# Latest papers in fluid mechanics

### Effect of density of a sphere launched vertically in water on the water-surface behavior and sphere motion in air

Submerged solid spheres with specific gravities relative to water ranging from 1.36 to 7.93 were launched vertically upward toward the free surface of calm water. The motion of each sphere and the behavior of the water surface were investigated from the time the sphere passed through the calm water surface until it attained its maximum displacement position. The energy lost in the interaction between the sphere and the water surface (i.e., the interfacial containing energy Eo) was estimated from energy conservation. A larger Eo at the maximum displacement position of the sphere led to a larger increase in the height and width of the interfacial water sheet where the upper side of the sphere intersected with the free surface of calm water. This result corresponded to the result obtained by changing the submergence depth, as reported by Takamure and Uchiyama [“Air–water interface dynamics and energy transition in air of a sphere passed vertically upward through the interface,” Exp. Therm. Fluid Sci. 118, 110167 (2020)]. This aspect suggests that the characteristics of the interfacial water sheet are the dominant parameters influencing Eo. The presented findings can facilitate the determination of parameters to model the water exit problem.

### Leidenfrost drop impact on inclined superheated substrates

In real applications, drops always impact on solid walls with various inclinations. For the oblique impact of a Leidenfrost drop, which has a vapor layer under its bottom surface to prevent its direct contact with the superheated substrate, the drop can nearly frictionlessly slide along the substrate accompanied by spreading and retracting. To individually study these processes, we experimentally observe the impact of ethanol drops on superheated inclined substrates using high-speed imaging from two different views synchronously. We first study the dynamic Leidenfrost temperature, which mainly depends on the normal Weber number We⊥. Then, the substrate temperature is set to be high enough to study the Leidenfrost drop behavior. During the spreading process, drops are always kept uniform, and the maximum spreading factor Dm/D0 follows a power-law dependence on the large normal Weber number We⊥ as [math] for We⊥ ≥ 30. During the retracting process, drops with low impact velocities become non-uniform due to the gravity effect. For the sliding process, the residence time of all studied drops is nearly a constant, which is not affected by the inclination and the We number. The frictionless vapor layer resulting in the dimensionless sliding distance L/D0 follows a power-law dependence on the parallel Weber number We|| as [math]. Without direct contact with the substrate, the behaviors of drops can be separately determined by We⊥ and We||. When the impact velocity is too high, the drop fragments into many tiny droplets, which is called the splashing phenomenon. The critical splashing criterion is found to be [math] 120 or [math] 5300 in the current parameter regime.

### A study on bubble nuclei population dynamics under reduced pressure

The existence of cavitation nuclei is one of the necessary conditions for liquid cavitation. Bubble nucleus is the most basic cavitation nucleus, and bubble nuclei size distribution is a parameter describing the population of gas nuclei. To study the dynamics of bubble nuclei population after artificial seeding under reduced pressure, a decompression chamber was built, combined with the artificial seeding system and the acoustic nuclei measurement system. After the nuclei seeding, the experimental study of the nuclei population dynamics with pressure and time was carried out. It is found that as the pressure decreases, the number density of larger size nuclei decreases, while the number density of smaller size nuclei increases. In the measured size range, the maximum value of number density of the nuclei size distribution increases. In addition, based on the theory of bubble dynamics, the growth process of the nucleus under reduced pressure is calculated and analyzed, which can realize the preliminary prediction of the nuclei population dynamics under reduced pressure.

### Richtmyer-Meshkov instability of an imploding flow with a two-fluid plasma model

Author(s): Y. Li, R. Samtaney, D. Bond, and V. Wheatley

The Richtmyer-Meshkov instability of a cylindrical light-heavy density interface is investigated in the framework of a two-fluid plasma model. Interfacial perturbations are enhanced by the induced Lorentz force. The Biermann battery effect is an important source of the self-generated magnetic field.

[Phys. Rev. Fluids 5, 113701] Published Fri Nov 20, 2020

### Vortex rings drive entrainment and cooling in flow induced by a spark discharge

Author(s): Bhavini Singh, Lalit K. Rajendran, Jiacheng Zhang, Pavlos P. Vlachos, and Sally P. M. Bane

In spark plasma discharges, vortex rings are shown to control the expansion and convective cooling of the hot gas kernel. The rates of both processes increase with the electrical energy deposited. This has implications on momentum transport and passive scalar mixing in plasma-based flow and combustion control applications.

[Phys. Rev. Fluids 5, 114501] Published Fri Nov 20, 2020

### Effect of precipitation mineralization reactions on convective dissolution of ${\mathrm{CO}}_{2}$: An experimental study

Author(s): C. Thomas, S. Dehaeck, and A. De Wit

When CO2 dissolves in a solution of calcium ions, a precipitation mineralization reaction can take place, producing solid calcium carbonate particles that sink to the bottom of the host phase. Convective motions present both above and below the reaction front favor the entrainment of CO2 toward the bottom, which is favorable for the security of carbon sequestration techniques. An experimental study of the influence of such a precipitation reaction on convective dissolution of CO2 is conducted.

[Phys. Rev. Fluids 5, 113505] Published Thu Nov 19, 2020

### Reservoir computing model of two-dimensional turbulent convection

Author(s): Sandeep Pandey and Jörg Schumacher

Reservoir computing models are one possible architecture of recurrent neural networks. Here, a reservoir computing model is applied to reproduce the low-order statistics of a two-dimensional turbulent Rayleigh-Bénard flow without solving the underlying Boussinesq equations.

[Phys. Rev. Fluids 5, 113506] Published Thu Nov 19, 2020

### Sounds of Leidenfrost drops

Author(s): Tanu Singla and M. Rivera

When Leidenfrost drops are confined on a spherical surface, they can oscillate in the form of stars; drops in this configuration are popularly known as Leidenfrost stars. Here, emission of sound in the form of periodic beats from the Leidenfrost stars is studied. It is shown that the vapors escaping from the drop are responsible for sound emission, and a theoretical framework is developed to establish that the frequencies of the sounds depend on the size of the drop, in the same way that frequencies of acoustic modes depend on the length of wind musical instruments.

[Phys. Rev. Fluids 5, 113604] Published Thu Nov 19, 2020

### Deposition of a particle-laden film on the inner wall of a tube

Author(s): Deok-Hoon Jeong, Anezka Kvasnickova, Jean-Baptiste Boutin, David Cébron, and Alban Sauret

The dispensing of liquids in tubing often involves repeated, intermittent flows that leave a thin liquid layer on the inner wall of the tube. The entrainment in the coating film of particles present in the liquid can lead to the contamination of the tube. A study demonstrates the conditions under which particles dispersed in a liquid are deposited on the wall of the tube when the liquid is displaced by air.

[Phys. Rev. Fluids 5, 114004] Published Thu Nov 19, 2020

### Size-dependent particle migration and trapping in three-dimensional microbubble streaming flows

Author(s): Andreas Volk, Massimiliano Rossi, Bhargav Rallabandi, Christian J. Kähler, Sascha Hilgenfeldt, and Alvaro Marin

Finite-sized particles in complex flow fields often experience migration and trapping. Using three-dimensional particle tracking and numerical simulations, it is shown that even density-matched microparticles can experience migration and trapping because of their interaction with boundaries. This effect is particularly sound when particles are being advected in the complex three-dimensional flow generated by oscillating microbubbles confined in a microchannel.

[Phys. Rev. Fluids 5, 114201] Published Thu Nov 19, 2020

### Preferential concentration in the particle-induced convective instability

Author(s): Sara Nasab and Pascale Garaud

Direct numerical simulations are used to study preferential concentration of heavy inertial particles in the particle-induced convective instability. This process and the resulting significant particle concentration enhancement are investigated using the two-fluid equations. Motivated by dominant balance arguments, the scaling of the particle concentration enhancement over the mean is found; the maximum scales as urms2τp/κp, and the typical as (urms2τp/κp)1/2, where urms is the rms of the fluid velocity, τp is the particle stopping time, and κp is the assumed particle diffusivity.

[Phys. Rev. Fluids 5, 114308] Published Thu Nov 19, 2020

### Dynamic subgrid-scale scalar-flux model based on the exact rate of production of turbulent fluxes

Author(s): Shujaut H. Bader and Paul A. Durbin

“We propose a dynamic subgrid scale (SGS) scalar flux model based on the exact turbulent flux production rate. The model incorporates a tensor diffusivity explicitly dependent on subgrid stresses and the resolved velocity gradient. Representing diffusivity by a tensor allows the scalar flux vector to be misaligned with the filtered temperature gradient. Since modeling the subgrid scales represents their influence on resolved scales as an average of small scales, we show that extending RANS type closures to an LES framework is a promising route to cost effective and robust subgrid modeling.

[Phys. Rev. Fluids 5, 114609] Published Thu Nov 19, 2020

### Fluid–particle drag and particle–particle drag in low-Reynolds-number bidisperse gas–solid suspensions

Particle-resolved direct numerical simulations (PR-DNSs) of dynamic bidisperse gas–solid suspensions are performed at low particle Reynolds numbers. Unlike the fixed-bed suspensions, the mobility of particles allows particles of different size types to develop different slip velocities relative to the fluid phase. The scaled slip velocity, defined as the ratio of the slip velocity of one particle type to the mean slip velocity of the mixture, varies profoundly depending on the specific properties of the bidisperse mixture. For large particles, the drag force, scaled by the mean drag force of the mixture, is reasonably predicted by the models obtained from fixed-bed suspensions, while for small particles, these models tend to underestimate the scaled drag force as the scaled slip velocity decreases. By introducing the scaled slip velocity, a new model for the fluid–particle drag on each particle type is proposed and agrees well with the PR-DNS data. For the situation where the monodisperse drag models are employed to predict the mixture mean drag force, a new mean diameter that is variant with the total solid volume fraction is suggested. This diameter increases as the total solid volume fraction decreases and approaches the Sauter mean diameter in the close-packed volume fraction. In dilute suspensions, due to the strong influence of surrounding fluids on the particle phase, the simulated particle–particle drag is significantly smaller than the predictions of models based on kinetic theory of granular flow. Based on the PR-DNS results, new relations for particle–particle drag are also proposed.

### Generalized friction and dilatancy laws for immersed granular flows consisting of large and small particles

The motion of fully immersed granular materials, composed of two distinct particle sizes, flowing down rough inclined planes is studied through fluid–particle numerical simulations. We focus on the effect of ambient fluids, as well as their interplay with particle size segregation, on the steady-state kinematic and rheological profiles of the granular-fluid mixture flow. Simulation results are analyzed in the framework of a visco-inertial rheological model, which is first validated in monodisperse flows with a wide range of the ambient fluid viscosity (i.e., from air to water and slurry) and then generalized for size-bidisperse mixtures. It is found that the local effective friction and volume fraction of mixtures with different particle sizes can be approximated from the rheology of single-component flows. While the presence of viscous ambient fluids slows down size segregation (perpendicular to the flow) depending on the mixture composition and flow viscosity, the effective bulk friction is shown to be independent of the state and progress of segregation.

### Dynamics of spheroids in an unbound quadratic flow of a general second-order fluid

This work employs the second-order fluid model to investigate the effect of first and second normal stresses on the motion of spheroidal particles in unbound parabolic flows, where particles migrate toward the flow center. We specifically examine the effects of fluid Weissenberg number Wi and the ratio of normal stress coefficients α = ψ2/ψ1. Previous works have considered the motion of spheroidal particles in the co-rotational limit (α = −0.5), where the effect of fluid viscoelasticity is to modify the fluid pressure but not the shear stresses. Here, we examine all ranges of α that are found for functional complex fluids such as dilute polymer solutions, emulsions, and particulate suspensions and determine how viscoelastic shear stresses alter particle migration. We use perturbation theory and the Lorentz reciprocal theorem to derive the O(Wi) corrections to the translational and rotational velocities of a freely suspended spheroid in an unbound tube or slit flow. Our results show that for both prolate and oblate particles, the viscoelasticity characterized by α significantly affects the particle cross-stream migration, but does not qualitatively change the trends seen in the co-rotational limit (α = −0.5). For a range of α (−0.9 ≤ α ≤ 0) investigated in this work, particles possess the largest mobility when α = −0.9 and smallest mobility when α = 0. Although α does not alter particle rotation at a given shear rate, we observe significant changes in particle orientation during migration toward the flow center because changes in migration speed give rise to particles experiencing different shear histories.

### Fingering instability in Marangoni spreading on a deep layer of polymer solution

Spreading on the free surface of a complex fluid is ubiquitous in nature and industry, such as drug delivery, oil spill, and surface treatment with patterns. Here, we report on a fingering instability that develops during Marangoni spreading on a deep layer of the polymer solution. In particular, the wavelength depends on the molecular weight and concentration of the polymer solution. We use the transmission lattice method to characterize the free surface morphology during spreading and the finger height at the micron scale. We use the Maxwell model to explain the spreading radius, which is dominated by elasticity at small time scales and by viscous dissipation at large time scales. In a viscous regime, with consideration of shear thinning, the spreading radius follows the universal 3/4 power law. Our model suggests a more generalized law of the spreading radius than the previous laws for Newtonian fluids. Furthermore, we give a physical explanation on the origin of the fingering instability as due to normal stresses at high shear rates generating a high contact angle, providing a necessary condition for the fingering instability. The normal stress also generates the elastic deformation at the leading edge and so selects the wavelength of the fingering instability. Understanding the spreading mechanism on a layer of viscoelastic fluid has a particular implication in airway drug delivery and surface coating.

### Vortex formation in starting buoyant jets at moderate Richardson numbers

In this paper, the formation process of the leading vortex ring in positively and negatively buoyant starting jets with moderate Richardson number in the range of 0.06 < |Ri| ≤ 0.321 has been investigated numerically and theoretically. Using the similarity variables |Ri| and |Ri|2/5 for the positively and negatively buoyant starting jets, respectively, fitting equations can be obtained to predict the buoyant jet penetration rate. Based on these fitting equations, a revised circulation model is proposed by incorporating the effects of both over-pressure and buoyancy. The revised model is well consistent with the numerical results for all positively buoyant starting jets. However, for the negatively buoyant starting jets, this model can predict well only during the initial period. The over-pressure has little influence on the vortex ring characteristics of the starting jets with positive buoyancy, whereas it can significantly affect the vortex ring formation of the negatively buoyant starting jets at moderate Richardson numbers. As the positive Richardson number increases, the instabilities of the trailing shear layer occur earlier. At moderately negative Richardson numbers, a “double plume” structure (an inner sinking circular forced plume and an outer rising annular plume) can be observed. The outer negative vorticity layers develop gradually due to the baroclinic effect. Consequently, the size and strength of the leading vortex progressively decrease. As the negative Richardson number decreases, the negative vorticity layers occur earlier and grow faster.

### Experimental visualization of sneezing and efficacy of face masks and shields

In the present work, we propose and demonstrate a simple experimental visualization to simulate sneezing by maintaining dynamic similarity to actual sneezing. A pulsed jet with Reynolds number Re = 30 000 is created using compressed air and a solenoid valve. Tracer particles are introduced in the flow to capture the emulated turbulent jet formed due to a sneeze. The visualization is accomplished using a camera and laser illumination. It is observed that a typical sneeze can travel up to 25 ft in ∼22 s in a quiescent environment. This highlights that the present widely accepted safe distance of 6 ft is highly underestimated, especially under the act of a sneeze. Our study demonstrates that a three-layer homemade mask is just adequate to impede the penetration of fine-sized particles, which may cause the spreading of the infectious pathogen responsible for COVID-19. However, a surgical mask cannot block the sneeze, and the sneeze particle can travel up to 2.5 ft. We strongly recommend using at least a three-layer homemade mask with a social distancing of 6 ft to combat the transmission of COVID-19 virus. In offices, we recommend the use of face masks and shields to prevent the spreading of droplets carrying the infectious pathogen. Interestingly, an N-95 mask blocks the sneeze in the forward direction; however, the leakage from the sides and top spreads the sneeze in the backward direction up to 2 ft. We strongly recommend using the elbow or hands to prevent droplet leakage even after wearing a mask during sneezing and coughing.

### Speed–direction description of turbulent flows

In this note, we introduce speed and direction variables to describe the motion of incompressible viscous fluid. Fluid velocity u is decomposed into u = ur, with u = |u| and r = u/|u|. We consider a directional split of the Navier–Stokes equations into a coupled system of equations for u and for r. The equation for u is particularly simple but solely maintains the energy balance of the system. Under the assumption of a weak correlation between fluctuations in speed and direction in a developed turbulent flow, we further illustrate the application of u–r variables to describe mean statistics of a shear turbulence. The standard (full) Reynolds stress tensor does not appear in a resulting equation for the mean flow profile.

### Editorial: Promoting Inclusive and Respectful Communications

Author(s): Michael Thoennessen

[Phys. Rev. Fluids 5, 110002] Published Wed Nov 18, 2020