# Latest papers in fluid mechanics

### Numerical convergence of volume of fluid based large eddy simulations of atomizing sprays

This paper presents three volume of fluid (VoF)-based methods for large eddy simulations of atomizing sprays with different treatments of the unresolved interface. The turbulent filtered VoF model uses conventional turbulent viscosity models to close the combined interfacial and turbulent sub-grid fluctuations. The hybrid turbulence filtering and artificial compression model includes an additional artificial compression term that is applied along regions where the liquid–air interface is continuous, while conventional turbulence filtering is activated in regions with discrete liquid objects. The new explicit volume diffusion model (EVD) is based on the concept of averaging the VoF equations over explicitly defined physical volumes that are independent of the numerical grid. Closure models of the sub-volume flux and stress terms introduce explicit volume diffusion and explicit volume viscosity that are physically defined and linked to the volume size. Numerical convergence is achieved by reducing the grid size while keeping the explicit volume size constant. The models are tested for two experimental atomizing spray cases with different Weber numbers. The superior numerical convergence of the EVD model is demonstrated by analysis of the mean and rms of the volume fraction and velocity fields. Two models for the surface tension force are investigated for the EVD simulations. Compared with the simple surface tension model which neglects sub-grid fluctuations, an improved volume-averaged model based on fractal properties of wrinkled sub-volume interfaces gives better predictions of the mean volume fraction relative to the experimental data but requires selection of a model constant.

### Non-Newtonian power-law fluid flow over obstacles embedded inside a cavity

In this study, the flow of non-Newtonian fluid inside the lid-driven cavity with obstacle(s) is examined. The behavior of the fluid is described by the Ostwald-de Waele or power-law model. The lattice Boltzmann method (LBM) with a multiple-relaxation-time (MRT) collision model is employed to simulate complex fluid flows around the circular and square obstacles embedded inside a cavity. The stability of the present MRT-LBM algorithm in terms of so-called, cell-Reynolds number is investigated. The physics of flow structure and examinations of streamlines and vorticity contours are carried out for power-law as well as Newtonian fluids. For a single obstacle, the effects of various parameters such as Reynolds number (with respect to lid-dimension), obstacle size, power-law index, and shape of the obstacle on the flow characteristics and vortex formation are investigated. Furthermore, the effect of two square obstacles arranged in side-by-side and tandem manners inside the cavity is analyzed. Finally, the complex fluid flow over the multiple square obstacles embedded inside the cavity as a porous block for two blockage ratios is examined.

### Efficacy of face coverings in reducing transmission of COVID-19: Calculations based on models of droplet capture

In the COVID-19 pandemic, among the more controversial issues is the use of masks and face coverings. Much of the concern boils down to the question—just how effective are face coverings? One means to address this question is to review our understanding of the physical mechanisms by which masks and coverings operate—steric interception, inertial impaction, diffusion, and electrostatic capture. We enquire as to what extent these can be used to predict the efficacy of coverings. We combine the predictions of the models of these mechanisms which exist in the filtration literature and compare the predictions with recent experiments and lattice Boltzmann simulations, and find reasonable agreement with the former and good agreement with the latter. Building on these results, we explore the parameter space for woven cotton fabrics to show that three-layered cloth masks can be constructed with comparable filtration performance to surgical masks under ideal conditions. Reusable cloth masks thus present an environmentally friendly alternative to surgical masks so long as the face seal is adequate enough to minimize leakage.

### Deflection of a bubble pair induced by negative magnetophoresis in a Hele-Shaw cell

To explore how a magnetic field act on the motion of a bubble pair suspended in a ferrofluid, we introduce an “effective magnetic dipole” to represent the air bubble and further solve the two-dimensional Laplace's equation to obtain the distribution of magnetic potential. The derived magnetic interaction force has two components. The tangential one allows the bubble pair to deflect to be parallel to the magnetic field, where the deflection is clockwise at an angle less than 90°. Inversely, it is counterclockwise. The radial component appears as attraction or repulsion depending on the relative position, which switches from attraction to repulsion at critical angles θc = 55° and 125°. Meanwhile, we performed a simple verification experiment in a Hele–Shaw cell to evaluate the deflection angle and spacing of the bubble pair, and the results are in good agreement with the model. This technique has promise in bubble manipulation for microfluidics.

### Vortex dynamics and fractal structures in reactive and nonreactive Richtmyer–Meshkov instability

Hydrodynamic instabilities caused by shock-flame interactions are a fundamental challenge in the accurate prediction of explosion loads in the context of nuclear and process plant safety. To investigate the Richtmyer–Meshkov instability, a series of three-dimensional numerical simulations of shock-flame interactions are performed, including lean, stoichiometric, and nonreactive homogeneous H2/Air mixtures. The equivalence ratio has a strong influence on the achievable flame wrinkling and mixing, by impacting key physical parameters such as the heat release parameter, flame thickness, and reactivity. The reactivity is found to be a decisive factor in the evolution of the wrinkled flame brush, as it can cause burnout of the developing fresh gas cusps and wrinkled structures. The importance of reactivity is further emphasized by comparisons to a nonreactive case. Analysis of the enstrophy (energy equivalent of vorticity) transport terms shows that baroclinic torque is dominant during shock-flame interactions. After the shock interaction, the vortex stretching, dissipation, and dilatation terms gain in importance significantly. A power-law based modeling approach of the flame wrinkling is investigated by explicitly filtering the present simulation data. The values determined for the fractal dimension show a nonlinear dependency on the chosen equivalence ratio, whereas the inner cutoff scale is found to be approximately independent of the equivalence ratio for the investigated cases.

### Deformation of soap bubbles in uniform electric fields

Author(s): S. Mawet, H. Caps, and S. Dorbolo

Soap bubbles are easy to deform: a child blowing, the wind, or an electric field imposed by a plane capacitor are some possible examples. When an electric field is applied, a bubble elongates along the direction of the field, deforming into a spheroid. For a sufficiently high electric field, bubbles eventually become conical, forming a so-called Taylor cone. In addition to the dependence on the electric field and the soapy solution used, the shape of a bubble is also related to the substrate on which it rests, namely a solid plate or a liquid bath.

[Phys. Rev. Fluids 6, 043603] Published Tue Apr 27, 2021

### Coupled x-ray high-speed imaging and pressure measurements in a cavitating backward facing step flow

Author(s): G. Maurice, N. Machicoane, S. Barre, and H. Djeridi

The two-phase flow generated behind a cavitating backward-facing step is studied using the combination of three experimental techniques: wall-pressure measurements, global high-speed imaging with visible light, and high spatial and temporal resolution x-ray imaging. Three zones are identified based on the topology of the vapor fraction maps, that correspond to vaporization, transport, and condensation. Simultaneous pressure and void fraction measurements reveal that extreme events are associated with a change from a shear layer mode to a wake mode, with a temporal signature that is heavily affected by the presence of the vapor phase.

[Phys. Rev. Fluids 6, 044311] Published Tue Apr 27, 2021

### Wake structure characteristics of three tandem circular cylinders at a low Reynolds number of 160

This paper reports the results of a numerical investigation into the flow around three isodiametric circular cylinders placed in an in-line configuration with identical spacing and the associated wake structures. The effect of spacing ratio (L/D, where L is the center-to-center spacing between two adjacent cylinders and D is the cylinder diameter) ranging from 1.5D to 10D with increment of 0.5D is examined at a low Reynolds number of 160. The results indicate that the wake structure experiences three evolutions as L/D increases, exhibiting four combined flow patterns: the overshoot, continuous reattachment-alternate reattachment (CR-AR), quasi-co-shedding (QCS), and co-shedding-co-shedding regimes. More than one frequency participates in the lift fluctuation for all three cylinders in the latter three patterns, signifying the wake interference. The evolution of the flow regime results in the variations of drag and lift coefficients, the alteration of pressure distribution around the cylinders' surface, and the switching of the phase lags of fluctuating lifts as well as the modification of vortex shedding characteristics, including the vortex formation location, wake width, and shedding frequencies. Particularly, the fluid forces and Strouhal number for the upstream and middle cylinders present a jump in the transition from the CR-AR to QCS regimes, while the fluid forces are reduced for the downstream cylinder. Furthermore, the transition from two layered vortices to the secondary vortex street is observed at 3.5 < L/D ≤ 6.5, where the downstream cylinder is sandwiched between the two shear layers detached from the middle cylinder, and two same-sign vortices in the same layer merge into a new vortex in the far wake.

### Reaction zone structure and detonation parameters of nitromethane/polymethylmethacrylate and its mixture with microballoons

In the present work, the detonation wave structure and detonation parameters for nitromethane (NM) and its mixtures with polymethylmethacrylate (PMMA) and glass microballoons (GMB) were studied by a velocity interferometer system for any reflector laser interferometer. The PMMA concentration varied from 2% to 4%. It is shown that PMMA additives lead to a change in the reaction zone structure, which can be observed as an appearance of a cellular instability of the detonation front. The detonation parameters of the mixture up to 3% PMMA are close to those of pure nitromethane and reduced when 4% PMMA is added. The addition of 2% GMB to the NM/PMMA mixture leads to the formation of a detonation front with a characteristic size of heterogeneities on the order of GMB diameter. In this case, the detonation parameters are reduced, and the values of the detonation velocity decrease by about 10% compared to NM/PMMA mixtures.

### Research on the contact time of a bouncing microdroplet with lattice Boltzmann method

The bouncing dynamics of microdroplets with various viscosities on a superhydrophobic surface is numerically investigated. An axisymmetric lattice Boltzmann method is developed on the basis of Zheng et al. capable of handling multiphase flows with a large density ratio, which is implemented to simulate the impact. It is shown that in the low-viscosity regime, the contact time tc remains constant over a wide Weber number range (10 < We < 120), which is consistent with macro-scale bouncing. Nevertheless, in the high-viscosity regime, tc increases with impact velocity. A contact number [math] is proposed to describe the viscosity effect; meanwhile, a new scaling [math] is deduced to characterize the contact time for this regime, and the simulated results for such droplets agree well with the new scaling. To find out the internal physical mechanism, the evolution of kinetic energy, dissipated energy, and velocity vector fields is studied, which quantifies the impact dynamics. Also, simulation data demonstrate that viscous dissipation is not negligible even for relatively low-viscosity fluids. These findings are highly useful for fundamental understanding of microdroplet dynamics with various viscosities, and it can be used to precisely control the contact time.

### Geometric and energy-aware decomposition of the Navier–Stokes equations: A port-Hamiltonian approach

A port-Hamiltonian model for compressible Newtonian fluid dynamics is presented in entirely coordinate-independent geometric fashion. This is achieved by the use of tensor-valued differential forms that allow us to describe the interconnection of the power preserving structure which underlies the motion of perfect fluids to a dissipative port which encodes Newtonian constitutive relations of shear and bulk stresses. The relevant diffusion and the boundary terms characterizing the Navier–Stokes equations on a general Riemannian manifold arise naturally from the proposed construction.

### Attenuating surface gravity waves with mechanical metamaterials

Metamaterials and photonic/phononic crystals have been successfully developed in recent years to achieve advanced wave manipulation and control, both in electromagnetism and mechanics. However, the underlying concepts are yet to be fully applied to the field of fluid dynamics and water waves. Here, we present an example of the interaction of surface gravity waves with a mechanical metamaterial, i.e., periodic underwater oscillating resonators. In particular, we study a device composed of an array of periodic submerged harmonic oscillators whose objective is to absorb wave energy and dissipate it inside the fluid in the form of heat. The study is performed using a state-of-the-art direct numerical simulation of the Navier–Stokes equation in its two-dimensional form with free boundary and moving bodies. We use a volume of fluid interface technique for tracking the surface and an immersed boundary method for the fluid–structure interaction. We first study the interaction of a monochromatic wave with a single oscillator and then add up to four resonators coupled only fluid-mechanically. We study the efficiency of the device in terms of the total energy dissipation and find that by adding resonators, the dissipation increases in a nontrivial way. As expected, a large energy attenuation is achieved when the wave and resonators are characterized by similar frequencies. As the number of resonators is increased, the range of attenuated frequencies also increases. The concept and results presented herein are of relevance for coastal protection applications.

### Flow in a ring-sheared drop: Drop deformation

The ring-sheared drop is a containerless system where shear is imparted by two contact rings, one rotating and the other stationary. In microgravity, aqueous drops can be studied in the air at the centimeter scale. Drops of this scale can also be studied experimentally on Earth, but the effects of gravity need to be mitigated by density matching the drop liquid and its surrounding fluid. The use of silicone oil drops surrounded by an aqueous solution allows density matching while retaining the viscosity ratio of the aqueous-air system in microgravity. The imposed shear drives a meridional flow in the drop which leads to a pear-shaped drop. A perturbation analysis with the capillary number as the small parameter is used to account for this mean drop deformation. The theory and time-averaged experiments agree, particularly at smaller ring rotation rates where the capillary number in the experiments is smaller. On top of the mean deformation, there is a smaller amplitude nonaxisymmetric deformation, which for slower ring rotation rates consists of a rotating wave with azimuthal wavenumber m = 1, that is, synchronous with the rotating ring. This is traced back to imperfections in the wetting and contact between the drop and the rotating ring in the experiment. At larger ring rotations, the experiments detect further unsteadiness with a broad frequency peak at about one third the ring rotation rate. Nonlinear simulations of the outer flow, assuming a nondeforming drop, find that at these ring rotations, the outer flow is unsteady with a similar frequency peak.

### Initial spreading dynamics of a liquid droplet: The effects of wettability, liquid properties, and substrate topography

The initial spreading of glycerol and silicon oil droplets on smooth, corrugated, and orthogonal surfaces is numerically investigated by an effective, sharp-interface modeling method. In this study, the temporal evolution of spreading radius during the initial phase is scaled by R/R0 = C(t/τi)α for inertial regime and R/R0 = C(t/τμ)α for the viscous regime. We focus on exploring how wettability, liquid properties, and substrate topography influence the exponent α and coefficient C. Instead of discussing the effects of density, viscosity, and surface tension separately, we use the Ohnesorge number Oh = μ/(ρD0γ)1/2 to unify the combined influence of liquid properties. The results show that in the inertial regime (Oh ≪ 1), α is determined by wettability and the capillary wave is observed to propagate along the droplet interface, whereas in the viscous regime (Oh ≫ 1), α is determined by Oh and no capillary wave is observed. Consequently, both qualitative (propagation of capillary wave) and quantitative (Ohnesorge number) criteria to distinguish the two distinct regimes are provided. Regarding the coefficient C, it is found to increase with the increasing hydrophilicity and decreasing Oh in the inertial regime. A larger C is also observed in orthogonal microgrooves with wider gap or narrower width. Besides, the hydrophobicity and hydrophilicity can be enhanced by the corrugated surfaces, inducing a higher and lower α on hydrophilic and hydrophobic corrugated surfaces, respectively. Meanwhile, some interesting phenomena are also observed, such as the faster contact line velocity on the inside of a single corrugation and the “stick-jump” advancing mode of the contact line on orthogonal surfaces.

### Linear and nonlinear hydromagnetic stability in laminar and turbulent flows

Author(s): Itzhak Fouxon, Joshua Feinberg, and Michael Mond

We consider the evolution of arbitrarily large perturbations of a prescribed pure hydrodynamical flow of an electrically conducting fluid. We study whether the flow perturbations as well as the generated magnetic fields decay or grow with time and constitute a dynamo process. For that purpose we der...

[Phys. Rev. E 103, 043104] Published Mon Apr 26, 2021

### Evaporation and propagation of liquid drop streams at vacuum pressures: Experiments and modeling

Author(s): Daniel R. Guildenbecher, John J. Barnard, Thomas W. Grasser, Anthony M. McMaster, Robert B. Campbell, David P. Grote, Prabal Nandy, and Max Light

Evaporation of streams of liquid droplets in environments at vacuum pressures below the vapor pressure has not been widely studied. Here, experiments and simulations are reported that quantify the change in droplet diameter when a steady stream of ≈100 μm diameter drops is injected into a chamber in...

[Phys. Rev. E 103, 043105] Published Mon Apr 26, 2021

### Front-back asymmetry controls the impact of viscoelasticity on helical swimming

Author(s): Veronica Angeles, Francisco A. Godínez, Jhonny A. Puente-Velazquez, Rodrigo Mendez-Rojano, Eric Lauga, and Roberto Zenit

We conduct experiments to study magnetic helical swimmers in viscoelastic fluids. The swimming speed is strongly influenced by the tail-to-head size ratio: the speed can be larger, similar, or smaller than the Newtonian one depending on the value of the size ratio. We conjecture that this size asymmetry induces a net viscoelastic force that affects the swimming speed.

[Phys. Rev. Fluids 6, 043102] Published Mon Apr 26, 2021

### Theory of bubble tips in strong viscous flows

Author(s): Jens Eggers

Like the bubble tip frozen into a drinking glass, very sharp tips are formed generically at the end of drops and bubbles in strong flows. We show that the tip curvature is exponentially large in the square of the flow strength, and that the bubble ends are almost conical, but with a slope that increases logarithmically as the tip is approached. This solution of the viscous flow equations is shown to match to the slender bubble shape valid away from the tip, found by G.I. Taylor.

[Phys. Rev. Fluids 6, 044005] Published Mon Apr 26, 2021

### Wetting dynamics of a sessile ferrofluid droplet on solid substrates with different wettabilities

There are several numerical approaches to define a permanent magnet in terms of mathematical equations, and each approach has progressed since its inception, but still endures some limitations on specific numerical phenomena. This study seeks to propose a novel numerical representation of a permanent magnet without incorporating its effect through boundary conditions, which overcomes the limitations of previous studies and enables us to introduce a magnetic field of desired strength at any location. A self-correcting method is modified to incorporate the magnetic field effects, while a simplified lattice Boltzmann method is utilized to solve the governing equations for flow field and interface. The validity of the proposed method is ensured by simulating some benchmark phenomena with and without the external magnetic field. This study also investigates the wetting dynamics of a sessile ferrofluid droplet deposited on solid substrates with different wettabilities. The influence of uniform and non-uniform magnetic fields on droplet spreading is discussed in detail. It is observed that for a non-uniform magnetic field in vertical direction, the ferrofluid droplet on a hydrophilic surface does not observe the spherical cap approximation unless the magnetic field strength is below saturation magnetization. Moreover, if the magnet is located above, the droplet undergoes large deformations and achieves pointy shapes with sharp tips on less wettable surfaces.

### Draining and spreading along geometries that cause converging flows: Viscous gravity currents on a downward-pointing cone and a bowl-shaped hemisphere

Author(s): Nan Xue and Howard A. Stone

We report experiments observing the gravitational axisymmetric spreading of a viscous liquid with a fixed volume on inclined geometries that cause converging flows, for example, on a funnel and a bowl. The spreading of the liquid on these geometries is different from that on typical geometries such as an inclined plate: the thickness of the spreading front first decreases in time and then increases. These geometries also induce different new thresholds of fingering instabilities.

[Phys. Rev. Fluids 6, 043801] Published Fri Apr 23, 2021