# Latest papers in fluid mechanics

### Statistical Lagrangian evaporation rate of droplets released in a homogeneous quasi-isotropic turbulence

Author(s): L. Méès, N. Grosjean, J. L. Marié, and C. Fournier

The effect of turbulence on the evaporation of diethyl ether droplets is investigated by means of digital in-line holography. Lagrangian tracking of thousands of droplets evidences an increase of the mean evaporation rate related not only to the mean relative velocity viewed by the droplets but also to the fluctuations of this velocity.

[Phys. Rev. Fluids 5, 113602] Published Tue Nov 03, 2020

### Expanded scaling relations for locomotion in sloped or cohesive granular beds

Author(s): Qiong Zhang, Stephen Townsend, and Ken Kamrin

Dynamic similarity, while commonly applied in fluid systems, has recently been extended to locomotion problems in flat beds of cohesionless grains by assuming a frictional continuum model. Here, expanded scaling relations are derived for beds that are sloped or composed of cohesive grains. The proposed scalings are validated by discrete element method simulations using rotating “wheels” of various shape families, which suggests the usage of these scalings as potential design tools for off-road vehicles and extraplanetary rovers, and as an analysis tool for biolocomotion in sands and soils.

[Phys. Rev. Fluids 5, 114301] Published Tue Nov 03, 2020

### Nano-particles in optimal concentration facilitate electrically driven dynamic spreading of a drop on a soft viscoelastic solid

Electrically driven dynamic spreading of drops on soft solids is of fundamental importance in a plethora of applications ranging from bio-medical diagnostics to liquid lenses and optoelectronics. However, strategies reported in this regard are challenged by the fact that the spreading gets significantly arrested due to viscoelastic dissipation at the three phase contact line. Circumventing these limits, here we bring out a possibility of substantial augmentation in the rate of electro-spreading on a soft matrix by deploying nano-scale fluidic suspensions of optimal volume fraction. We attribute these findings to a consequent increment in the electrical stresses toward combating the viscoelastic dissipation in the interfacial layer. We also present a simple scaling theory that unveils the manner in which the nano-suspension alters the spreading dynamics of a droplet, effectively by changing the final equilibrium contact angle. These findings open up new possibilities of using nano-fluids of optimal concentration toward modulating the dynamic spreading of a drop on a deformable substrate, a paradigm hitherto remaining unexplored.

### Pulsed-jet propulsion of a squid-inspired swimmer at high Reynolds number

An inflation–deflation propulsion system inspired by the jet propulsion mechanism of squids and other cephalopods is proposed. The two-dimensional squid-like swimmer has a flexible mantle body with a pressure chamber and a nozzle that serves as the inlet and outlet of water. The fluid–structure interaction simulation results indicate that larger mean thrust production and higher efficiency can be achieved in high Reynolds number scenarios compared with the cases in laminar flow. The improved performance at high Reynolds number is attributed to stronger jet-induced vortices and highly suppressed external body vortices, which are associated with drag force. Optimal efficiency is reached when the jet vortices start to dominate the surrounding flow. The mechanism of symmetry-breaking instability under the turbulent flow condition is found to be different from that previously reported in laminar flow. Specifically, this instability in turbulent flow stems from irregular internal body vortices, which cause symmetry breaking in the wake. A higher Reynolds number or smaller nozzle size would accelerate the formation of this symmetry-breaking instability.

### Dispersion of evaporating cough droplets in tropical outdoor environment

The ongoing Covid-19 pandemic has focused our attention on airborne droplet transmission. In this study, we simulate the dispersion of cough droplets in a tropical outdoor environment, accounting for the effects of non-volatile components on droplet evaporation. The effects of relative humidity, wind speed, and social distancing on evaporative droplet transport are investigated. Transmission risks are evaluated based on SARS-CoV-2 viral deposition on a person standing 1 m or 2 m away from the cougher. Our results show that the travel distance for a 100 µm droplet can be up to 6.6 m under a wind speed of 2 m/s. This can be further increased under dry conditions. We found that the travel distance of a small droplet is relatively insensitive to relative humidity. For a millimetric droplet, the projected distance can be more than 1 m, even in still air. Significantly greater droplets and viral deposition are found on a body 1 m away from a cougher, compared to 2 m. Despite low inhalation exposure based on a single cough, infection risks may still manifest through successive coughs or higher viral loadings.

### On the structure and patterns of von Kármán vortices in two-dimensional high Reynolds number flows

This study explores the dynamics and statistical patterns of coherent long-lived vortices spontaneously forming in bluff body wakes. The analysis is based on a series of two-dimensional direct numerical simulations performed for a wide range of Reynolds numbers. We demonstrate that the majority of coherent vortices beyond the recirculation zone are well represented by the canonical Lamb–Oseen solution. This observation is used to develop a low-order census of long-lived eddies in terms of their core sizes and vorticity magnitudes. We demonstrate that the increase in the Reynolds number (Re) leads to the systematic reduction in the initial core radii (r0), whereas the core vorticity (ζ0) increases. These dependencies exhibit singular behavior in the inviscid limit (Re → ∞), which is captured by the proposed explicit relations for r0(Re) and ζ0(Re).

### Theoretical analysis for dynamic contact angle hysteresis on chemically patterned surfaces

A dynamic wetting problem is studied for a moving thin fiber inserted in fluid and with a chemically inhomogeneous surface. A reduced model is derived for contact angle hysteresis by using the Onsager principle as an approximation tool. The model is simple and captures the essential dynamics of the contact angle. From this model, we derive an upper bound of the advancing contact angle and a lower bound of the receding angle, which are verified by numerical simulations. The results are consistent with the quasi-static results. The model can also be used to understand the asymmetric dependence of the advancing and receding contact angles on the fiber velocity, which was observed recently in the physical experiments reported in the work of Guan et al. [“Asymmetric and speed-dependent capillary force hysteresis and relaxation of a suddenly stopped moving contact line,” Phys. Rev. Lett. 116, 066102 (2016)].

### Multiphysics flow simulations using D3Q19 lattice Boltzmann methods based on central moments

In a recent work [A. De Rosis, R. Huang, and C. Coreixas, “Universal formulation of central-moments-based lattice Boltzmann method with external forcing for the simulation of multiphysics phenomena,” Phys. Fluids 31, 117102 (2019)], a multiple-relaxation-time lattice Boltzmann method (LBM) has been proposed by means of the D3Q27 discretization, where the collision stage is performed in the space of central moments (CMs). These quantities relax toward an elegant Galilean invariant equilibrium and can also include the effect of external accelerations. Here, we investigate the possibility to adopt a coarser lattice composed of 19 discrete velocities only. The consequences of such a choice are evaluated in terms of accuracy and stability through multiphysics benchmark problems based on single-, multi-phase, and magnetohydrodynamics flow simulations. In the end, it is shown that the reduction from 27 to 19 discrete velocities has only little impact on the accuracy and stability of the CM-LBM for moderate Reynolds number flows in the weakly compressible regime.

### Characteristics of self-oscillating jets in a confined cavity

Jets emanating into a confined cavity exhibit self-oscillating behavior. This study is focused on evaluating characteristics of oscillating square and round jets. The jet exits from a submerged square or round nozzle of the same hydraulic diameter into a thin rectangular cavity at a Reynolds number of 54 000 based on the nozzle hydraulic diameter and average jet exit velocity. An investigation of the three-dimensional self-oscillatory flow structures is conducted using the unsteady Reynolds-averaged Navier–Stokes equations with the Reynolds stress turbulence model. Vortex identification using the λ2-criterion is used to investigate the flow dynamics. For the oscillating square jet, vortex rings initially have a square shape near the nozzle exit, before axis-switching and transforming into a circular ring. Upon impact on the walls, two tornado-like vortices are produced. The decay rate of oscillating square and round jets initially shows a trend traditionally noted in the corresponding free jets but changes significantly with distance from the nozzle as the effects of oscillation and confinement begin to dominate. Reynolds stress profiles for both types of jets are qualitatively similar and show two peaks on either side of the centerline, which convert to mild peaks farther downstream. Spread and decay rates of oscillating square jets are higher, while oscillating round jets have higher turbulence intensities near the jet center. Compared to free jets, more uniform Reynolds stresses at farther distances from the jet centerline in oscillating jets will enhance heat transfer over a larger area, making oscillating jets suitable in many cooling applications.

### Unsteady combustion mode with a super-high frequency induced by a curved shock

Previous studies of a high-speed blunt projectile in a combustible mixture found two oscillating unsteady combustion modes induced by the curved shock, referred to as high- and low-frequency modes. A new unsteady combustion mode is observed in the present study. The frequency reaches approximately twice the high frequency and is referred to as the super-high frequency to maintain consistency with the terminology used in previous works. The super-high-frequency mode appears in cases of a small sphere diameter, and with a proper diameter, an intermediate mode arises with the co-existence of both high and the super-high frequencies. An analysis of pressure and temperature gradients along the stagnation streamline attributes the oscillation of combustion to the interaction of compression and entropy waves between the shock and flame front. If the compression/entropy waves affect the flame front of the next cycle, the high-frequency mode arises; this is consistent with the results of previous works. However, weakened compression/entropy waves in cases of a small sphere diameter only affect the flame front of every other cycle, leading to the super-high-frequency mode.

### Artificial neural network-based nonlinear algebraic models for large eddy simulation of turbulence

In this work, artificial neural network-based nonlinear algebraic models (ANN-NAMs) are developed for the subgrid-scale (SGS) stress in large eddy simulation (LES) of turbulence at the Taylor Reynolds number Reλ ranging from 180 to 250. An ANN architecture is applied to construct the coefficients of the general NAM for the SGS anisotropy stress. It is shown that the ANN-NAMs can reconstruct the SGS stress accurately in the a priori test. Furthermore, the ANN-NAMs are analyzed by calculating the average, root mean square values, and probability density functions of dimensionless model coefficients. In an a posteriori analysis, we compared the performance of the dynamic Smagorinsky model (DSM), dynamic mixed model (DMM), and ANN-NAM. The ANN-NAM yields good agreement with a filtered direct numerical simulation dataset for the spectrum, structure functions, and other statistics of velocity. Besides, the ANN-NAM predicts the instantaneous spatial structures of SGS anisotropy stress much better than the DSM and DMM. The NAM based on the ANN is a promising approach to deepen our understanding of SGS modeling in LES of turbulence.

### Coronavirus rotational diffusivity

Just 11 weeks after the confirmation of first infection, one team had already discovered and published [D. Wrapp et al., “Cryo-EM structure of the 2019-nCoV spike in the prefusion conformation,” Science 367(6483), 1260–1263 (2020)] in exquisite detail about the new coronavirus, along with how it differs from previous viruses. We call the virus particle causing the COVID-19 disease SARS-CoV-2, a spherical capsid covered with spikes termed peplomers. Since the virus is not motile, it relies on its own random thermal motion, specifically the rotational component of this thermal motion, to align its peplomers with targets. The governing transport property for the virus to attack successfully is thus the rotational diffusivity. Too little rotational diffusivity and too few alignments are produced to properly infect. Too much, and the alignment intervals will be too short to properly infect, and the peplomer is wasted. In this paper, we calculate the rotational diffusivity along with the complex viscosity of four classes of virus particles of ascending geometric complexity: tobacco mosaic, gemini, adeno, and corona. The gemini and adeno viruses share icosahedral bead arrangements, and for the corona virus, we use polyhedral solutions to the Thomson problem to arrange its peplomers. We employ general rigid bead–rod theory to calculate complex viscosities and rotational diffusivities, from first principles, of the virus suspensions. We find that our ab initio calculations agree with the observed complex viscosity of the tobacco mosaic virus suspension. From our analysis of the gemini virus suspension, we learn that the fine detail of the virus structure governs its rotational diffusivity. We find the characteristic time for the adenovirus from general rigid bead–rod theory. Finally, from our analysis of the coronavirus suspension, we learn that its rotational diffusivity descends monotonically with its number of peplomers.

### Experimental measurement of coherent structures in turbulent boundary layers using moving time-resolved particle image velocimetry

A moving time-resolved particle image velocimetry (MTRPIV) system was designed to measure the turbulent boundary layer (TBL). The combination of time-resolved particle image velocimetry and a translational moving system enables the MTRPIV to track the coherent structures with a long period and high temporal resolution. Based on the MTRPIV, the time-evolving of coherent structures within the TBL was measured and analyzed. The observation of the large-scale sweep collision with ejection shows that the strong collision causes the large-scale high- and low-speed coherent structures to break down. The time-evolving process of the hairpin packets shows that the low-speed fluid mass under the hairpin vortices is important for the generation of a whole hairpin packet. The small-scale low-speed structures increase their spatial scales by merging so that the independent hairpin vortices can be organized by merged larger-scale structures. The shear layer exceeding the length of 0.7–0.8 δ (δ is thickness of TBL) or 350–400 [math] (υ and Uτ denote the kinematic viscosity and friction velocity, respectively) is unstable, and it will roll-up to generate a hairpin vortex. In the hairpin packet growth process, the inclination angle of the hairpin packet decreases from ∼13° to 8° in a time duration of 120 [math], and the underlying low-speed fluid is elongated and then split. The analysis of the uniform momentum zones (UMZs) shows that the topmost UMZ has a relatively stable wall-normal position and convection speed. The lower UMZ is quasi-periodically generated and tends to move upward to merge with the upper UMZs. The hairpin packets impact the lower UMZs by inducing large-scale low-speed fluid mass to modulate the probability density function distribution of instantaneous streamwise velocity. The evolution of UMZs with velocity less than 0.5U∞ (U∞ denotes the free-stream velocity) is the result of the interaction of large- and small-scale streamwise fluctuation velocity.

### Dynamics of viscoelastic fluid in a rotating soft microchannel

In this study, we numerically investigate the effects of rotational forces, viz., centrifugal force and Coriolis force, on the flow dynamics of a viscoelastic fluid in a polymeric layer grafted microchannel. The viscoelastic fluid is represented by the Oldroyd-B model, and the effect of viscoelasticity on the underlying transport is studied. A numerical procedure consistent with the finite difference method is used to solve the system of partial differential equations. The numerical model takes into consideration, among many others, the drag effects of the “soft layer” and the transiences in the flow dynamics leading to the steady state. The complex interplay between the effect of rotational forcing and the presence of the soft layer is observed to lead to vital conclusions that could improve the design of many lab-on-a-compact disc based microfluidic devices. In addition, the effect of elasticity on the flow dynamics in the presence of rotational forces and soft layer induced drag force is studied. The in-house numerical code employs the finite difference numerical scheme to discretize the equations and consequently solves the obtained system of linear algebraic equations using the Gauss–Seidel iterative scheme. By demonstrating the velocity profiles, we discuss the effect of the various rheological parameters on the underlying transport feature. Finally, the effect of the rotation on the net throughput is studied extensively.

### Turbulent boundary layer flow over two side-by-side wall-mounted cylinders: Wake characteristics and aerodynamic loads

The distinctive wake characteristics and aerodynamic loads of two side-by-side wall-mounted cylinders were experimentally studied under turbulent boundary layer flows with various gaps. Time-resolved particle image velocimetry was used to analyze the mean and unsteady wake features, whereas a high-resolution load cell was applied to measure the characteristics of lift and drag forces. The results show that the decrease in gap between two cylinders can effectively delay the wake recovery and suppress both the downwash and upwash flows near the top and bottom ends. Overall, with smaller gaps, the turbulence intensity near the top end becomes higher due to the stronger local velocity shear. The distribution of integral time scales indicates that the velocity fluctuations in the near wake region along the middle cylinder span are highly influenced by the local recirculation flows, whereas those near the top end are dominated by the mixing of boundary layer flows. By accounting the equivalent incoming velocity along the cylinder span, both lift and drag coefficient present a similar trend compared to the “infinite length” cylinder cases from previous works. Interestingly, different from cylinders with “infinite length,” no clear intermittency of aerodynamic loads was observed in the current work. This can be attributed to the suppression of two-dimensional vortex shedding due to the three-dimensional flow effects and strong background turbulence. The joint distribution of the lift and drag forces reveals that the lift fluctuations increase significantly with the growth of cylinder gaps, whereas that of drag force remains nearly constant.

### Influence of Prandtl number on bifurcation and pattern variation of non-isothermal annular Poiseuille flow

The relative influence of momentum diffusivity and thermal diffusivity, in terms of the Prandtl number (Pr), on the finite-amplitude instability of a non-isothermal annular Poiseuille flow (NAPF) is analyzed. The limiting value of the growth of instabilities under nonlinear effects is studied by deriving a cubic Landau equation. Emphasis is given especially on studying the impact of the low Prandtl number and the curvature parameter (C) on the bifurcation and the pattern variation of the secondary flow for both axisymmetric and non-axisymmetric disturbances. The finite-amplitude analysis predicts that in contrast to NAPF of water or fluid with Pr ≥ O(1) where the flow is supercritically unstable, the NAPF of low Pr fluids, particularly liquid metals, has shown both supercritical and subcritical bifurcation in the vicinity as well as away from the critical point. The nonlinear interaction of different harmonics for the liquid metal predicts a lower heat transfer rate than those by the laminar flow model, whereas for a fluid with Pr > 2, it is the other way. The maximum heat transfer takes place for the considered minimum value of C. For fluids with low Pr, a probable lower critical Rayleigh number is obtained. The corresponding variation in neutral stability curves as a function of wavenumber reveals that the instability that is supercritical for some wavenumber may be subcritical or vice versa at other nearby wavenumbers. The structural feature of the pattern of the secondary flow under the linear theory differs significantly from those of the secondary flow under nonlinear theory away from the bifurcation point. This is a consequence of the intrinsic interaction of different harmonics that are responsible for the stabilizing or the destabilizing nature of different components in the disturbance kinetic energy balance.

### Poiseuille number behavior in an adiabatically choked microchannel in the slip regime

The influence of subsonic adiabatic choking on frictional resistance inside three-dimensional (3D) microchannels has not been studied for rarefied gas flows. In the present work, the variation of the Poiseuille number with respect to the Mach number has been documented for a 3D microchannel of aspect ratio (width/height) 0.49. Measurements of mass flow rate, static pressure, and temperature have been conducted with nitrogen in highly compressible and slightly rarefied (slip flow) regime: outlet Mach number (0.43–0.99), outlet Knudsen number (4.04 × 10−3–7.04 × 10−3), and pressure ratio (8.17–8.72). The present 3D measurements are compared with available analytical solutions for isothermal and adiabatic flows. A maximum deviation of only 4.8% from the adiabatic slip flow solution points toward the adiabatic nature of the exit choked state, which is being experimentally demonstrated for the first time in the highly compressible slip flow regime. Furthermore, the influence of losses of microchannel end manifolds on the overall pressure drop is calculated to be negligible. We further propose the ranges of the area ratio, Reynolds number, and Knudsen number for which these losses continue to be unimportant for gaseous slip flow. This study gives insights into the influence of subsonic choking on the frictional resistance at various mass flow rates and is relevant for future space expeditions and in certain biological applications.

### High-speed droplet impingement on dry and wetted substrates

High-speed droplet impact is of great interest to power generation and aerospace industries due to the accrued cost of maintenance in steam and gas turbines. The repetitive impacts of liquid droplets onto rotor blades, at high relative velocities, result in blade erosion, which is known as liquid impingement erosion (LIE). Experimental and analytical studies in this field are limited due to the complexity of the droplet impact at such conditions. Hence, numerical analysis is a very powerful and affordable tool to investigate the LIE phenomenon. In this regard, it is crucial to understand the hydrodynamics of the impact in order to identify the consequent solid response before addressing the LIE problem. The numerical study of the droplet impingement provides the transient pressure history generated in the liquid. Determining the transient behavior of the substrate, in response to the pressure force exerted due to the droplet impact, would facilitate engineering new types of surface coatings that are more resistant to LIE. To that end, quantifying the impact pressure of compressible liquid droplets impinged at very high velocities, up to 500 m/s, on rigid solid substrates and liquid films is the main objective of the present work. A wide range of scenarios that commonly arise in the LIE problem are considered, i.e., droplet sizes between 200 µm and 1000 μm, impact velocities ranging from 100 m/s to 500 m/s, and liquid film thicknesses of 0 µm–200 μm. The maximum pressure exerted on the solid surface due to the droplet impact is calculated for both dry and wetted substrates. The results obtained from compressible fluid modeling are compared to those of other numerical studies and analytical correlations, available in the open literature. New correlations are developed for maximum impact pressure on rigid solids and liquid films that can be used to characterize the solid stress and estimate the lifetime of the material by carrying out the fatigue analysis.

### Laboratory rivers adjust their shape to sediment transport

Author(s): A. Abramian, O. Devauchelle, and E. Lajeunesse

An alluvial river builds its own bed with the sediment it transports; its shape thus depends not only on its water discharge but also on the sediment supply. Here we investigate the influence of the latter in laboratory experiments. We find that, as their natural counterpart, laboratory rivers widen...

[Phys. Rev. E 102, 053101] Published Mon Nov 02, 2020

### Linear stability analysis of bubble-induced convection in a horizontal liquid layer

Author(s): Kotaro Nakamura, Harunori N. Yoshikawa, Yuji Tasaka, and Yuichi Murai

We investigate with a linear analysis the stability of a horizontal liquid layer subjected to injection of gas bubbles through a bottom wall. The injection is assumed uniform in space and constant in time. Injected bubbles ascend in the liquid layer due to the Archimedean buoyancy force and are ejec...

[Phys. Rev. E 102, 053102] Published Mon Nov 02, 2020