# Latest papers in fluid mechanics

### Scale dependence and cross-scale transfer of kinetic energy in compressible hydrodynamic turbulence at moderate Reynolds numbers

Author(s): Petr Hellinger, Andrea Verdini, Simone Landi, Emanuele Papini, Luca Franci, and Lorenzo Matteini

Compressible isotropic spectral transfer and Karman-Howarth-Monin equations equivalently quantify different processes in weakly and moderately compressible direct simulations of decaying hydrodynamic turbulence with moderate Reynolds numbers. The simulation results show that pressure dilatation does not lead to a net exchange between the kinetic and internal energies but that it may lead to a cross-scale energy transfer of the kinetic energy.

[Phys. Rev. Fluids 6, 044607] Published Tue Apr 13, 2021

### Scaling effects on the free surface backward facing step flow

A set of large eddy simulations for the free surface backward facing step (FSBFS) are carried out to study wave formation behind the step. The volume-of-fluid ghost fluid method is employed to capture the free surface. Previous studies have indicated that the wave physics depend on the step draught-based Froude number (Fr). For small Fr, the rear face of the step (transom) becomes wet, while for large Fr, the wave separates smoothly from the transom. Close to a critical Fr separating wet and dry transoms, both conditions may occur. Here, we study wet, critical, and dry conditions based on the Fr classification with three different inflow boundary layer profiles ([math]). For Fr = 1.75 (wet conditions), we observe a weak dependence on the ReL. A proper orthogonal decomposition of the velocity field at Fr = 1.75 shows a coherent vortex street forming beneath the free surface. At Fr = 2.66 (critical conditions), we observe that an increase in the ReL results in a decrease in the wavelength and pronounced gas entrainment due to wave breaking. For Fr = 3.17 (dry conditions), we also observe shorter wavelength at increased ReL. Further, in the dry conditions, a breaking wave is noticed to occur at higher ReL, while breaking waves are not observed for the smallest studied ReL. Based on the results, we conclude that the wave shape for FSBFS cannot be characterized by the Froude number alone.

### Surface roughness effect on the shear thinning of non-colloidal suspensions

The shear thinning behavior of non-colloidal suspensions is investigated experimentally with emphasis on the effect of surface roughness of suspending particles. The first shear thinning at a low shear-rate is observed, which originates from particle–particle interaction, and the second shear thinning at a high shear rate is also reported as the polymeric solvent shear thins. Due to the decrease of the size of particle clusters, the viscosity of suspensions decreases in the first shear thinning regime. The surface asperities on rough particles hinders the lubricative interaction between close-contact particles suppressing the growth of clusters, and therefore, the first shear thinning behavior weakens. The shielding of the lubricative interaction also prevents the local shear rate enhancement, corresponding to the suppressions second shear thinning and the rising of a second-order first normal stress difference from the polymeric solvent. A theoretical model describing the first shear thinning behavior of non-colloidal suspension is developed, and the predications agree well with experimental data. The roughness effect on dynamic rheological behavior is also investigated.

### Lattice Boltzmann analysis for electro–thermo-convection with a melting boundary in horizontal concentric annuli

In this paper, we perform a two-dimensional numerical investigation into the electro–thermoconvection with a melting boundary in horizontal concentric annuli filled with a dielectric phase change material. The whole set of coupled equations is solved by lattice Boltzmann method: Navier–Stokes equations, electrohydrodynamics (EHD) equations, and the energy equation. It is found that there exist three regimes during melting with EHD, namely, diffusive regime, thermal convection regime, and electroconvection regime, and the augmentation of melting heat transfer is due to the radial electroconvective flow induced by Coulomb force in the third regime. Moreover, the continuous melting of solid leads to the dynamical transition between the different flow patterns of electro–thermo-convection, as well as the interesting evolutions of temperature and charge density distribution. In different regimes of melting, the liquid fraction fl and Nusselt number Nu follow different power laws. In detail, before the onset of radial flow motion, fl scales as Fo1/2 whereas Nu scales as fl−4/5 (Fo represents the Fourier number), and in the electroconvection dominated regime, we have fl ∼ Fo and Nu ∼ fl0.

### Acoustic radiation force on a free elastic sphere in a viscous fluid: Theory and experiments

An expression was derived from the theory for the acoustic radiation force (ARF) acting on a free spherical particle in a viscous fluid subject to an incident plane wave. In deriving this ARF, the viscosity of the fluid, the elasticity of the particle, and the particle's state when suspended freely in the liquid were considered together. Corresponding experiments were designed and conducted. To compare the ARFs measured in experiments with those predicted by theory, a sphere made of polystyrene was taken as the target particle. Based on experimental and theoretical calculations, the effects of the incident sound pressure amplitude, the frequency of the acoustic wave, and fluid viscosity were analyzed. The analysis showed that the ARF increases with increasing pressure amplitude or dynamic viscosity. There is a series of maxima or minima in the ARF that depends on dimensionless frequency kR. Moreover, the theoretical and experimental values are in good agreement. This work provides an advanced ARF theory that is able to predict real-world behavior more accurately.

### Qian Jian (1939–2018) and his contribution to small-scale turbulence studies

Qian (Tsien) Jian (1939–2018), a Chinese theoretical physicist and fluid dynamicist, devoted the second part of his scientific life to the physical understanding of small-scale turbulence to the exclusion of all else. To place Qian's contribution in an appropriate position in the field of small-scale turbulence, a historical overview and a state-of-the art review are attempted. Qian developed his own statistical theory of small-scale turbulence based on the Liouville [“Sur l'équation aux différences partielles,” J. Math. Pures Appl. 18, 71–72 (1853)] equation and a perturbation variational approach to non-equilibrium statistical mechanics, which is compatible with the Kolmogorov–Oboukhov energy spectrum. Qian's statistical theory of small-scale turbulence, which appears mathematically and physically valid, successfully led to his contributions to (i) the closure problem of turbulence; (ii) one-dimensional turbulence; (iii) two-dimensional turbulence; (iv) the turbulent passive scalar field; (v) the cascade model of turbulence; (vi) the universal equilibrium range of turbulence; (vii) a simple model of the bump phenomenon; (viii) universal constants of turbulence; (ix) the intermittency of turbulence; and perhaps most importantly, and (x) the effect of the Taylor microscale Reynolds number ([math]) on both the width of the inertial range of finite [math] turbulence and the scaling exponents of velocity structure functions. In particular, Qian found that the inertial range cannot exist when [math]. In contrast to the prevailing intermittency models, he discovered that normal scaling is valid in the real Kolmogorov inertial range when [math] approaches infinity while the anomalous scaling observed in experiments reflects the finite [math] effect ([math]). He then made a correction to the famous Kolmogorov [“Dissipation of energy in the locally isotropic turbulence,” Dokl. Akad. Nauk SSSR 32(1), 19–21 (1941c) (in Russian); reprinted in Proc. R. Soc. London A 434, 15–17 (1991)] equation and obtained the finite [math] effect equation or the Kolmogorov–Novikov–Qian equation. He also independently derived the decay law of the finite [math] effect. Qian steered all of us along the right path to an improved understanding of small-scale turbulence and solutions to its problems. Qian is credited with his contribution to enhanced knowledge about the finite [math] effect of turbulence, which has profoundly shaped and stimulated thinking about the K41 turbulence, the K62 turbulence, and the finite [math] turbulence.

### Diffusion modeling of COVID-19 under lockdown

Viral immune evasion by sequence variation is a significant barrier to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine design and coronavirus disease-2019 diffusion under lockdown are unpredictable with subsequent waves. Our group has developed a computational model rooted in physics to address this challenge, aiming to predict the fitness landscape of SARS-CoV-2 diffusion using a variant of the bidimensional Ising model (2DIMV) connected seasonally. The 2DIMV works in a closed system composed of limited interaction subjects and conditioned by only temperature changes. Markov chain Monte Carlo method shows that an increase in temperature implicates reduced virus diffusion and increased mobility, leading to increased virus diffusion.

### Discrete unified gas kinetic scheme simulation of microflows with complex geometries in Cartesian grid

Microscale gas flow attracts significant research interest in recent years since it is concerned with a wide range of engineering applications. It is noted that the Navier–Stokes equations-based scheme and the standard lattice Boltzmann method both encounter a great challenge in the simulation of such flows. The newly developed discrete unified gas kinetic scheme (DUGKS) has been demonstrated to be capable of modeling microflows, but presently it is mainly limited to the problems with straight boundaries. In this study, the ghost-cell (GC) immersed boundary method is introduced to the DUGKS for handling curved boundaries. The most attractive feature of the GC method is to set a ghost point inside the solid domain, at which the information is unknown and will be extrapolated linearly from the corresponding wall and image nodes. As for the two latter points, the distribution functions are first evaluated by the inverse distance weighted (IDW) method and then should be corrected according to the impenetrability condition and Maxwellian diffuse-scattering rule. Three typical test cases, including the plane Poiseuille flow, cylindrical Couette flow and flow through porous media are simulated to validate the present IDW-GC-DUGKS. The results demonstrate the accuracy and feasibility of the method for the gaseous microflows.

### Role of pulsatility on particle dispersion in expiratory flows

Expiratory events, such as coughs, are often pulsatile in nature and result in vortical flow structures that transport respiratory particles. In this work, direct numerical simulation (DNS) of turbulent pulsatile jets, coupled with Lagrangian particle tracking of micron-sized droplets, is performed to investigate the role of secondary and tertiary expulsions on particle dispersion and penetration. Fully developed turbulence obtained from DNS of a turbulent pipe flow is provided at the jet orifice. The volumetric flow rate at the orifice is modulated in time according to a damped sine wave, thereby allowing for control of the number of pulses, duration, and peak amplitude. Thermodynamic effects, such as evaporation and buoyancy, are neglected in order to isolate the role of pulsatility on particle dispersion. The resulting vortex structures are analyzed for single-, two-, and three-pulse jets. The evolution of the particle cloud is then compared to existing single-pulse models. Particle dispersion and penetration of the entire cloud are found to be hindered by increased pulsatility. However, the penetration of particles emanating from a secondary or tertiary expulsion is enhanced due to acceleration downstream by vortex structures.

### Numerical analysis of two hollow drops simultaneously impacting a wet surface

The impingement behaviors of two hollow drops or two continuous dense drops simultaneously impacting a thin liquid film were analyzed numerically using a three-dimensional coupled level-set and volume-of-fraction method. The findings indicate the formation of a counter-jet during the simultaneous impact of two hollow drops, whereas a relatively stable residual film is formed during the impingement of two continuous dense drops. This counter-jet generates heat-transfer blind spots in the case of simultaneous impact by hollow drops, leading to the easy splitting of the residual liquid film. The heat around the blind spot region is difficult to release due to flow stagnation and the squeezing of the initial cold liquid film to the symmetric point. These findings indicate that more focus should be placed on the uniformity of heat transfer in realistic applications involving drop impingement. Finally, analyses of pressure gradient and flow separation revealed the formation process of the counter-jet and central liquid sheet. The findings are valuable for guiding industrial technical practice.

### Spontaneous knotting of a flexible fiber in chaotic flows

Author(s): Benjamin Favier

We consider the problem of an inextensible but flexible fiber advected by a steady chaotic flow, and ask the simple question of whether the fiber can spontaneously knot itself. Using a one-dimensional Cosserat model, a simple local viscous drag model and discrete contact forces, we explore the proba...

[Phys. Rev. E 103, 043101] Published Mon Apr 12, 2021

### Stop-and-go locomotion of superwalking droplets

Author(s): Rahil N. Valani, Anja C. Slim, and Tapio P. Simula

Vertically vibrating a liquid bath at two frequencies, f and f/2, having a constant relative phase difference can give rise to self-propelled superwalking droplets on the liquid surface. We have numerically investigated such superwalking droplets in the regime where the phase difference varies slowl...

[Phys. Rev. E 103, 043102] Published Mon Apr 12, 2021

### Anomalous diffusion in a bench-scale pulsed fluidized bed

Author(s): Jonathan E. Higham, Mehrdad Shahnam, and Avinash Vaidheeswaran

We present our analysis on microrheology of a bench-scale pulsed fluidized bed, which represents a weakly confined system. Nonlinear gas-particle and particle-particle interactions resulting from pulsed flow are associated with harmonic and subharmonic modes. While periodic structured bubble pattern...

[Phys. Rev. E 103, 043103] Published Mon Apr 12, 2021

### Thin film instability driven dimple mode of air film failure during drop impact on smooth surfaces

Author(s): Lige Zhang, Tejaswi Soori, Arif Rokoni, Allison Kaminski, and Ying Sun

Drop impact with a smooth surface can produce a dimple mode of contact due to a combined effect of a capillary wave and a thin film instability.

[Phys. Rev. Fluids 6, 044002] Published Mon Apr 12, 2021

### Macroscale transport in channel-matrix systems via integral transforms

Author(s): B. Ling, C. B. Rizzo, I. Battiato, and F. P. J. de Barros

We develop a semi-analytical solution based on integral transforms (GITT) that can be employed to predict macroscopic transport in channel-matrix shear flows in a computationally efficient manner. We further demonstrate that the newly developed solution enables real-time macroscale concentration estimation in relevant applications.

[Phys. Rev. Fluids 6, 044501] Published Mon Apr 12, 2021

### Propagation and overturning of three-dimensional Boussinesq wave packets with rotation

Author(s): Alain D. Gervais, Quinlan Ede, Gordon E. Swaters, Ton S. van den Bremer, and Bruce R. Sutherland

Simulations of fully localized internal gravity wave packets with their induced mean flow superimposed reveal that waves overturn even for initial amplitudes significantly lower than the critical amplitudes predicted by linear theory, in contrast with previous results of one- and two-dimensional wave packets without rotation.

[Phys. Rev. Fluids 6, 044801] Published Mon Apr 12, 2021

### Investigating the lubrication mechanism and stiffness of oil-based ferrofluids in spur gear drives

Due to both liquid properties and ferromagnetic material characteristics, ferrofluids are developed as the favored component solvents. The art of investigating the lubrication mechanism of ferrofluids in spur gear drives is significant for improving the anti-wear of gear pairs and prolonging the service life. This paper proposes a mathematical model of oil-based ferrofluids lubrication and derives a system of governing equations. The tribology performances of oil-based ferrofluids are investigated in comparison with their counterparts of pure base oil. Furthermore, the effects of ferromagnetic particle size and bulk concentration on the tribological property and film stiffness of oil-based ferrofluids are studied. Finally, the influence of magnetic field intensity is analyzed and discussed. Results show that oil-based ferrofluids induce greater increases in film thickness and film normal stiffness in comparison with their counterparts of pure base oil; the decrease in ferromagnetic particle size causes considerable increases in film thickness and remarkable decreases in friction coefficient; the increase in bulk concentration induces a significant increase in film thickness and a remarkable decrease in friction coefficient, meanwhile the normal stiffness of ferrofluids film maintains stable; the increase in magnetic field intensity causes small increases in film thickness and small reductions in friction coefficient. Therefore, ferrofluids with ferromagnetic particles of small size and large bulk concentration are beneficial to lubrication and anti-wear of magnetized spur gear drives.

### Modification of modal characteristics in wakes of square cylinders with multi-scale porosity

Wake flows behind porous patches are complex and host several spatiotemporal features associated with multi-scale excitation. This is in stark contrast to flow past a square cylinder dominated by nonlinear energy cascade stemming from primary vortex shedding instability. In this study, we analyze wakes created by multi-scale patches containing three iterations while maintaining a constant plan porosity. The results are compared to flows obstructed by a square cylinder and a single-scale patch of uniformly distributed elements from the second iteration having the same footprint. Multi-scale porous patches show a protracted wake having a greater spanwise dimension compared to square cylinder. The characteristics are dependent on the arrangement of elements within the patch which affect the extent of bleed flow through the configuration. Besides, we use proper orthogonal decomposition and dynamic mode decomposition to elucidate instability mechanisms at different scales. Distributions of spatial modes reveal element-scale flow structures in the near-wake region with patch-scale turbulence further downstream. Our analysis confirms manipulation of characteristic scales and the associated high-energy events driven by the arrangement of elements within a given patch despite having the same plan porosity.

### Modeling of combined effects of surface roughness and blowing for Reynolds-averaged Navier–Stokes turbulence models

A new modeling strategy adapted to Reynolds-averaged Navier–Stokes turbulence models is proposed to predict combined effects of roughness and blowing boundary conditions. First, an analysis of experimental data is presented, leading to a specific description of the velocity profile in the logarithmic region of transpired turbulent boundary layers over rough walls. This analysis points out the deficiencies of existing roughness corrections to predict the effect of blowing in the presence of surface roughness. Indeed, these corrections tend to underestimate skin friction coefficients and Stanton numbers with the addition of blowing. The failure of existing models derives from an inaccurate estimation of the velocity shift of the logarithmic law given by roughness corrections. Concretely, roughness corrections underestimate the apparent velocity shift of the logarithmic law with blowing. To recover the expected law of the wall, an additional contribution on the velocity shift, characterizing blowing/roughness interactions, is integrated to standard roughness corrections. To that end, a modification of the equivalent sand grain height, adapted to [math] based turbulence models, is proposed to take blowing effects into account. Furthermore, an extension of Aupoix's thermal correction [B. Aupoix, Int. J. Heat Fluid Flow 56, 160–171 (2015)] to blowing is presented to predict combined thermal effects of roughness and blowing. The assessment of the proposed corrections is performed using [math] shear stress transport model on a large set of experimental data and proves the relevance of the strategy for incompressible and compressible turbulent boundary layers.

### Antibacterial effects of combined non-thermal plasma and photocatalytic treatment of culture media in the laminar flow mode

Acceleration of antibacterial properties is the targeted fashion of the recent part of our project by studying different techniques, on the culture media of E. coli., including the non-thermal effect using atmospheric pressure plasma jet (APPJ) and the non-thermal effects combined with the photocatalytic effects using APPJ coupled with a titanium dioxide TiO2 precursor. The electrical, non-thermal, and optical characteristics of the laminar and turbulent mode flow of a dry argon discharge afterglow using APPJ were vital in the study of the antibacterial properties, with the measured characteristics in the laminar mode flow as follows: frequency 25 kHz; applied voltage 11.2 kV; flow rate, 2.4 slm; power, 2.34 W; jet temperature, 340 K; jet length, 11.5 mm; jet width, 1.6 mm; energy, 96 mJ; and Reynolds number, 2819. Under all the measured characteristics of maximum laminar flow mode with the flow rate, 2.4 slm, the optical emission spectroscopy data of APPJ for dry Ar discharge and for wet argon (coupled with TiO2 precursor with the emerging jet) were measured. Survival curves of live microbes confirmed that as TiO2 precursor concentration increases in the range from 0 to 0.5 g l−1, the deactivation rate of E. coli increases due to the photocatalytic disinfection performance, because of the TiO2 precursor concentrations dosage enhances the effect of the incident plume of the non-thermal jet, leading to the generation of more active substances that can be absorbed by the cells causing acceleration of the sterilization efficiency.