# Latest papers in fluid mechanics

### Oscillatory Couette flow of rarefied binary gas mixtures

The oscillatory Couette flow of binary gas mixtures is numerically investigated on the basis of the McCormack model. The dependence of the velocity and shear stress amplitudes and the penetration depth on the gas rarefaction and the oscillation parameters is studied numerically. Two typical mixtures of noble gases, i.e., a neon–argon (Ne–Ar) mixture with a molecular mass ratio less than 2 and a helium–xeon (He–Xe) mixture with a molecular mass ratio of about 32, are considered to explore the influences of the molecular mass ratio and molar concentration. It is found that the Ne–Ar mixture exhibits similar behavior with a single gas, while significant deviations can be observed between a single gas and the He–Xe mixture. Particularly when the gases are in the transitional and near-continuum regimes and the oscillation frequency is high, the amplitudes of velocity and shear stress for the He–Xe mixture vary non-monotonically between the plates as the molar concentration of the light species He exceeds 50% due to the oscillation superposition of the two species. These findings are helpful to design the structure of micro-electromechanical devices.

### Rayleigh-Taylor instability in elastic-plastic solid slabs bounded by a rigid wall

Author(s): S. A. Piriz, A. R. Piriz, N. A. Tahir, S. Richter, and M. Bestehorn

The linear evolution of the incompressible Rayleigh-Taylor instability for the interface between an elastic-plastic slab medium and a lighter semi-infinite ideal fluid beneath the slab is developed for the case in which slab is attached to a rigid wall at the top surface. The theory yields the maps ...

[Phys. Rev. E 103, 023105] Published Wed Feb 10, 2021

### Unsteady mass transfer from a core-shell cylinder in crossflow

Author(s): Clément Bielinski, Nam Le, and Badr Kaoui

Computer simulations are used to study mass transfer from a stationary composite cylinder—made of an inner, initially loaded, core and an outer-coating semipermeable shell—subjected to a crossflow. The transition from steady to unsteady laminar flow regime alters the released solute spatial distribution and the mass transfer efficiency (Sherwood number), which is found to depend explicitly on the shell solute permeability. The cylinder internal structure and the initial condition considered in this study differ and, thus, complement classical studies dealing with homogeneous uncoated cylinders for which surfaces are sustained at either constant concentration or constant mass flux.

[Phys. Rev. Fluids 6, 023501] Published Wed Feb 10, 2021

### Singular behavior of microfluidic pulsatile flow due to dynamic curving of air-fluid interfaces

Author(s): Pamela Vazquez-Vergara, Ulises Torres-Herrera, Luis F. Olguin, and Eugenia Corvera Poiré

A theoretical and experimental study shows that the coupled effect of interfaces and pulsatile forcing of fluid slugs, at microscales, allows for controlling the magnitude of flow velocity by simply changing the frequency of the driving. This behavior, which at low frequencies, is radically different from that of a single fluid, could potentially be exploited in organ-on-a-chip devices to tune the physiological mechanical conditions of cells, or to study how cells would respond to various nonphysiological stresses.

[Phys. Rev. Fluids 6, 024003] Published Wed Feb 10, 2021

### Simple model for mean stress in turbulent boundary layers

Author(s): Praveen Kumar and Krishnan Mahesh

The governing equations for mean flow and available turbulent databases are used to derive a model for the mean shear stress in turbulent boundary layers. The model requires mean wall-normal velocity, for which a simple and compact fit is derived using existing data and scaling arguments. The model shows good agreement with available data over a range of Reynolds number.

[Phys. Rev. Fluids 6, 024603] Published Wed Feb 10, 2021

### Marangoni-driven instability patterns of an N-hexadecane drop triggered by assistant solvent

Flows of thin fluid layers spreading, which have a distinguished history, have been studied since the days of Reynolds, who was among the early researchers to examine flows. Different from surfactant-driven spreading, which is currently the most common subject of study, we observe the spreading process of n-hexadecane driven by volatile silicone oil at the surface of the aqueous substrates and explore the influence of Marangoni flow caused by surface tension gradient on liquid-driven spreading. We find that on different substrates, the initial state of n-hexadecane is different, and there are two instability patterns during the spreading, subsequently, which are analyzed theoretically. While the n-hexadecane drop stationed on the liquid surface is small, it is driven to form a rim and then breaks up into beads, which shows the Rayleigh–Plateau instability patterns. When we put the n-hexadecane drop on the surface of the saturated sodium chloride solution, which spreads out more, it is driven to form a circular belt first and fingering instability subsequently occurs at the inner edge of the circular belt.

### A conservative and consistent scalar filtered mass density function method for supersonic flows

A novel scalar filtered mass density function (SFMDF) method is developed for high-speed flows, especially for supersonic reactive flows. The total energy is proposed as the energy form for SFMDF, instead of the commonly used enthalpy or sensible enthalpy. Such an energy form is entirely consistent with the one typically used in large eddy simulation (LES) for fully compressible flows, so that the exact/modeled energy equations in both LES and SFMDF are readily identical. Moreover, the total energy can formulate the SFMDF energy transport equation in such a way that the high-speed source term is strictly conservative. Following the conservative formulation, numerically robust conservative schemes are readily available for flows with discontinuities. Tests in one-dimensional Euler equations show that the temperature redundantly obtained based on the total energy (with conservative high-speed source terms) shows better agreement with the analytical result than the one based on the enthalpy. The proposed LES-SFMDF method is further tested in a shock tube interacting with an isotropic turbulent flow, a compressible two-dimensional non-reactive temporally developing mixing layer, and a supersonic three-dimensional reactive temporally developing mixing layer. Results show that SFMDF with the total energy can considerably improve the temperature distribution in both non-reactive and reactive flows. The proposed LES-SFMDF method with the total energy predicts the turbulence–chemistry interaction better than LES-SFMDF with the enthalpy as well as LES with the well-stirred reactor model in supersonic combustion. This conservative and consistent SFMDF method can be readily extended to more sophisticated probability density function methods in high-speed flows.

### An experimental investigation of the viscosity behavior of solutions of nanoparticles, surfactants, and electrolytes

Several studies have reported that the viscosity profile of nanofluids has a similar trend to electrolytes. This behavior is attributed to the complex interactions of the ions of nanoparticles (NPs) with the ions of aqueous solutions. Recently, laboratory experiments have shown that nanofluids are suitable candidates for enhanced oil recovery in different reservoirs. The improvement in oil recovery during nanofluid injection is attributed to the wettability alteration, interfacial tension reduction, and viscosity modification. Low salinity water and surfactants are used to stabilize and prevent the aggregation of NPs, which are injected into the reservoir. However, the interactions between the reservoir/injected fluids with NPs alter the properties of the fluid. The complex interactions among the ions present in the solutions of NPs, surfactants, and electrolytes (NSE) that result in the viscosity modification are not completely understood. Therefore, this work presents a detailed study on the complex interactions existing between the ions of NPs and other ions of aqueous solution present in the reservoir fluid using the dynamic light scattering, transmission electron microscopy, and Fourier transform infrared spectroscopy techniques to understand the viscosity behavior of NSE solutions. The viscosity profile of NSE solutions with increasing concentration of NPs has the same trend as aqueous solutions, while that with increasing concentration of the sodium dodecyl sulfate surfactant behaves like spherical particles. The explained mechanisms behind the viscosity behavior of NSE solutions in this study can improve the optimization design for nanofluid injection into the reservoir.

### Characterizing pore-scale structure-flow correlations in sedimentary rocks using magnetic resonance imaging

Author(s): K. Karlsons, D. W. de Kort, A. J. Sederman, M. D. Mantle, J. J. Freeman, M. Appel, and L. F. Gladden

Quantitative, three-dimensional (3D) spatially resolved magnetic resonance flow imaging (flow MRI) methods are presented to characterize structure-flow correlations in a 4-mm-diameter plug of Ketton limestone rock using undersampled **k**- and **q**-space data acquisition methods combined with compressed se...

[Phys. Rev. E 103, 023104] Published Tue Feb 09, 2021

### Dynamics of a compound droplet under the combined influence of electric field and shear flow

Author(s): Manash Pratim Borthakur, Binita Nath, and Gautam Biswas

The work demonstrates the dynamics of a compound droplet under the combined influence of an applied electric field and shear flow. For the case of dielectric fluids, the deformation of both the inner and outer interfaces can be modulated by either variation of the permittivity contrast between the fluids or the applied electric field. The investigations for leaky dielectric fluids reveal that the ratio of electrical permittivity and conductivity between the two phases play a critical role in deciding the magnitude of deformation and orientation of the compound droplet. The electric field can be suitably applied to engender breakup of the compound

[Phys. Rev. Fluids 6, 023603] Published Tue Feb 09, 2021

### Simulation-based study of COVID-19 outbreak associated with air-conditioning in a restaurant

COVID-19 has shown a high potential of transmission via virus-carrying aerosols as supported by growing evidence. However, detailed investigations that draw direct links between aerosol transport and virus infection are still lacking. To fill in the gap, we conducted a systematic computational fluid dynamics (CFD)-based investigation of indoor airflow and the associated aerosol transport in a restaurant setting, where likely cases of airflow-induced infection of COVID-19 caused by asymptomatic individuals were widely reported by the media. We employed an advanced in-house large eddy simulation solver and other cutting-edge numerical methods to resolve complex indoor processes simultaneously, including turbulence, flow–aerosol interplay, thermal effect, and the filtration effect by air conditioners. Using the aerosol exposure index derived from the simulation, we are able to provide a spatial map of the airborne infection risk under different settings. Our results have shown a remarkable direct linkage between regions of high aerosol exposure index and the reported infection patterns in the restaurant, providing strong support to the airborne transmission occurring in this widely reported incident. Using flow structure analysis and reverse-time tracing of aerosol trajectories, we are able to further pinpoint the influence of environmental parameters on the infection risks and highlight the need for more effective preventive measures, e.g., placement of shielding according to the local flow patterns. Our research, thus, has demonstrated the capability and value of high-fidelity CFD tools for airborne infection risk assessment and the development of effective preventive measures.

### Why coronavirus survives longer on impermeable than porous surfaces

Previous studies reported that the drying time of a respiratory droplet on an impermeable surface along with a residual film left on it is correlated with the coronavirus survival time. Notably, earlier virus titer measurements revealed that the survival time is surprisingly less on porous surfaces such as paper and cloth than that on impermeable surfaces. Previous studies could not capture this distinct aspect of the porous media. We demonstrate how the mass loss of a respiratory droplet and the evaporation mechanism of a thin liquid film are modified for the porous media, which leads to a faster decay of the coronavirus on such media. While diffusion-limited evaporation governs the mass loss from the bulk droplet for the impermeable surface, a much faster capillary imbibition process dominates the mass loss for the porous material. After the bulk droplet vanishes, a thin liquid film remaining on the exposed solid area serves as a medium for the virus survival. However, the thin film evaporates much faster on porous surfaces than on impermeable surfaces. The aforesaid faster film evaporation is attributed to droplet spreading due to the capillary action between the contact line and fibers present on the porous surface and the modified effective wetted area due to the voids of porous materials, which leads to an enhanced disjoining pressure within the film, thereby accelerating the film evaporation. Therefore, the porous materials are less susceptible to virus survival. The findings have been compared with the previous virus titer measurements.

### Three-dimensional spectral proper orthogonal decomposition analyses of the turbulent flow around a seal-vibrissa-shaped cylinder

The flow around a seal-vibrissa-shaped cylinder (SVSC) is numerically investigated using the large eddy simulation framework at a Reynolds number of 20 000. Compared with a circular cylinder (CC), the wake of the SVSC presents more stable three-dimensional separation, a longer vortex formation length, and a weaker vortex strength. The mean drag and fluctuation of the lift coefficient are 59.5% and 87.7% lower than those of the CC, respectively. Three-dimensional spectral proper orthogonal decomposition (SPOD) is used to investigate the turbulent flow around these two types of cylinders in terms of the spatial modes, mode energy, mode coefficients, and reconstructed flow by a reduced-order modeling. Four typical vortex shedding patterns are first extracted by SPOD for the SVSC, producing crescent-, twist-, branch-, and knot-shaped vortices. A concept model is proposed for the wake dynamics of the SVSC, allowing the formation and transformation of these modes to be elucidated. Detailed analysis of the impact of the flow pattern on the associated forces indicates that the dominant out-phase vortex shedding at the upper and lower saddle planes makes a significant contribution to the reduction in lift fluctuations.

### Effects of wing-to-body mass ratio on insect flapping flights

Bio-flyers of insects, birds, and bats are observed to have a broad range of wing-to-body mass ratio (WBMR) from 0.1% to 15%. The WBMR and wing mass distribution can lead to large inertial forces and torques in fast-flapping wings, particularly in insect flights, comparable with or even greater than aerodynamic ones, which may greatly affect the aerodynamic performance, flight stability, and control, but still remain poorly understood. Here, we address a simulation-based study of the WBMR effects on insect flapping flights with a specific focus on unraveling whether some optimal WBMR exists in balancing the flapping aerodynamics and body control in terms of body pitch oscillation and power consumption. A versatile, integrated computational model of hovering flight that couples flapping-wing-and-body aerodynamics and three degree of freedom body dynamics was employed to analyze free-flight body dynamics, flapping aerodynamics, and power cost for three typical insects of a fruit fly, a bumblebee, and a hawkmoth over a wide range of Reynolds numbers (Re) and WBMRs. We found that the realistic WBMRs in the three insect models can suppress the body pitch oscillation to a minimized level at a very low cost of mechanical power. We further derived a scaling law to correlate the WBMR with flapping-wing kinematics of stroke amplitude (Φ), flapping frequency (f), and wing length (R) in terms of [math], which matches well with measurements and, thus, implies that the WBMR-based body pitch minimization may be a universal mechanism in hovering insects. The realistic WBMR likely offers a novel solution to resolve the trade-off between body-dynamics-based aerodynamic performance and power consumption. Our results indicate that the WBMR plays a crucial role in optimization of flapping-wing dynamics, which may be useful as novel morphological intelligence for the biomimetic design of insect- and bird-sized flapping micro-aerial vehicles.

### Computational analysis of obstructive disease and cough intensity effects on the mucus transport and clearance in an idealized upper airway model using the volume of fluid method

This study provides a quantitative analysis to investigate the effects of cough intensity and initial mucus thickness on the mucus transport and clearance in a mouth-to-trachea airway geometry using an experimentally validated Volume of Fluid (VOF) based multiphase model. In addition, the accuracy of simplifying mucus as Newtonian fluid is also quantified by the comparisons of mucus transport and clearance efficiencies with the simulations using realistic shear-thinning non-Newtonian fluid viscosities as a function of shear rate. It proves that the VOF model developed in this study can capture air–mucus interface evolution and predict the mucus transport behaviors driven by the expiratory cough waveforms. Numerical results show that noticeable differences can be identified between the simulations using simplified Newtonian fluid and the realistic non-Newtonian fluid viscosity models, which indicates that an appropriate non-Newtonian fluid model should be applied when modeling mucus transport to avoid the possible inaccuracy induced by the Newtonian fluid simplification. Furthermore, the results also indicate that an intense cough can enhance the mucus clearance efficiency in chronic obstructive pulmonary disease (COPD) upper airways. Additionally, although higher mucus clearance efficiency is observed for severe COPD conditions with a thicker mucus layer, there is a possibility of mucus accumulation and obstruction in the upper airway for such a COPD condition if the cough is not strong enough, which will possibly cause further breathing difficulty. The VOF model developed in this study can be further refined and integrated with discrete phase models to predict the mucus clearance effect on inhaled particles explicitly.

### Enhanced air stability of superhydrophobic surfaces with flexible overhangs of re-entrant structures

The stability of air plastron entrapped in a submerged superhydrophobic (SHPo) surface determines the sustainability of the surface properties including drag reduction, self-cleaning, and anti-icing. To increase the stability for high water pressure, various microstructures have been adopted for SHPo surfaces. A re-entrant structure is a typical example to provide high stability for air plastrons. This work proposes flexible overhangs of the re-entrant structures as a new strategy for additional stability. Several SHPo surfaces with re-entrant structures of different sizes are fabricated, and their Young's moduli (E) are controlled from 715.3 kPa to 2509 kPa. Pressurization of water and air diffusion from the plastrons to the surrounding water cause deformation of the air–water meniscus until air plastron disruption starts to occur. The critical water pressure for air plastron disruption is gradually increased as the E of the overhangs decreases. The critical value is also increased as the gap distance between the adjacent overhangs increases. When the water pressure is less than the critical value, the air plastron is also gradually disrupted by the air diffusion. The lifetime elapsed to the air disruption increases by 19%–44% as the value of E decreases. The present results would pave the way for utilizing flexible overhangs of re-entrant structures as a novel approach for increasing the air stability of SHPo surfaces.

### How <i>Euglena gracilis</i> swims: Flow field reconstruction and analysis

Author(s): Nicola Giuliani, Massimiliano Rossi, Giovanni Noselli, and Antonio DeSimone

*Euglena gracilis* is a unicellular organism that swims by beating a single anterior flagellum. We study the nonplanar waveforms spanned by the flagellum during a swimming stroke and the three-dimensional flows that they generate in the surrounding fluid. Starting from a small set of time-indexed imag...

[Phys. Rev. E 103, 023102] Published Mon Feb 08, 2021

### Mechanism of hysteresis in shock wave reflection

Author(s): Yan-Chao Hu (胡延超), Wen-Feng Zhou (周文丰), Zhi-Gong Tang (唐志共), Yan-Guang Yang (杨彦广), and Zhao-Hu Qin (秦兆虎)

This paper reports on the mechanism of the hysteresis in the transition between regular and Mach shock wave reflections. We disclose that, for a given inflow Mach number, a stable reflection configuration should maintain the minimal dissipation. As the wedge angle varies, the set of the minimal diss...

[Phys. Rev. E 103, 023103] Published Mon Feb 08, 2021

### Announcement: PRFluids publishes Invited Perspective on Grand Challenges in Environmental Fluid Mechanics

[Phys. Rev. Fluids 6, 020001] Published Mon Feb 08, 2021

### Confronting Grand Challenges in environmental fluid mechanics

Author(s): T. Dauxois, T. Peacock, P. Bauer, C. P. Caulfield, C. Cenedese, C. Gorlé, G. Haller, G. N. Ivey, P. F. Linden, E. Meiburg, N. Pinardi, N. M. Vriend, and A. W. Woods

Environmental fluid mechanics underlies a wealth of natural, industrial, and, by extension, societal challenges. As we strive toward a more sustainable planet, there is a wide range of problems to be tackled, from fundamental advances in understanding and modeling of stratified turbulence and consequent mixing to applied studies of pollution transport in the ocean, atmosphere, and urban environments. The discussions and outcomes of a recent Les Houches School of Physics meeting are summarized here with the intent of providing a resource for the community going forward and a plan of action for the coming decade.

[Phys. Rev. Fluids 6, 020501] Published Mon Feb 08, 2021