# Latest papers in fluid mechanics

### Lifetime of a single bubble on the surface of a water and ethanol bath

Author(s): Elise Lorenceau and Florence Rouyer

The time a single bubble stays on a liquid bath surface depends on deterministic drainage. However, for pure water, stochastic local disturbances also affect bubble death. For binary systems like water/alcohol mixtures (WAM), preferential evaporation of one component is crucial. We examine stochastic and deterministic effects on WAM bubble lifetime statistically using an automated bubble generator. The bubble lifetime probability density and the increase in its average with ethanol concentration depends on stabilizing Marangoni stresses arising from evaporation-induced heterogeneities.

[Phys. Rev. Fluids 5, 063603] Published Mon Jun 08, 2020

### Microfluidic slug transport on traveling-wave surface topographies by mechanowetting

Author(s): Edwin de Jong, Jaap M. J. Den Toonder, and Patrick R. Onck

A theoretical study shows that mechanowetting can transport fluid compartments by means of traveling surface waves. Mechanowetting is a propulsion mechanism that exploits capillary forces at fluid interfaces and deforming surface topographies, enabling fluid slugs to be transported at the speed of the surface waves. The effectiveness of the method for microfluidic propulsion is quantified by means of computational fluid dynamics simulations and an intuitive theoretical model.

[Phys. Rev. Fluids 5, 063604] Published Mon Jun 08, 2020

### Quasinormal scale elimination theory of the anisotropic energy spectra of atmospheric and oceanic turbulence

Author(s): Boris Galperin and Semion Sukoriansky

Quasinormal scale elimination theory of rotating turbulence offers a new explanation of physics governing atmospheric and oceanic spectra including the well-known Nastrom and Gage spectra observed in the upper troposphere and lower stratosphere. The terrestrial circulations may be characterized as flows with “compactified dimensionality” (spatial dimension between 2 and 3). Such flows may have both inverse and direct cascades in the same inertial range (dual cascade) and their spectral amplitudes may be determined not by energy/enstrophy fluxes, but by the magnitude of the Coriolis parameter.

[Phys. Rev. Fluids 5, 063803] Published Mon Jun 08, 2020

### Formation of twisted liquid jets

Author(s): Akira Kageyama and Yuna Goto

Surface oscillations of a liquid jet, like water falling from a faucet, are common. For an orifice with n-fold rotational symmetry, the jet cross section oscillates between two symmetrical shapes. Called axis switching, it is a standing wave superposition of two opposite azimuthal ripples. We show that by adjusting the velocity profile at the orifice just one ripple can form. The jet surface is twisted from the single ripple, although the jet has no axial angular momentum. Simulations show that twisted jets can form with various n-fold rotational symmetries, including the regular square.

[Phys. Rev. Fluids 5, 064002] Published Mon Jun 08, 2020

### Saturation and coercivity limit the velocity of rotating active magnetic microparticles

Author(s): Kiarash Samsami, Seyed Amir Mirbagheri, Farshad Meshkati, and Henry Chien Fu

The magnetization of real materials responds to the applied magnetic field, notably by saturating at a maximum magnitude and being coerced to be closer to the applied field direction. These effects are particularly important for soft magnetic materials, which are often used in magnetic microrobotic swimmers. Previous understanding has been based on models of permanent magnets which neglect these effects, but new work shows that taking them into account leads to an unappreciated physical limit on swimming velocities for magnetically rotated microswimmers.

[Phys. Rev. Fluids 5, 064202] Published Mon Jun 08, 2020

### From waves to convection and back again: The phase space of stably stratified turbulence

Author(s): N. E. Sujovolsky and P. D. Mininni

An efficient path for energy dissipation is often looked for in wave turbulence systems. Fluid elements in stratified turbulence are shown to alternate between two invariant sets of solutions: waves and local convection, the latter connected to effective dissipation of energy. The fast evolution between these solutions explains enhancement of extreme events and balance relations in stratified flows.

[Phys. Rev. Fluids 5, 064802] Published Mon Jun 08, 2020

### Likelihood of survival of coronavirus in a respiratory droplet deposited on a solid surface

We predict and analyze the drying time of respiratory droplets from a COVID-19 infected subject, which is a crucial time to infect another subject. Drying of the droplet is predicted by using a diffusion-limited evaporation model for a sessile droplet placed on a partially wetted surface with a pinned contact line. The variation in droplet volume, contact angle, ambient temperature, and humidity are considered. We analyze the chances of the survival of the virus present in the droplet based on the lifetime of the droplets under several conditions and find that the chances of the survival of the virus are strongly affected by each of these parameters. The magnitude of shear stress inside the droplet computed using the model is not large enough to obliterate the virus. We also explore the relationship between the drying time of a droplet and the growth rate of the spread of COVID-19 in five different cities and find that they are weakly correlated.

### Erratum: “A vortex identification method based on local fluid rotation” [Phys. Fluids 32, 015104 (2020)]

### Field-induced shaping of sessile paramagnetic drops

We use the electromagnetic stress tensor to describe the elongation of paramagnetic drops in uniform magnetic fields. This approach implies a linear relationship between the shape of the drops and the square of the applied field, which we confirm experimentally. We show that this effect scales with the volume and susceptibility of the drops. By using this unified electromagnetic approach, we highlight the potential applications of combining electric and magnetic techniques for controlled shaping of drops in liquid displays, liquid lenses, and chemical mixing of drops in microfluidics.

### Spherical and cylindrical shocks in a non-ideal dusty gas with magnetic field under the action of heat conduction and radiation heat flux

In this article, the propagation of spherical or cylindrical shock waves in a mixture of small solid particles of microsize and a non-ideal gas with conductive as well as radiative heat fluxes are studied under the influence of an azimuthal or axial magnetic field. The solid particles are uniformly distributed in the mixture, and the shock wave is assumed to be driven by a piston. It is assumed that the equilibrium flow conditions are maintained and the moving piston continuously supplies the variable energy input. The density of the undisturbed medium is assumed to be constant in order to obtain the self-similar solutions. Heat conduction is expressed in terms of Fourier’s law, and the radiation is considered to be of diffusion type for an optically thick gray gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density. Numerical calculations have been performed to obtain the flow profiles of variables. The effects of different values of the non-idealness parameter, the strength of the magnetic field, the mass concentration, the ratio of the density of solid particles to the initial density of the gas, the piston velocity index, and the adiabatic index are shown in detail. It is interesting to note that in the presence of an azimuthal magnetic field, the pressure and density vanish at the piston, and hence, a vacuum is formed at the center of symmetry, which is in excellent agreement with the laboratory condition to produce the shock wave.

### Investigating the effect of reagent parameters on the efficiency of cell lysis within droplets

Cell lysis is an essential primary step in cell assays. In the process of cell lysis, the cell membrane is destroyed and the substances inside the cell are extracted. By utilizing a droplet-based microfluidic platform for cell lysis, the mixer unit that is required for mixing lysis reagents with the cells can be excluded, and thus, the complexity of the fabrication process is reduced. In addition, lysing the cells within the droplets will prevent the cells from exposure to the channel walls, and as a result, cleanliness of the samples and the device is maintained. In this study, cell lysis within the droplets and the parameters affecting the efficiency of this process are investigated using a computational fluid dynamics model. Both the cell solution and the lysis reagents are encapsulated within a droplet and the lysis procedure is simulated inside the droplet. It is known that the secondary flows generated inside the droplet facilitate the mixing process. In this study, we used this effect to improve the efficiency of cell lysis in droplet and the improvement is shown to be attributed to activating an advection mechanism besides the diffusion mechanism inside the droplet. It is also shown that increasing the concentration of the lysis reagents does not have a significant effect on the efficiency of the cell lysis. The effect of the volume fraction of the lysis reagents is also studied, which is shown to be an effective factor in controlling the efficiency of the cell lysis. The lysis procedure is simulated with lysis reagent volume fractions of 50%, 66%, 80%, 90%, and 97%. The lysis efficiency is found to be 38.45%, 45.3%, 57.6%, 82.4%, and 100%, respectively, while the droplet travels through a 2 mm-long microchannel within 0.25 s. This study shows that the droplet microfluidic platform is a powerful tool for performing fast and reliable cell lysis.

### Stationary scaling in small-scale turbulent dynamo problem

Author(s): A. V. Kopyev, A. S. Il'yn, V. A. Sirota, and K. P. Zybin

We consider forced small-scale magnetic field advected by an isotropic turbulent flow. The random driving force is assumed to be distributed in a finite region with a scale smaller than the viscous scale of the flow. The two-point correlator is shown to have a stationary limit for any reasonable vel...

[Phys. Rev. E 101, 063102] Published Fri Jun 05, 2020

### Nonwetting droplet oscillation and displacement by viscoelastic fluids

Author(s): Chiyu Xie, Ke Xu, Kishore Mohanty, Moran Wang, and Matthew T. Balhoff

Simulations and theory reveal oscillations of droplets when driven by viscoelastic fluids because of their elastic memory effect. The viscoelastic oscillation helps release trapped droplets from hard-to-displace positions.

[Phys. Rev. Fluids 5, 063301] Published Fri Jun 05, 2020

### Characteristics of quasistationary near-wall turbulence subjected to strong stable stratification in open-channel flows

Author(s): Amir Atoufi, K. Andrea Scott, and Michael L. Waite

Turbulent open channel-flow under strongly stable thermal stratification is investigated. It is shown that the dominant effects of strong stable stratification on the characteristics of near-wall turbulence are transient. The budget of turbulent kinetic energy, the budget for the tangential Reynolds stress, and the relevant length scales are discussed. It is shown that near-wall turbulence at quasistationarity is approximately insensitive to the choice of upper thermal boundary condition.

[Phys. Rev. Fluids 5, 064603] Published Fri Jun 05, 2020

### Steady-state modeling of extrusion cast film process, neck-in phenomenon, and related experimental research: A review

This review provides the current state of knowledge of steady-state modeling of the extrusion cast film process used to produce flat polymer films, as well as related experimental research with a particular focus on the flow instability neck-in. All kinematic models used (i.e., 1-, 1.5-, 2-, and 3-dimensional models) together with the utilized constitutive equations, boundary conditions, simplified assumptions, and numerical methods are carefully summarized. The effect of draw ratio, Deborah number (i.e., melt relaxation time related to experimental time), film cooling, second to first normal stress difference ratio at the die exit, uniaxial extensional strain hardening, and planar-to-uniaxial extensional viscosity ratio on the neck-in is discussed.

### Thermal convection studies in liquid metal flow inside a horizontal duct under the influence of transverse magnetic field

An experiment is conducted to study the effect of magnetic field on heat transfer in a magnetohydrodynamic flow of molten lead–lithium, in a stainless steel thin-wall duct, with a uniform surface heat flux at its bottom wall. A novel technique of measuring fluid temperature inside the duct is applied to map the temperature profile in a flow cross section, at both ends of the heated section, using a 4 × 4 array of 16 equidistantly placed thermocouples. Surface temperature, as well as electric potential, is measured at seven different locations along the heated section. Based on the temperature profiles obtained at the outlet of the heated section, various flow regimes have been identified over the experimentally investigated flow parameters. Distinctively, three flow regimes have been recognized depending on the dominance of buoyancy force, electromagnetic force, and inertial force. In order to better understand the experimental data, numerical simulations are performed using COMSOL. In the buoyancy force dominated flow regime, a quasi-two-dimensional turbulence flow is predominant, determining the overall heat transfer mechanism. In the electromagnetic force dominated regime, the perturbation due to buoyancy force is suppressed by the magnetic field. Finally, in the inertial force dominated regime, the electromagnetic force and buoyancy force do not play a significant role in determining the heat transfer mechanism. The transition between observed flow regimes has been identified in terms of Grashof, Reynolds, and Hartmann numbers, and the Nusselt number has been calculated for quantitative comparison of heat transfer in these flow regimes.

### The hierarchy of multi-point probability density functions and characteristic functions in compressible turbulence

The hierarchies of equations for a general multi-point probability density function (PDF) and its characteristic function (CF) are derived for compressible turbulent flows, obeying the ideal gas law. The closure problem of turbulence is clearly exhibited in each of the approaches, with n-point statistics being dependent on the (n + 1)-point statistics and, for some cases, even the (n + 2)-point statistics. When dynamic viscosity and heat conductivity are dependent on temperature as a power-law, the CF hierarchy could contain fractional derivatives if the exponent is a non-integer. The additional conditions satisfied by all the PDFs and CFs in both the hierarchies are also prescribed. The PDF and CF equations derived in this paper, with the unclosed terms explicitly written in terms of higher order PDF/CF, act as a starting point in constructing symmetry-based invariant solutions of compressible turbulence, analogous to the works of Wacławczyk et al. [“Statistical symmetries of the Lundgren–Monin–Novikov hierarchy,” Phys. Rev. E 90, 013022 (2014)] and Oberlack and Rosteck [“New statistical symmetries of the multi-point equations and its importance for turbulent scaling laws,” Discrete Contin. Dyn. Syst. 3, 451–471 (2010)] for incompressible turbulence.

### Acoustic-wave-induced cooling in onset of hypersonic turbulence

We report a newly identified aerodynamic cooling mechanism in the onset of hypersonic wall-bounded turbulence. We first experimentally investigated a flared cone with a smooth surface in a Ma 6 wind tunnel using fast-response pressure sensors, Rayleigh scattering flow visualization, and infrared thermography, which confirmed a cooled region (denoted as CS) downstream of a highly heated region (denoted as HS) on the model, as shown by Franko and Lele [J. Fluid Mech. 730, 491–532 (2013)] and Sivasubramanian and Fasel [J. Fluid Mech. 768, 175–218 (2015)]. We then performed calculations based on both linear stability theory and direct numerical simulations to understand this mechanism. We found that the phase difference ϕpθ between the periodic pressure and dilatation waves plays an important role in the interchange between thermal and mechanical energy in a hypersonic wall-bounded flow. Using porous steel to modify the model surface’s sound admittance, we experimentally show that it is possible to modify the cosine value of ϕpθ to be negative near the wall and thus reduce the temperature growth. These results can provide insight into the thermal protection design of future hypersonic vehicles.

### Unsteady characteristics of compressible reattaching shear layers

Compressible reattaching flows occur in many aerospace applications and are characterized by high aerothermal loads at reattachment and a broad range of characteristic time scales. The flowfield in this study involves a separated shear layer reattaching onto a 20° ramp at a freestream unit Reynolds number of 6.7 × 107 m−1 and Mach number of 2.9. Delayed detached eddy simulations were carried out using OVERFLOW 2.2K by Leger et al. [“Detached-eddy simulation of a supersonic reattaching shear layer,” AIAA J. 55, 3722–3733 (2017)], and the corresponding results were analyzed to determine the unsteady features of this flowfield using statistical techniques. The simulations were run for long integration times, which ensured sufficient temporal resolution of low-frequency unsteadiness in the range of [math]. The mean flow data highlighted essential flow components such as an expansion fan at the separation point, a large recirculation vortex, and a reattachment shock. Fourier analysis of wall pressure data revealed several high energy frequency bands, which appeared to correspond to separation bubble breathing, shear-layer flapping, and shedding of vortices from the recirculation zone. The spectra also highlighted the possible presence of Rossiter modes, suggesting a feedback mechanism through the recirculation zone. Correlations in the shear-layer and recirculation zone confirmed the presence of large-scale turbulence structures, with an increase in length and time scales downstream. The spectra of reattachment shock location suggested a broadband nature of the oscillations. The role of upstream events on the same was investigated by examining coherence, conditional averages, and correlations. A similar exercise was carried out to investigate the nature of unsteadiness at the mean reattachment location.