplifies appreciably the calculations of the mean square displacement and its time-derivatives which can also be expressed in terms of the two-parameter Mittag–Leffler function.

### Discrete SQG models with two boundaries and baroclinic instability of jet flows

In this paper, new vertically discrete versions of the surface quasigeostrophic (SQG) model with two boundaries are formulated. For any number of partition levels, the equations of the discrete model are written in the form of conservation laws for two Lagrangian invariants, which have the meaning of buoyancy distributions at the horizontal boundaries of the fluid layer. The values of the invariants are expressed in terms of the values of the stream function at two internal levels and contain higher order elliptic operators. The use of discrete models greatly simplifies the solution of problems of the linear theory of hydrodynamic stability and provides high accuracy even with a small number of vertical discrete levels. Using the two-level version of the SQG model, which is similar to the classical two–layer Phillips model, we investigated the linear stability of jet flows induced by piecewise constant boundary distributions of buoyancy. For these flows, analytical expressions for the growth rate of perturbations have been obtained and it is shown that the most unstable perturbation has a wavelength of the order of the Rossby baroclinic radius of deformation. Flows with vertical shear induced by smooth and slowly varying boundary buoyancy distributions are also considered. The instability of these flows is found to be absolute, that is, independent of the velocity profile horizontal structure.

### Effect of serum starvation on rheology of cell monolayers

The rheological properties of cells and tissues are central to embryonic development and homeostasis in adult tissues and organs and are closely related to their physiological activities. This work presents our study of rheological experiments on cell monolayer under serum starvation compared to healthy cell monolayer with full serum. Serum starvation is one of the most widely used procedures in cell biology. However, the effect of deprivation of serum concentration on the material properties of cells is still unknown. Therefore, we performed macro-rheology experiments to investigate the effect of serum starvation on a fully confluent Madin–Darby Canine Kidney cell monolayer. The material properties, such as linear and non-linear viscoelastic moduli, of the monolayer, were measured using oscillatory shear experiments under serum-free [0% fetal bovine serum (FBS)] and full serum (10% FBS) conditions. Our results indicate that a serum-starved cell monolayer shows a different rheological behavior than a healthy cell monolayer. The loss and storage moduli decrease for the step-change in oscillatory strain amplitude experiments for a serum-starved cell monolayer and do not recover fully even after small deformation. In comparison, a healthy cell monolayer under full serum condition remains flexible and can fully recover even from a large deformation at higher strain. The effect of adhesion due to fibronectin was also studied in this work, and we found a significant difference in slip behavior for cell monolayer with and without serum.

### Nanoscale morphology of thin liquid films near the advancing contact line during condensation

The extended thin-film region adjacent to the contact line is crucial in heat transfer because of its capability to enhance heat transfer and its critical role in wetting dynamics. The present investigation focused on the study of advancing contact line morphology induced by water vapor condensation. The condensation was at low rates with the advancing velocities <60 nm/s. Two modes of atomic force microscopy were utilized to measure the morphology of a liquid film with the nanometer resolution. The results indicated that the profile of the film went straight down to the apparent contact line when viewed in a sub-micron window, which is in contrast to nonvolatile cases, such as glycerol and silicon oil, which would have a convex nanobending around 20 nm from the substrate surface due to the local dynamic friction. Furthermore, a precursor nanofilm was detected beyond the contact line during condensation, and nanodroplets hundreds of nanometers in height were sitting on the nanofilm, representing the structure of the advancing contact line, and being adjacent to the condensation plays an essential role in contact line dynamics.

### Mitral valve asymmetry in healthy, pathological, and repaired cases

The entry of blood into the left ventricle is regulated by the two valve leaflets. Mitral valve prolapse is the primary cause of mitral regurgitation. Mitral valve repair is the gold standard therapeutic procedure for patients with degenerative mitral valve regurgitation and follows two fundamental principles: restoring a good coaptation surface of the flap and correcting annular dilation. This study presents a first step in the direction of addressing the influence of valve geometry on valve fluid dynamics and mitral regurgitation. To this end, it develops a systematic analysis to identify how the level of regurgitation and the efficiency of flow transit in the left ventricle depend on the degree of asymmetry of the leaflets. The analysis is performed starting from a mathematically designed mitral valve and then extended to the actual valves extracted from medical imaging. The specific objective is to evaluate the changes in mitral regurgitation associated with the symmetrical properties of the mitral valve. The broader aim is to begin building physics-based means for evaluating repair options and prosthetic design. Results showed that valve shape does not affect flow; sub-volumes are similar to inflow and vary to outflow due to the presence of false regurgitation under healthy/repaired conditions and regurgitation under pathological conditions affecting the amount of direct flow, delayed and finally the Stroke volume. The best valve asymmetry point was found to be 0.25, while the optimal range was between 0.4 and 0.2, giving an important suggestion to valve surgery.

### Air swirl effect on spray characteristics and droplet dispersion in a twin-jet crossflow airblast injector

Spray characterization in a novel twin-jet airblast injector is reported in this paper with the focus on the study of the effect of injector air swirl on droplet characteristics and dispersion behavior. The operational principle of the injector is based on achieving atomization of two liquid jets, injected in a radially opposite direction from a central hub by high-speed annular swirling cross-stream flow of air. Liquid jet atomization within model atomizers and the resulting spray study have not gained much attention in spite of its practical importance, for example, in lean premixed prevaporized combustors. In the present work, droplet size and three-component velocity measurements are measured in the above injector using the phase Doppler particle analyzer technique. Air velocity without liquid injection is also obtained using the laser Doppler velocimetry technique. For given inlet air and liquid mass flow rates, experiments are conducted in the absence and presence of annular air swirl corresponding to swirl number, S = 0 and 0.74, respectively. The addition of air swirl is found to dramatically affect the spray topology and also the measured spray characteristics as the droplet size reduces significantly downstream of the injector exit, which is explained. Droplet dispersion is studied by evaluating droplet size velocity correlation and also droplet Stokes number. The results not only provide insight into the physics behind improved atomization due to air swirl, but also demonstrate the ability of the novel injector to achieve atomization quality and high spray dispersion over a wide operating range.

### Molecular droplets vs bubbles: Effect of curvature on surface tension and Tolman length

Droplets and bubbles are thought to be two sides of the same coin; this work determines how true this is at the molecular scale. Stable cylindrical nanodroplets and nanobubbles are obtained in Molecular Dynamics (MD) simulations with three-phase contact lines pinned by alternate hydrophobic and hydrophilic patterns. The surface tension and Tolman length for both types of curved interfaces are obtained with the Kirkwood–Buff method, based on the difference between normal and tangential pressure components. Both bubble and droplet cases are compared to the flat interface case for reference. Results show that the surface tension decreases linearly while the Tolman length increases linearly with the gas/liquid density ratio. By running a careful parameter study of the flat interface over a range of densities, the effect of the density ratio can be corrected isolating the effects of curvature on the surface tension and Tolman length. It is found that such effects start to be seen when the equimolar curvature radius goes down to 20 reduced Lennard–Jones (LJ) units. They have the same magnitude but act with opposite signs for nanodroplet and nanobubble interfaces. Considering effects of the density ratio and curvature, a fitted Tolman equation was obtained, which predicts the surface tension of a curved interface. Results obtained by the fitted Tolman equation agree well with those obtained by the MD simulations except at very small curvature radius (<10 reduced LJ units) due to the accumulation of the curvature dependence of the Tolman length.

### Numerical simulation on double diffusion natural convection of a power-law nanofluid within double wavy cavity

In the present paper, the effect of double diffusion natural convection fluid flow inside the double wavy enclosure using the mesh-free method is investigated. The enclosure is filled with nanofluid whose base fluid is non-Newtonian. The results are obtained for the variation in Brownian motion parameter ([math]), buoyancy ratio parameter ([math]), power-law index ([math]), thermophoresis parameter ([math]), Rayleigh number ([math]), and Lewis number ([math]) on mass and heat transfer. It is explored that the mass and heat transfer rate increases with increase in the Rayleigh number and buoyancy ratio. Heat transfer rate decreases with increase in the thermophoresis parameter, Lewis number, Brownian motion, and power-law index, whereas mass transfer rate increases. Such type of enclosure has direct application in heat exchanger devices, the double-wall thermal insulation system, and microelectronic devices. Parallel implementation with the hybrid [EFGM (element free Galerkin method)/FEM (finite element method)] method has been used for the reduction of the running cost to ensure efficiency, which is the novel contribution of the author.

### Effect of moving boundaries on the modeling of heat and mass transfer from an evaporating spherical drop

The effect of unsteadiness of the energy and vapor transport within the gas phase from an evaporating drop is studied by solving a moving boundary problem taking into account the effect of drop temperature variation and radius shrinking. The effect of convection is also taken into account in a simplified way by means of the film theory approach, which yields a double moving boundary problem. A proper change of the reference system leads to the numerical solution of a partial differential equation system with fixed boundaries. A comparison with the commonly adopted quasi-steady model allows to point out the effect of ambient temperature and pressure, convection and chemical species, by quantifying the discrepancies between the two predictions for sixteen different compounds, Reynolds number ranging between 0 and 20 and gas pressure up to 20 bar. The simplified approach used in this paper was chosen to maintain the same simplifying assumptions of the widely used quasi-steady model, with the only exception of the drop shrinking. Therefore, the discrepancies between the two predictions can solely be ascribed to the unsteadiness caused by the interface movement, allowing to quantitatively point out this specific effect.

### Publisher's Note: “Recycling and rheology of poly(lactic acid) (PLA) to make foams using supercritical fluid” [Phys. Fluids 33, 067119 (2021)]

### Mechanistic modeling of flow and heat transfer in turbulent–laminar/turbulent gas–liquid stratified flow

Two-phase gas–liquid stratified flow is characterized by a structure in which the gas and liquid phases are separated from each other by a continuous interface. Adequately understanding its flow mechanism and heat transfer is important for analyzing two-phase stratified flow. This paper develops a mechanistic model of flow and heat transfer in turbulent–laminar/turbulent two-phase stratified flow in horizontal and slightly inclined pipes. First, a hydrodynamic model of two-phase stratified flow is developed by using the concept of two-fluid model. Second, a mechanistic model of heat transfer is derived based on the hydrodynamic model. The overall heat transfer coefficient is integrated by using the coefficients of local heat transfer of the liquid film and the gas core. Third, the effect of such flow geometries and parameters as the superficial Reynolds numbers for liquid and superficial gas, void fraction, pressure drop, and inclination angle of the pipe on heat transfer in two-phase stratified flow is comprehensively investigated. Finally, the relationships between the two-phase heat transfer multiplier and the overall void fraction and pressure drop multipliers are quantified. A simple correlation of the heat transfer multiplier for two-phase stratified flow is developed by using the void fraction as the input parameter serving as a quick but rough prediction of the heat transfer multiplier in two-phase stratified flow.

### Electrical explosion across gas–liquid interface: Aerosol breakdown, shock waves, and cavity dynamics

The electrical explosion of a conductor driven by a pulsed current can be used to simulate the effects of explosions in the laboratory, including the resulting shock waves and bubble dynamics. A fine metallic wire can also be used to initiate pulsed discharge in different media. This study shows images of an exploding wire across an air–water interface for the first time in the literature. The transient process was analyzed using high-speed backlit photography as well as waveforms of the spectrum and discharge. Streamer-like discharge developed from a triple-junction point within the current pause to induce a restrike in metallic aerosol, verifying that gas discharge was prevalent in the system. An upward dense plasma jet accompanied by a crown-like water spike was then observed and led to violent plasma–water interactions (mushroom cloud-like cluster) that were examined through a hydrodynamic simulation. The Stark broadening of the Hα line at 656.28 nm suggested that the electron density of the reaction zone could be 1018 cm−3 or higher. The resolved spatial–temporal images revealed that the plasma evolution process (in μs) was much faster than hydrodynamic processes, including damage to the interface and perturbations of the bubbles (in ms). Water, thus, remained in a “rigid” state during the pulsed discharge, and the explosion of the wire in it was not an adiabatic process at a timescale of 102 μs. Recombination and heat loss through the electrode governed the evolution of the post-discharge plasma, and the microscopic images revealed nano-lamellate nucleation on the surface of the electrode.

### The post-impact dynamics of drop rebound on inclined hydrophobic surfaces of various wettabilities

In this work, the post-impact drop motions of the rebound regime on inclined hydrophobic surfaces are investigated using a numerical technique. The effects of impact velocity ([math] = 0.5–1.5 m/s), drop diameter ([math] = 1.0–2.5 mm), surface wettability ([math] = 120°–160°), and inclined angle ([math] = 0°–80°) on the post-impact regimes, contact time ([math]) and spreading time ([math]), nondimensionalized maximum spreading diameter ([math]), and drop displacement prior to the rebound ([math]) are examined and analyzed, some of which exhibit markedly different outcomes at [math] = 80° compared to [math] 60°. It has been discovered that the rebound regime occurs in most impact conditions at [math] = 160° and 140° but transitions to sliding for all [math] = 80° cases at [math] = 120°. When [math] 60°, [math] and [math] of [math] = 160° and 140° are very close and hardly affected by [math] and [math], which are generally smaller than those of [math] = 80°, resulting from the rapid decline of the normal impact velocity that diminishes drop deformation and prolongs drop sliding motion. [math] is barely influenced by [math] but increases with [math] and [math] and decreases when [math] increases owing to a greater normal inertial force. [math] generally increases with [math], [math], and [math] but with different mechanisms. More importantly, the nondimensionalized parameters [math], [math], and [math] are found to scale with the normal or tangential Weber numbers according to the power law, while the exponents vary with [math] and [math].

### Subgrid scale modeling considerations for large eddy simulation of supercritical turbulent mixing and combustion

This paper presents a systematic investigation of large eddy simulation (LES) and subgrid scale (SGS) modeling with application to transcritical and supercritical turbulent mixing and combustion. There remains uncertainty about the validity of extending the LES formalism developed for low-pressure, ideal-gas flows to simulations of high-pressure real-fluid flows. To address this concern, we reexamine the LES theoretical framework and the underlying assumptions in the context of real-fluid mixing and combustion. Two-dimensional direct numerical simulations of nonreacting and reacting mixing layers of gaseous methane and liquid oxygen in the thermodynamically transcritical and supercritical fluid regimes are performed. The computed results are used to evaluate the exact terms in the LES governing equations and associated SGS models. Order of magnitude analysis of the exact filtered and subgrid terms in the LES equations and a priori analysis of the simplifications are performed at different filter widths. It is shown that several of these approximations do not hold for supercritical turbulent mixing. Subgrid scale terms, which are neglected in the LES framework for ideal-gas flows, become significant in magnitude compared to the other leading terms in the governing equations. In particular, the subgrid term arising from the filtering of the real-fluid equation of state is shown to be important.