# Latest papers in fluid mechanics

### Development of magnetoelastic fingering patterns in a rectangular Hele-Shaw cell

Author(s): Írio M. Coutinho and José A. Miranda

A ferrofluid and a nonmagnetic fluid flow in a rectangular Hele-Shaw cell subjected to an in-plane magnetic field. A chemical reaction occurs, and the two-fluid interface becomes elastic. The produced patterns range from straight front to sharp tip ones, and they differ from usual Saffman-Taylor fingers.

[Phys. Rev. Fluids 5, 094002] Published Tue Sep 08, 2020

### Recharging and rejuvenation of decontaminated N95 masks

N95 respirators comprise a critical part of the personal protective equipment used by frontline health-care workers and are typically meant for one-time usage. However, the recent COVID-19 pandemic has resulted in a serious shortage of these masks leading to a worldwide effort to develop decontamination and re-use procedures. A major factor contributing to the filtration efficiency of N95 masks is the presence of an intermediate layer of charged polypropylene electret fibers that trap particles through electrostatic or electrophoretic effects. This charge can degrade when the mask is used. Moreover, simple decontamination procedures (e.g., use of alcohol) can degrade any remaining charge from the polypropylene, thus severely impacting the filtration efficiency post-decontamination. In this report, we summarize our results on the development of a simple laboratory setup allowing measurement of charge and filtration efficiency in N95 masks. In particular, we propose and show that it is possible to recharge the masks post-decontamination and recover filtration efficiency.

### Azimuthal instability of the radial thermocapillary flow around a hot bead trapped at the water–air interface

We investigate the radial thermocapillary flow driven by a laser-heated microbead in partial wetting at the water–air interface. Particular attention is paid to the evolution of the convective flow patterns surrounding the hot sphere as the latter is increasingly heated. The flow morphology is nearly axisymmetric at low laser power ([math]). Increasing [math] leads to symmetry breaking with the onset of counter-rotating vortex pairs. The boundary condition at the interface, close to no-slip in the low-[math] regime, turns about stress-free between the vortex pairs in the high-[math] regime. These observations strongly support the view that surface-active impurities are inevitably adsorbed on the water surface where they form an elastic layer. The onset of vortex pairs is the signature of a hydrodynamic instability in the layer response to the centrifugal forced flow. Interestingly, our study paves the way for the design of active colloids capable of achieving high-speed self-propulsion via vortex pair generation at a liquid interface.

### Freely decaying turbulence in a finite domain at finite Reynolds number

We perform direct numerical simulations to study the effects of the finite Reynolds number and domain size on the decay law of Saffman turbulence. We observe that the invariant for Saffman turbulence, u2ℓ3, and non-dimensional dissipation coefficient, Cϵ = ϵ/(u3/ℓ), are sensitive to finite domain size; here, u is the rms velocity, ℓ is the integral length scale, and ϵ is the energy dissipation rate. Consequently, the exponent n in the decay law u2 ∼ t−n for Saffman turbulence deviates from 6/5. Due to the finite Reynolds number and the domain size, Saffman turbulence decays at a faster rate (i.e., n > 6/5). However, the exponent n = 6/5 is more sensitive to the domain size than to the Reynolds number. From the simulations, we find that n remains close to 6/5 as long as Rλ ≳ 10 and ℓ ≲ 0.3Lbox; here, Rλ is the Reynolds number based on the Taylor microscale and Lbox is the domain size. We also notice that n becomes slightly lower than 6/5 for a part of the decay period. Interestingly, this trend n < 6/5 is also observed earlier in freely decaying grid-generated turbulence.

### Active control for drag reduction of turbulent channel flow based on convolutional neural networks

An active controller based on convolutional neural networks (CNNs) is designed for drag reduction of turbulent channel flow. CNNs are constructed to predict the normal velocities on the detection plane as wall blowing and suction using measurable quantities at the wall, i.e., spanwise or streamwise wall shear stress. The training data of CNNs are generated from the direct numerical simulation of channel flow. With different wall quantities, we design and train different CNNs for flow prediction. The purpose is to identify which wall quantity is associated with substantial drag reduction. A linear neural network based on the spanwise wall shear stress shows sufficient capability to predict the inflow field and obtain almost the same drag reduction rate as the opposite control, which does not perform well when using the streamwise wall shear stress as the input. Hence, a nonlinear CNN model with activation function and multiple convolutional layers is established to use the streamwise wall shear stress for flow prediction and drag reduction control. Applying the trained CNNs to a low Reynolds number turbulent channel flow at Reτ = 100, we obtain up to 19% and 10% drag reduction rates based on the spanwise and streamwise wall-shear stresses, respectively. These networks are also tested at different Reynolds numbers, i.e., Reτ = 180 and Reτ = 390, where substantial drag reduction rates are obtained as well. Effects of the controller on turbulent instantaneous flow field and statistics are presented.

### Isolator characteristics under steady and oscillatory back pressures

Experiments are carried out to characterize the un-start/re-start phenomena in an isolator with steady and low-frequency oscillatory back pressures (0.75 Hz–2.5 Hz) in Mach 1.7 flow. In the present study, the effect of shock train interaction with the intake shocks is focused to capture these phenomena. It is demonstrated that the un-start mechanism is a continuous process with steady back pressures, whereas it is a discontinuous process under oscillatory back pressures. The un-start mechanism is triggered once the oscillatory back pressure is above the maximum isolator pressure. As the frequency of back pressure oscillation is increased, the isolator experiences an early un-start and a delayed re-start. On the other hand, if the oscillatory back pressure is decreased, the re-start process is initiated. During the re-start process, the time lag is found to be increased, and the hysteresis loss is decreased with an increase in oscillatory frequencies. These phenomena are studied through both the steady and unsteady pressure measurements along with instantaneous schlieren images for different dynamic pressures. Furthermore, the un-start can be avoided or delayed by increasing the freestream dynamic pressure.

### Unified simplified multiphase lattice Boltzmann method for ferrofluid flows and its application

A unified simplified multiphase lattice Boltzmann method (USMLBM) is constructed in this work for simulating complex multiphase ferrofluid flows with large density and viscosity ratios. In USMLBM, the Navier–Stokes equations, the Poisson equation of the magnetic potential, and the phase-field equation are utilized as the ferrohydrodynamics behavior modeling and interface tracking algorithm. Solutions of the macroscopic governing equations are reconstructed with the lattice Boltzmann framework and resolved in a predictor–corrector scheme. Various benchmark tests demonstrate the efficiency and accuracy of USMLBM in simulating multiphase ferrofluid flows. We further adopt USMLBM to analyze in detail the mechanisms of bubble merging inside a ferrofluid under a uniform external magnetic field. The numerical results indicate that the bubbles tend to move toward each other and further merge together, even for a large initial separation between the bubbles. Due to complex interaction between the bubbles and the ferrofluid during the magnetophoretic acceleration process, the nonlinear effect on bubble merging is observed when the initial separation increases. Moreover, at a larger initial separation, the shape of bubbles seems to be not sensitive to the initial separation.

### Transmission of airborne virus through sneezed and coughed droplets

The spread of COVID19 through droplets ejected by infected individuals during sneezing and coughing has been considered a matter of key concern. Therefore, a quantitative understanding of the propagation of droplets containing the virus assumes immense importance. Here, we investigate the evolution of droplets in space and time under varying external conditions of temperature, humidity, and wind flow by using laws of statistical and fluid mechanics. The effects of drag, diffusion, and gravity on droplets of different sizes and ejection velocities have been considered during their motion in air. In still air, we found that bigger droplets traverse a larger distance, but smaller droplets remain suspended in air for a longer time. Therefore, in still air, the horizontal distance that a healthy individual should maintain from an infected one is based on the bigger droplets, but the time interval to be maintained is based on the smaller droplets. We show that in places with wind flow, the lighter droplets travel a larger distance and remain suspended in air for a longer time. Therefore, we conclude that both temporal and geometric distance that a healthy individual should maintain from an infected one is based on the smaller droplets under flowing air, which makes the use of a mask mandatory to prevent the virus. Maintenance of only stationary separation between healthy and infected individuals is not substantiated. The quantitative results obtained here will be useful to devise strategies for preventing the spread of other types of droplets containing microorganisms.

### Experimental investigation on pulsating pressure of a cone-cylinder-hemisphere model under different flow velocities

This paper presents the results of wall pulsating pressure experiments on a cone-cylinder-hemisphere model with lengths of 95 cm and maximum diameters of 20 cm under conditions of different flow velocities. By comparative analysis of experimental data, it has been found that the pulsating pressure on the wall surface of the flow-induced structure continues to rise as the flow velocity increases. It was also found that the pulsating pressure value of the shoulder and stern of the cone-cylinder-hemisphere structure is larger than in other positions. Additionally, the reliability and accuracy of the test results are verified by comparing the measured results with numerical simulation, and the characteristics and rules of the pulsating pressure of the flow-induced structure are analyzed. The pulsating pressure level is higher at the highest point and decays rapidly within 500 Hz; then, the decay rate slows down, and the pulsating pressure gradually decreases with frequency. Underwater vehicles usually adopt the form of a cone-cylindrical-hemisphere. Therefore, studying the pulsating pressure of a cone-cylinder-hemisphere structure is of great significance to the research of pulsating pressure and flow-induced noise of underwater vehicles.

### Sound propagation in porous materials containing rough tubes

A theoretical model is developed to quantify the influence of surface roughness on sound propagation in porous materials containing rough tubes by extending the Johnson–Champoux–Allard–Lafarge (JCAL) model. The five transport parameters of the JCAL model, including the viscous permeability, thermal permeability, tortuosity, viscous characteristic length, and thermal characteristic length, are calculated by modeling the rough tubes in the porous material as parallel rough tubes having idealized sinusoidal morphologies. The transport parameters obtained using the proposed model are validated by full finite element simulations. Based on these transport parameters, the sound absorption coefficient of the porous material containing idealized rough tubes is calculated, which agrees well with the FE result. The roughness effect is investigated by comparing sound absorption performance between parallel smooth tubes and parallel rough tubes. The existence of tube roughness weakens the thermal effect but dramatically strengthens the viscous effect in sound energy dissipation, resulting in enhanced sound absorption. This work provides fundamental insights on how surface roughness affects the acoustic performance of sound-absorbing porous materials.

### Ultrafast tomographic particle image velocimetry investigation on hypersonic boundary layers

For the first time, a tomographic particle image velocimetry system with a 1 MHz sampling rate is used to investigate the evolution of three-dimensional instabilities in a Mach 6 flat plate boundary layer. The system is combined with three ultrafast cameras, one eight-channel ultrafast laser, and one 36-channel synchronization controller. PCB® fast response pressure sensors are also applied to detect the instability evolution in the streamwise direction. Two near-wall volumes are investigated, the upstream one (volume 1) being in a laminar state and the downstream one (volume 2) containing evolving instabilities. For the laminar flow in volume 1, increasing the boundary layer thickness reduces distortion compared to the hypersonic Blasius solution; decreasing the streamwise location or increasing the angle of attack from 0° to 2° increases the distortion. For the disturbed flow in volume 2, the time-resolved evolution of a three-dimensional instability wave is captured in three snapshots, with its phase speed, wavelength, and frequency about 732 m/s, 49 mm, and 20 kHz. Because of the superposition effect of oblique waves, the instability travels like a chain of wavepackets in the streamwise direction, which is accompanied by an alternative distribution of high-speed and low-speed streaks in the spanwise direction.

### Pressure statistics of gas nuclei in homogeneous isotropic turbulence with an application to cavitation inception

The behavior of the pressure along the trajectories of finite-sized nuclei in isotropic homogeneous turbulence is investigated using direct numerical simulations at Reλ = 150. The trajectories of nuclei of different sizes are computed by solving a modified Maxey–Riley equation under different buoyancy conditions. Results show that larger nuclei are more attracted to the vortex cores and spend more time at low-pressure regions than smaller nuclei. The average frequency of pressure fluctuations toward negative values also increases with size. These effects level off as the Stokes number becomes greater than 1. Buoyancy, characterized by the terminal velocity [math], counteracts the attraction force toward vortex cores while simultaneously imposing an average vertical drift between the nuclei and the fluid. Computational results indicate that weak vortices, associated with moderately low pressures, lose their ability to capture finite-sized nuclei if [math] ≥ u′. The attraction exerted by the strongest vortices on the largest of the considered nuclei, on the other hand, can only be overcome by buoyancy if [math] ≥ 8u′. The quantitative results of this study are shown to have a significant impact on modeling cavitation inception in water. For this purpose, the Rayleigh–Plesset equation is solved along the nuclei trajectories with realistic sizes and turbulence intensities. The simulations predict cavitation inception at mean pressures several kPa above vapor pressure.

### Effect of co-flow velocity ratio on evolution of poly-disperse particles in coaxial turbulent jets: A large-eddy simulation study

In the present work, the particle-laden coaxial turbulent jet flow is studied using large-eddy simulation (LES). An Eulerian–Lagrangian framework is used to study the interaction between the continuous phase (air) and the discrete phase (glass bead particles). The solver is validated, using single-phase and particle-laden simulations, with reference data from experiments. A good match is observed between the present results and the reference data, for centerline velocity decay and radial profiles of axial velocity. Simulations are performed for three co-flow velocity ratios of 0, 1, and 1.5. The results pertaining to particle characteristics are presented for three different particle size-classes. The effect of the co-flow velocity ratio on the particle size–velocity correlation and velocity statistics of both phases are studied with an emphasis on understanding the differences in the particle dispersion due to co-flow around the central jet. It is observed that the particle size–velocity correlation is negative in the potential core region, and it becomes positive as one moves downstream. For heavy particles, the axial distance required to attain the same velocity as that of air increases with an increase in the co-flow velocity ratio. The size-conditioned particle number density profiles along the axial and radial directions of coaxial jets showed some interesting trends that could be explained based on the particle Stokes number effect. Significant radial dispersion of particles is realized when the corresponding Stokes number (StL), defined based on large-scale turbulent eddies, is of the order of one. The axial evolution of the characteristic particle size exhibited non-monotonic trends for all co-flow ratios. Overall, the present work demonstrates potential application of LES for an in-depth study of dispersion of poly-disperse particles in turbulent coaxial jets.

### Breakup of an electrified viscoelastic liquid bridge

Author(s): Manuel Rubio, Emilio J. Vega, Miguel A. Herrada, José M. Montanero, and Francisco J. Galindo-Rosales

We study both numerically and experimentally the breakup of a viscoelastic liquid bridge formed between two parallel electrodes. The polymer solutions and applied voltages are those commonly used in electrospinning and near-field electrospinning. We solve the leaky-dielectric finitely extensible non...

[Phys. Rev. E 102, 033103] Published Thu Sep 03, 2020

### A numerical study of particle jetting in a dense particle bed driven by an air-blast

In this work, the particle jetting behavior in a blast-driven dense particle bed is studied at early times. Four-way coupled Euler–Lagrange simulations are performed using a high-order discontinuous Galerkin spectral element solver coupled with a high-order Lagrangian particle solver, wherein the inter-particle collisions are resolved using a discrete element method collision model. Following the experiments of Rodriguez et al. [“Formation of particle jetting in a cylindrical shock tube,” Shock Waves 23(6), 619–634 (2013)] and the simulations of Osnes et al. [“Numerical simulation of particle jet formation induced by shock wave acceleration in a Hele-Shaw cell,” Shock Waves 28(3), 451–461 (2018)], the simulations are performed in a quasi-two-dimensional cylindrical geometry (Hele-Shaw cell). Parametric studies are carried out to assess the impact of the coefficient of restitution and the strength of the incident shock on the particle jetting behavior. The deposition of vorticity through a multiphase (gas–particle) analog of Richtmyer–Meshkov instability is observed to play a crucial role in channeling the particles into well-defined jets at the outer edge of the particle bed. This is confirmed by the presence of vortex pairs around the outer jets. Furthermore, the effect of the relaxation of the relative velocity between the two phases on the vorticity generation is explored by analyzing the correlation between the radial velocity of particles and the radial velocity of the gas at the particle location.

### Three-dimensional multiscale flow structures behind a wall-mounted short cylinder based on tomographic particle image velocimetry and three-dimensional orthogonal wavelet transform

Author(s): Hiroka Rinoshika, Akira Rinoshika, and Jin-Jun Wang

Three-dimensional (3D) flow structures around a wall-mounted short cylinder of height-to-diameter ratio 1 were instantaneously measured by a high-resolution tomographic particle image velocimetry (Tomo-PIV) at Reynolds number of 10 720 in a water tunnel. 3D velocity fields, 3D vorticity, the Q crite...

[Phys. Rev. E 102, 033101] Published Wed Sep 02, 2020

### Scaling laws of electroconvective flow with finite vortex height near permselective membranes

Author(s): Wei Liu, Yueting Zhou, and Pengpeng Shi

In a steady state, the linear scaling laws are confirmed between the intensity characteristics of electroconvective (EC) vortex (including the vortex height and electroosmotic slip velocity) and the applied voltage for the nonshear EC flow with finite vortex height near permselective membranes. This...

[Phys. Rev. E 102, 033102] Published Wed Sep 02, 2020

### Stability of gravity-driven liquid films overflowing microstructures with sharp corners

Author(s): Henning Bonart, Sangitha Rajes, Johannes Jung, and Jens-Uwe Repke

Detailed numerical simulations of a thin liquid film overflowing separated microstructures with sharp corners were conducted. The two-phase flows were described by the coupling between the Cahn-Hilliard and the Navier-Stokes equations. Our results indicate a strong influence of the microstructures on the stability of the liquid film.

[Phys. Rev. Fluids 5, 094001] Published Wed Sep 02, 2020

### Hydrodynamics of gas/shear-thinning liquid two-phase flow in a co-flow mini-channel: Flow pattern and bubble length

The flow patterns and bubble characteristics formed during gas–liquid flows in a circular co-flow mini-channel with carboxymethyl cellulose (CMC) aqueous solutions are investigated experimentally. The pattern transition and bubble length are elucidated by systematically analyzing the influences of the various factors of the ratio of gas–liquid flow rates, CMC solution mass fraction, and surfactant [sodium dodecyl sulfate (SDS)] mass fraction. Five kinds of flow regimes, namely, bubbly flow, Taylor flow, Taylor-annular flow, annular flow, and churn flow, are identified visually in the fully developed region of the inlet side of the channel, and a universal flow-regime map in terms of the gas and liquid inlet flow rates is constructed using water, CMC solution, and polyacrylamide solution to cover a broad range of material properties. It is found that the ratio of gas–liquid flow rates has a remarkable influence on the flow pattern transitions. The CMC solution mass fraction and SDS mass fraction can also affect the flow-regime map by varying the flow drag force and surface tension acting on the bubble in the mini-channel. The bubble length increases with the ratio of gas–liquid flow rates but decreases with the increase in the CMC fraction and SDS fraction. Based on consideration of the rheological properties of the liquid, a scaling law of bubble length in a co-flow mini-channel with shear-thinning liquids is developed, and the results predicted by it can agree with the measurement data very well under present conditions.

### Instability and interface coupling of coaxial liquid jets in a driving stream

The behavior of jet breakup and interface coupling in a co-flow focusing (CFF) process is studied theoretically. A physical model of coaxial liquid jets moving in an infinite annular driving stream is established, and the dimensionless dispersion relation for temporally axisymmetric perturbations is solved numerically. The effects of process parameters such as flow velocities, liquid physical properties, and radius ratio between the inner and outer jets on the jet instability are analyzed. The evolutions of interface perturbations are observed in CFF experiments, and the perturbation wavelengths under different liquid flow rates are measured in comparison with theoretical predictions. Moreover, the coupling of interface instabilities in CFF is studied through changing the radius ratio between the inner and outer liquid jets. In particular, two simplified single jet models under the assumption of minimum inner and outer liquid flow rates are proposed to reveal the transition from weak coupling to strong coupling of jet interfaces. This work provides great insight into the physical mechanism of interface instability in CFF advantageous for producing monodisperse microdroplets with fine robustness and high throughput.