# Latest papers in fluid mechanics

### Hidden scale invariance of intermittent turbulence in a shell model

Author(s): Alexei A. Mailybaev

A study shows that the shell model of turbulence has a hidden scaling symmetry, which involves nonlinear transformations of shell speeds and time. This symmetry is restored statistically in the developed turbulence despite all original scaling symmetries being broken by the intermittency.

[Phys. Rev. Fluids 6, L012601] Published Mon Jan 04, 2021

### Spectral energy transfers and kinetic-potential energy exchange in rotating stratified turbulence

Author(s): Tianyi Li, Minping Wan, Jianchun Wang, and Shiyi Chen

Rotating stratified turbulence is of great importance for geophysical flows and industrial applications. Here, the effects of different stratification on energy transfers across scales and kinetic-potential energy exchange in the inverse cascade range are addressed. Moreover, the issue of scale locality in rotating stratified turbulence is studied.

[Phys. Rev. Fluids 5, 124804] Published Thu Dec 31, 2020

### Dynamical heterogeneities in non-entangled polystyrene and poly(ethylene oxide) star melts

Star polymers can exhibit a heterogeneous dynamical behavior due to their internal structure. In this work, we employ atomistic molecular dynamics simulations to study translational motion in non-entangled polystyrene and poly(ethylene oxide) star-shaped melts. We focus on the local heterogeneous dynamics originating from the multi-arm star-like architecture and quantify the intramolecular dynamical gradient. By examining the translational motion at length scales of the order of the Kuhn length, we aim at finding common features for both studied chemistries and at providing a critical and direct comparison with theoretical models of polymer dynamics. We discuss the observed tendencies with respect to the continuous Rouse model adjusted for the star-like architectures. Two versions of the Rouse model are examined: one assuming uniform friction on every Rouse bead and another one considering larger branch point friction. Apart from chain connectivity between neighboring beads, both versions disregard interactions between the chains. Despite the tolerable description of the simulation data, neither model appears to reflect the mobility gradient accurately. The detailed quantitative atomistic models employed here bridge the gap between the theoretical and general, coarse-grained models of star-like polymers, which lack the indispensable chemical details.

### Dynamical heterogeneities in non-entangled polystyrene and poly(ethylene oxide) star melts

Star polymers can exhibit a heterogeneous dynamical behavior due to their internal structure. In this work, we employ atomistic molecular dynamics simulations to study translational motion in non-entangled polystyrene and poly(ethylene oxide) star-shaped melts. We focus on the local heterogeneous dynamics originating from the multi-arm star-like architecture and quantify the intramolecular dynamical gradient. By examining the translational motion at length scales of the order of the Kuhn length, we aim at finding common features for both studied chemistries and at providing a critical and direct comparison with theoretical models of polymer dynamics. We discuss the observed tendencies with respect to the continuous Rouse model adjusted for the star-like architectures. Two versions of the Rouse model are examined: one assuming uniform friction on every Rouse bead and another one considering larger branch point friction. Apart from chain connectivity between neighboring beads, both versions disregard interactions between the chains. Despite the tolerable description of the simulation data, neither model appears to reflect the mobility gradient accurately. The detailed quantitative atomistic models employed here bridge the gap between the theoretical and general, coarse-grained models of star-like polymers, which lack the indispensable chemical details.

### Experimental investigation of the return flow instability in magnetized spherical Couette flows

We conduct magnetized spherical Couette (MSC) flow experiments in the return flow instability regime with GaInSn as the working fluid, the ratio of the inner to the outer sphere radii ri/ro = 0.5, the Reynolds number Re = 1000, and the Hartmann number Ha ∈ [27.5, 40]. Rotating waves with different azimuthal wavenumbers m ∈ {2, 3, 4} manifest in certain ranges of Ha in the experiments, depending on whether the values of Ha were fixed or varied from different initial values. These observations demonstrate the multistability of rotating waves, which we attribute to the dynamical system representing the state of the MSC flow tending to move along the same solution branch of the bifurcation diagram when Ha is varied. In experiments with both fixed and varying Ha, the rotation frequencies of the rotating waves are consistent with the results of nonlinear stability analysis. A brief numerical investigation shows that differences in the azimuthal wavenumbers of the rotating waves that develop in the flow also depend on the azimuthal modes that are initially excited.

### Inertial migration of a deformable capsule in an oscillatory flow in a microchannel

Author(s): Ali Lafzi, Amir Hossein Raffiee, and Sadegh Dabiri

Dynamics of a deformable capsule in an oscillatory flow of a Newtonian fluid in a microchannel has been studied numerically. The effects of oscillation frequency, capsule deformability, and channel flow rate have been explored by simulating the capsule within a microchannel. In addition, the simulat...

[Phys. Rev. E 102, 063110] Published Wed Dec 30, 2020

### Strong shock as a stringent test for Onsager-Burnett equations

Author(s): Ravi Sudam Jadhav and Amit Agrawal

A new set of thermodynamically consistent Onsager-Burnett equations [Singh, Jadhav, and Agrawal, Phys. Rev. E **96**, 013106 (2017)] has recently been derived. In this work, we subject these equations to a severe test case of strong shock (Mach number = 134) for a dilute gas system composed of hard-sphe...

[Phys. Rev. E 102, 063111] Published Wed Dec 30, 2020

### Pattern formation of the three-layer Saffman-Taylor problem in a radial Hele-Shaw cell

Author(s): M. Zhao, Pedro H. A. Anjos, J. Lowengrub, and Shuwang Li

Nonlinear simulations are utilized to investigate the viscous fingering formation in a three-layer radial Hele-Shaw cell. The two interfaces of this system are coupled, and the initial distance between them has a great impact on the interfacial morphologies. This work supplements previous studies, which examined the system via linear and weakly nonlinear analyses.

[Phys. Rev. Fluids 5, 124005] Published Wed Dec 30, 2020

### Comment on “Evolution of wall shear stress with Reynolds number in fully developed turbulent channel flow experiments”

Author(s): R. Örlü and P. Schlatter

The recent study by Gubian *et al.* [Phys. Rev. Fluids **4**, 074606 (2019)], based on a new wall-shear-stress sensor in a low-Reynolds-number Re turbulent channel flow, came to the surprising conclusion that the magnitude of the fluctuating wall-shear stress τw,rms+ reaches an asymptotic value of 0.44 be...

[Phys. Rev. Fluids 5, 127601] Published Wed Dec 30, 2020

### Reply to “Comment on ‘Evolution of wall shear stress with Reynolds number in fully developed turbulent channel flow experiments' ”

Author(s): Pierre-Alain Gubian, Jordan Stoker, James Medvescek, Laurent Mydlarski, and B. Rabi Baliga

Örlü and Schlatter [R. Örlü and P. Schlatter, preceding Comment, Phys. Rev. Fluids **5**, 127601 (2020)] claim that the evolution of the turbulent intensity of the wall-shear stress (τwRMS/〈τw〉) to a constant value at sufficiently large Reynolds number in our previous work [P.-A. Gubian *et al.*, Phys. R...

[Phys. Rev. Fluids 5, 127602] Published Wed Dec 30, 2020

### Insights on drying and precipitation dynamics of respiratory droplets from the perspective of COVID-19

We isolate a nano-colloidal droplet of surrogate mucosalivary fluid to gain fundamental insights into airborne nuclei’s infectivity and viral load distribution during the COVID-19 pandemic. The salt-water solution containing particles at reported viral loads is acoustically trapped in a contactless environment to emulate the drying, flow, and precipitation dynamics of real airborne droplets. Similar experiments validate observations with the surrogate fluid with samples of human saliva samples from a healthy subject. A unique feature emerges regarding the final crystallite dimension; it is always 20%–30% of the initial droplet diameter for different sizes and ambient conditions. Airborne-precipitates nearly enclose the viral load within its bulk while the substrate precipitates exhibit a high percentage (∼80–90%) of exposed virions (depending on the surface). This work demonstrates the leveraging of an inert nano-colloidal system to gain insights into an equivalent biological system.

### Insights on drying and precipitation dynamics of respiratory droplets from the perspective of COVID-19

We isolate a nano-colloidal droplet of surrogate mucosalivary fluid to gain fundamental insights into airborne nuclei’s infectivity and viral load distribution during the COVID-19 pandemic. The salt-water solution containing particles at reported viral loads is acoustically trapped in a contactless environment to emulate the drying, flow, and precipitation dynamics of real airborne droplets. Similar experiments validate observations with the surrogate fluid with samples of human saliva samples from a healthy subject. A unique feature emerges regarding the final crystallite dimension; it is always 20%–30% of the initial droplet diameter for different sizes and ambient conditions. Airborne-precipitates nearly enclose the viral load within its bulk while the substrate precipitates exhibit a high percentage (∼80–90%) of exposed virions (depending on the surface). This work demonstrates the leveraging of an inert nano-colloidal system to gain insights into an equivalent biological system.

### Hybrid continuum-molecular modeling of fluid slip flow

Experiments on fluid systems in micro-/nano-scale solid conveyors have shown a violation of the no-slip assumption that has been adopted by the classical fluid mechanics. To correct this mechanics for the fluid slip, various approaches have been proposed to determine the slip boundary conditions. However, these approaches have revealed contradictory results for a variety of systems, and a debate on the mechanisms and the conditions of the fluid slip/no-slip past solid surfaces is sustained for a long time. In this paper, we establish the hybrid continuum-molecular modeling (HCMM) as a general approach of modeling the fluid slip flow under the influence of excess fluid–solid molecular interactions. This modeling approach postulates that fluids flow over solid surfaces with/without slip depending on the difference between the applied impulse on the fluid and a drag due to the excess fluid–solid molecular interactions. In the HCMM, the Navier–Stokes equations are corrected for the excess fluid–solid interactions. Measures of the fluid–solid interactions are incorporated into the fluid’s viscosity. We demonstrate that the correction of the fluid mechanics by the slip boundary conditions is not an accurate approach, as the fluid–solid interactions would impact the fluid internally. To show the effectiveness of the proposed HCMM, it is implemented for the water flow in nanotubes. The HCMM is validated by an extensive comparison with over 90 cases of experiments and molecular dynamics simulations of different fluid systems. We foresee that the HCMM of the fluid slip flow will find many important implementations in fluid mechanics.

### A microstructure model for viscoelastic–thixotropic fluids

A microstructure model to describe the viscoelasticity and thixotropy properties of complex fluids is proposed. The model is based on the Lodge–Yamamoto network theory and is an extension of the Phan-Thien–Tanner model, with a kinetic process in which specific forms of creation and destruction rates are assumed. The final equation is simple with a small number of empirical parameters required and can be conveniently employed in engineering simulations. The predictions based on the model in a variety of shear and oscillatory shear flows are given. The stress response obtained from the model prediction agrees well with experiments on both shear and oscillatory flow histories.

### A comparative study of quasi-stable sheet cavities at different stages based on fast synchrotron x-ray imaging

The cavitating flows in a small convergent–divergent channel are studied experimentally using a fast synchrotron x-ray imaging method that enables simultaneous acquisition of the velocity and void fraction fields as well as the two-phase morphology inside the opaque cavitation areas. According to the x-ray measurement results, the quasi-stable sheet cavitation is classified into three representative stages based on the status of the re-entrant flow: (i) at the early stage, the incipient cavity is short and no reverse flow is observed, (ii) at the intermediate stage, an intermittent re-entrant flow is identified underneath the sheet cavity, and (iii) at the developed stage, the re-entrant flow becomes continuous and it can penetrate the entire sheet cavity. The comparison of the three typical sheet cavities illustrates that the occurrence of the re-entrant flow does not result in the transition of sheet-to-cloud cavitation, but it influences the distribution of the mean void fraction and the spectrum of the void fraction variation. The development of cavitation also influences the turbulent velocity fluctuations. On one hand, cavitation alters mean velocity field, which affects velocity fluctuations due to the positive correlation between the velocity gradient and turbulence intensity. One the other hand, the presence of vapor/liquid mixture is observed to greatly suppress velocity fluctuations. The collapse of small vapor structures does not cause an evident augmentation of streamwise velocity fluctuations but increases the shear stress significantly.

### Giant plasmonic bubbles nucleation under different ambient pressures

Author(s): Binglin Zeng, Yuliang Wang, Mikhail E. Zaytsev, Chenliang Xia, Harold J. W. Zandvliet, and Detlef Lohse

Water-immersed gold nanoparticles irradiated by a laser can trigger the nucleation of plasmonic bubbles after a delay time of a few microseconds [Wang *et al.*, Proc. Natl. Acad. Sci. USA **122**, 9253 (2018)]. Here we systematically investigated the light-vapor conversion efficiency, *η*, of these plasmoni...

[Phys. Rev. E 102, 063109] Published Tue Dec 29, 2020

### Effects of surface proximity and force orientation on the feeding flows of microorganisms on solid surfaces

Author(s): Mads Rode, Giulia Meucci, Kristian Seegert, Thomas Kiørboe, and Anders Andersen

Many aquatic microorganisms attach to solid surfaces while creating feeding flows that bring prey particles to them. A theoretical exploration quantifies the flow structures, clearance rates, and recirculation times in such flows using a simple low-Reynolds-number flow model.

[Phys. Rev. Fluids 5, 123104] Published Tue Dec 29, 2020

### Heat transfer enhancement in Rayleigh-Bénard convection using a single passive barrier

Author(s): Shuang Liu and Sander G. Huisman

Efficient thermal transport using passive means is highly desirable for many technological applications. A numerical study of Rayleigh-Bénard convection with a single passive conductive barrier over a broad range of barrier geometric parameters is presented, aiming to control the thermal transport and flow organization. It is found that, although the resistance induced by the barrier always reduces the flow strength, the global heat transfer can be markedly enhanced because of the funneling of the ascending hot plumes and descending cold plumes and the modifications of boundary layer properties.

[Phys. Rev. Fluids 5, 123502] Published Tue Dec 29, 2020

### Scale-by-scale kinetic energy budget near the turbulent/nonturbulent interface

Author(s): T. Watanabe, C. B. da Silva, and K. Nagata

A scale-by-scale energy budget is investigated near the turbulent–nonturbulent interfacial layer with direct numerical simulations of a local turbulent front evolving without mean shear. The forward interscale energy transfer is caused by the velocity gradient in the interface normal direction. The pressure diffusion removes the energy at small scales within the interfacial layer.

[Phys. Rev. Fluids 5, 124610] Published Tue Dec 29, 2020

### Unsteady flow of Carreau fluids around an impulsively moving cylinder

Unsteady flow of Carreau fluids around an impulsively moving circular cylinder is numerically investigated in this study. Both shear-thinning and shear-thickening fluids are used with the range of the power-index number 0.4 ≤ n ≤ 2. Unsteady laminar flow with the influence of shear-dependent viscosity and impulsive motions of the cylinder are analyzed with various Carreau numbers 10 ≤ Cu ≤ 40 and Reynolds numbers 10 ≤ Re ≤ 100. Both starting and stopping flows are numerically simulated. Systematic validation is conducted for current numerical approaches using literature data before the investigation of the unsteady flow. The effects of major Carreau fluid flow parameters, namely, n, Cu, and Re, on the unsteady vortical flow are studied with a focus on the formation of vortices, zero-shear point on the cylinder, and transitory hydrodynamic loads. In general, increased shear-thickening (n > 1 with higher Cu and lower Re) leads to higher viscous effect, delaying the formation of additional vortices and promoting the drag force due to the dominant viscous drag. More interesting flow aspects are noticed with shear-thinning fluids. Increased shear-thinning (n < 1 with higher Cu and higher Re) results in complicated vortical flow including secondary, tertiary, quaternary vortices, and even more. Highly oscillated drag force is obtained in such vortical flow due to the oscillated pressure drag, which dominates the total drag in the current unsteady flow. It is expected that the results reported in this study could be used for a better understanding of unsteady non-Newtonian fluid flow and for the validation of numerical simulation of unsteady non-Newtonian fluid flow.