# Latest papers in fluid mechanics

### Three-dimensional simulation of ligament formation and breakup caused by external vibration

Ligament formation followed by breakup is the primary process that controls external vibration-driven liquid atomization. In this paper, single-mode Faraday instabilities with detailed interfacial dynamics are studied via three-dimensional simulations with a validated numerical methodology. The detailed mechanisms of ligament formation and its breakup are illuminated. Colliding flow from adjacent troughs results in a pressure increase at the root of the crest. This nonlinear flow structure produces a local maximum pressure point that liberates the liquid region above it from the bulk liquid layer that synchronously moves with the bottom substrate. The appearance of the maximum pressure point can thus be recognized as the indicator of ligament formation. The freed ligament with capillary waves on its surface continues to grow until successive breakup occurs at its tip, which is driven by the “short-wave mode” breakup mechanism. It is found that the tip contraction dynamics of Faraday-type ligament can be well described by a one-dimensional theoretical model of a low-speed liquid jet under temporally periodic acceleration. Finally, the development behaviors of Faraday-type ligament and liquid jet are compared quantitatively, which reveals the analogy in their breakup dynamics in the tip regions.

### Evaporation driven detachment of a liquid bridge from a syringe needle in repose

In this paper, a study of the stability of an evaporating semi-unbounded axisymmetric liquid bridge that forms between a syringe needle tip and a horizontal interface by using both theory and experiments is presented. Here, the evaporation produces slow quasistatic motion such that it allows one to use hydrostatics to analyze interface profiles via solutions to the Young–Laplace equation. The two main parameters, in the hydrostatic limit, are the familiar Bond number and a slenderness parameter that often appears in the literature that studies liquid bridge stability. The axisymmetric Young–Laplace equation yields a semi-analytical solution for capillary pressure at zero Bond number using boundary conditions appropriate for this study. At finite Bond numbers, computation of interface profiles is used to estimate the maximum slenderness. Experiments using water for Bond numbers 0.01 < Bo < 0.1 show good agreement for the maximum slenderness when comparing those results with predictions based on solutions to the Young–Laplace equation.

### Wettability and capillary effects: Dynamics of pinch-off in unconstricted straight capillary tubes

Author(s): Soheil Esmaeilzadeh, Zhipeng Qin, Amir Riaz, and Hamdi A. Tchelepi

We study the interfacial evolution of immiscible two-phase flow within a capillary tube in the partial wetting regime using direct numerical simulation. We investigate the flow patterns resulting from the displacement of a more viscous fluid by a less viscous one under a wide range of wettability co...

[Phys. Rev. E 102, 023109] Published Wed Aug 12, 2020

### Resonance of droplets in constricted capillary tubes: Critical factors and nonlinearity

Author(s): Chao Zeng, Wen Deng, and M. Bayani Cardenas

A stationary nonwetting droplet in a constricted tube can attain resonance in response to external seismic stimulation. Key parameters controlling droplet resonance are analyzed through a proposed theoretical model. The nonlinear effect of a fluid system on the resonance is also addressed.

[Phys. Rev. Fluids 5, 083604] Published Wed Aug 12, 2020

### Forward, reverse, and no motion of Marangoni surfers under confinement

Author(s): Saeed Jafari Kang, Samrat Sur, Jonathan P. Rothstein, and Hassan Masoud

The propulsion characteristics of Marangoni surfers under confinement is examined. Through experimental measurements and numerical simulations, it is demonstrated that, contrary to what might be the usual expectation, the surfers may propel themselves in the direction of lower surface tension. It is discovered that negative pressure is the primary contributor to the fluid force experienced by the surfer and that this suction force is mainly responsible for the reverse Marangoni propulsion.

[Phys. Rev. Fluids 5, 084004] Published Wed Aug 12, 2020

### Modal analysis of the behavior of inertial particles in turbulence subjected to Stokes drag

Author(s): Mahdi Esmaily and Ali Mani

The complexity of the problem of clustering of inertial particles in turbulence has intrigued researchers for decades. Here it is shown how a simple one-dimensional flow oscillating at a single frequency explains much of that complexity, and a solution for the Lyapunov exponents of inertial particles subjected to oscillator fluid motion is derived.

[Phys. Rev. Fluids 5, 084303] Published Wed Aug 12, 2020

### Turbulent universality and the drift velocity at the interface between two homogeneous fluids

The drift velocity U0 at the interface between two homogeneous turbulent fluids of arbitrary relative densities in differential mean motion is considered. It is shown that an analytical expression for U0 follows from the classical scaling for these flows when the scaling is supplemented by standard turbulent universality and symmetry assumptions. This predicted U0 is the weighted mean of the free-stream velocities in each fluid, where the weighting factors are the square roots of the densities of the two fluids, normalized by their sum. For fluids of nearly equal densities, this weighted mean reduces to the simple mean of the free-stream velocities. For fluids of two widely differing densities, such as air overlying water, the result gives U0 ≈ αV∞, where α ≪ 1 is the square root of the ratio of the fluid densities, V∞ is the free-stream velocity of the overlying fluid, and the denser fluid is assumed nearly stationary. Comparisons with two classical laboratory experiments for fluids in these two limits and with previous numerical simulations of flow near a gas–liquid interface provide specific illustrations of the result. Solutions of a classical analytical model formulated to reproduce the air–water laboratory flow reveal compensating departures from the universality prediction, of order 15% in α, including a correction that is logarithmic in the ratio of dimensionless air and water roughness lengths. Solutions reproducing the numerical simulations illustrate that the logarithmic correction can arise from asymmetry in the dimensionless laminar viscous sublayers.

### Experimental study of breathers and rogue waves generated by random waves over non-uniform bathymetry

We present experimental evidence of formation and persistence of localized waves, breathers, and solitons, occurring in a random sea state and uniformly traveling over non-uniform bathymetry. Recent studies suggest connections between breather dynamics and irregular sea states and between extreme wave formation and breathers, random sea states, or non-uniform bathymetry individually. In this paper, we investigate the joint connection between these phenomena, and we found that breathers and deep-water solitons can persist in more complex environments. Three different sets of significant heights have been generated within a Joint North Sea Wave Observation Project wave spectrum, and the wave heights were recorded with gauges in a wave tank. Statistical analysis was applied to the experimental data, including the space and time distribution of kurtosis, skewness, Benjamin–Feir index, moving Fourier spectra, and probability distribution of wave heights. Stable wave packages formed out of the random wave field and traveling over shoals, valleys, and slopes were compared with exact solutions of the nonlinear Schrödinger equation with a good match, demonstrating that these localized waves have the same structure as deep-water breathers. We identify the formation of rogue waves at moments and over regions where the kurtosis and skewness have local maxima. These results provide insights for understanding of the robustness of Peregrine and higher-order Akhmediev breathers, Kuznetsov–Ma solitons, and rogue waves, and their occurrence in realistic oceanic conditions, and may motivate analogous studies in other fields of physics to identify limitations of exact weakly nonlinear models in non-homogeneous media.

### Rarefied gas flow past a flat plate at zero angle of attack

We consider subsonic, transonic, and moderate supersonic rarefied monatomic gas flows past a flat plate at zero angle of attack in the transitional regime. The influence of the rarefaction on the flow pattern is investigated mainly by the direct simulation Monte Carlo method. We study the shear stress, normal momentum flux transferred to the plate, and energy flux transferred to the plate at various Knudsen numbers, Mach numbers, and plate temperatures. We show that if the plate temperature is equal to the temperature of the undisturbed gas, then at any Mach number of the incoming flow, the average dimensionless normal momentum transferred to the plate has at least one extreme with respect to the Knudsen number. Specifically, in the supersonic and sonic cases, these dependences have a maximum. In the case of subsonic transonic Mach number M = 0.8, the dependence has a weak maximum and a weak minimum. At M = 0.5, it has weak minimum. We show that in a wide temperature range at subsonic and moderate supersonic Mach numbers in the transitional regime, the plate temperature very weakly affects the average friction force acting on the plate. We show that there exist certain intervals of plate temperatures ratios and Mach numbers such that the average dimensionless energy flux transferred to the plate changes the sign if the Knudsen number increases, previously reaching a local negative minimum.

### Head-on collision of two immiscible droplets of different components

We numerically study the head-on collisions of two immiscible droplets of different components and focus on the effects of droplet inertia and interfaces, which are expected to play a crucial role in the interaction between the two droplets. A ternary-fluid diffuse-interface method is used here after being validated by comparing against experiments of the collision between an aqueous droplet and a silicone oil droplet. In order to figure out how the droplet inertia and interfaces affect the dynamic behavior after the collision, axisymmetric simulations are performed with various Weber number We and surface tension ratio λ, i.e., the ratio of the surface tension coefficient of the liquid–liquid to the liquid–gas interfaces. Their effects on the film thickness, maximal deformation of the colliding droplets, and the corresponding contact time are investigated. To describe the collision dynamics, we propose an equivalent surface tension σ* based on the analysis of the energy conservation and morphology of the colliding droplets. Using the equivalent surface tension σ*, we theoretically predict the film thickness, maximal spreading time, and deformation of the colliding droplets. The theoretical predictions are in good agreement with the numerical results.

### Coherent vortex in two-dimensional turbulence: Interplay of viscosity and bottom friction

Author(s): I. V. Kolokolov and V. V. Lebedev

We examine coherent vortices appearing as a result of the inverse cascade of two-dimensional turbulence in a finite box in the case of pumping with arbitrary correlation time in the quasilinear regime. We demonstrate that the existence of the vortices depends on the ratio between the values of the b...

[Phys. Rev. E 102, 023108] Published Tue Aug 11, 2020

### Lift induced by slip inhomogeneities in lubricated contacts

Author(s): Aidan Rinehart, Uğis Lācis, Thomas Salez, and Shervin Bagheri

A small change of slip boundary condition within a lubrication region breaks the fore-aft symmetry, which leads to a significant lift force. The change of slippage arises naturally on surfaces where physical and/or chemical properties are not perfectly constant. The induced lift force may result in nontrivial trajectories of particles traveling near surfaces.

[Phys. Rev. Fluids 5, 082001(R)] Published Tue Aug 11, 2020

### Inertial dynamics of an interface with interfacial mass flux: Stability and flow fields’ structure, inertial stabilization mechanism, degeneracy of Landau’s solution, effect of energy fluctuations, and chemistry-induced instabilities

This work focuses on the long-standing problem of inertial dynamics of an interface with interfacial mass flux and reports new mechanisms for the interface stabilization and destabilization. The interface is a phase boundary separating fluids of different densities and having interfacial mass flux. To analyze the interface dynamics from a far field, we develop and apply the general matrix method to rigorously solve the boundary value problem involving the governing equations in the fluid bulk and the boundary conditions at the interface and at the outside boundaries of the domain. We find the fundamental solutions for the linearized system of equations and analyze the interplay of interface stability with flow fields’ structure by directly linking rigorous mathematical attributes to physical observables. We find that the interface is stable when the dynamics conserves the fluxes of mass, momentum, and energy; the stabilization is due to an inertial mechanism causing small oscillations of the interface velocity. In the classic Landau’s dynamics, the postulate of perfect constancy of the interface velocity leads to the development of Landau–Darrieus instability. This destabilization is also linked to the imbalance of the perturbed energy at the interface. The classic Landau’s solution is found to have degeneracy; lifting of the degeneracy may lead to singularity and self-similar dynamics. Our results compare well with traditional theories of combustion and propose new experiments to study the dynamics of the interface and the flow fields in combustible systems. We further conduct reactive molecular dynamics simulations to elucidate the complexity of chemical processes, to study the destabilizing effect of energy fluctuations on the interface stability, and to illustrate the chemistry-induced instabilities. In summary, we identify the extreme sensitivity of the interface dynamics to the interfacial boundary conditions, including the formal properties of fundamental solutions and the qualitative and quantitative properties of the flow fields. This provides new opportunities for studies, diagnostics, and control of multiphase flows in a broad range of processes in nature and technology.

### Tailoring surface wettability to reduce chances of infection of COVID-19 by a respiratory droplet and to improve the effectiveness of personal protection equipment

Motivated by the fact that the drying time of respiratory droplets is related to the spread of COVID-19 [R. Bhardwaj and A. Agrawal, “Likelihood of survival of coronavirus in a respiratory droplet deposited on a solid surface,” Phys. Fluids 32, 061704, (2020)], we analyze the drying time of droplets ejected from a COVID-19 infected subject on surfaces of personal protection equipment (PPE), such as a face mask, of different wettabilities. We report the ratio of drying time of the droplet on an ideal superhydrophobic surface (contact angle, θ → 180°) to an ideal hydrophilic surface (θ → 0°) and the ratio of the maximum to minimum drying time of the droplet on the surfaces with different contact angles. The drying time is found to be maximum if θ = 148°, while the aforementioned ratios are 4.6 and 4.8, respectively. These ratios are independent of the droplet initial volume, ambient temperature, relative humidity, and thermophysical properties of the droplet and water vapor. We briefly examine the change in drying time in the presence of impurities on the surface. Besides being of fundamental interest, the analysis provides insights that are useful while designing the PPE to tackle the present pandemic.

### Effect of inflow temperature on root canal irrigation: A computational fluid dynamics study

Root canal therapy is one of the main treatment options for endodontic diseases in which an effective irrigation is key to a successful therapy. In the present paper, the irrigation flow inside an instrumented root canal is numerically investigated, and then the effect of inflow temperature on the irrigation is analyzed based on the computational fluid dynamics results. The magnitude of the shear stress and its corresponding coverage of the irrigation flow on the wall is adopted to characterize the clean efficiency. The axial velocity is used to represent the replacement of local flow field, which stands for the capability to carry away the cleaning residue. Results show that the effective area that the shear stress covers on the root canal wall behind the needle outlet is usually larger than that in front of the outlet, and both the effective coverage of the shear stress and the replacement of the irrigant are improved when the velocity increases. It is convinced that the critical shear stress, namely, the lowest shear stress required to peel off the smear layer on the root canal wall, decreases with the increase in the temperature. Although no apparent variation of the shear stress on the wall can be observed while improving the inflow temperature, the effective surface to be cleaned is improved to some extent because of the decrease in the critical shear stress. Meanwhile, the power consumption is reduced obviously. If the input power remains constant when the temperature increases, both the shear stress on the wall and the replacement are significantly improved besides the decrease in the critical shear stress. This means both the clean efficiency on the wall and the clearing capability (namely replacement) in local flow field are significantly promoted.

### Jeffery orbits for an object with discrete rotational symmetry

We theoretically investigate the motions of an object immersed in a background flow at a low Reynolds number, generalizing the Jeffery equation for the angular dynamics to the case of an object with n-fold rotational symmetry (n ≥ 3). We demonstrate that when n ≥ 4, the dynamics are identical to those of a helicoidal object for which two parameters related to the shape of the object, namely, the Bretherton constant and a chirality parameter, determine the dynamics. When n = 3, however, we find that the equations require a new parameter that is related to the shape and represents the strength of triangularity. On the basis of detailed symmetry arguments, we show theoretically that microscopic objects can be categorized into a small number of classes that exhibit different dynamics in a background flow. We perform further analyses of the angular dynamics in a simple shear flow, and we find that the presence of triangularity can lead to chaotic angular dynamics, although the dynamics typically possess stable periodic orbits, as further demonstrated by an example of a triangular object. Our findings provide a comprehensive viewpoint concerning the dynamics of an object in a flow, emphasizing the notable simplification of the dynamics resulting from the symmetry of the object’s shape, and they will be useful in studies of fluid–structure interactions at a low Reynolds number.

### Numerical modeling of the distribution of virus carrying saliva droplets during sneeze and cough

Violent respiratory diseases, i.e., coronavirus (COVID-19), spread through saliva in coughs and sneezes or are even exhaled in the form of microbial pathogen micro-droplets. Therefore, in this work, a comprehensive fully coupled Eulerian–Lagrangian method has been applied for infection control, thus leading to a deeper understanding of the saliva-disease-carrier droplet transmission mechanisms and also of their trajectory tracking by using the OpenFOAM package. This model determines the droplet–air interactions, the breakup process, and turbulent dispersion forces on each micro-droplet that is expelled within the respiratory tract in a correct way. By examining a broad range of initial velocities, size distributions, injection angles of saliva micro-droplets, and mouth opening areas, we predict the maximum opening area that can be driven by micro-droplets. One important contribution of this work is to present a correlation for the length and width of the overall direct maximum reach of the micro-droplets, driven by a wide range of mild coughs to intense sneezes. Our results indicate that the movement of the expelled droplets is mainly influenced by their size, angle, velocity, and environmental factors. During a virus crisis, like COVID-19, this paper can be used to determine the “social distance” between individuals to avoid contamination, by inhaling or touching their bodies, due to these saliva-disease-carrier droplets in sneezing, at various social distance positions such as face-to-face, meeting standing, and near equipment. The safe distance must be increased to around 4 m during a sneeze. By wearing a face mask and by bending the head during a sneeze as a protective action, we can reduce the contamination area to one-third and three-quarters, respectively. Furthermore, the dispersion of the film of the expelled saliva micro-droplets and the spatial relationship between the subjects, which affects the airflow inside the room, are also analyzed in detail.

### Predicting turbulent flows in butterfly valves with the nonlinear eddy viscosity and explicit algebraic Reynolds stress models

The development of turbulence modeling is crucial for the numerical prediction of the flow behavior, especially for separation, stagnation, reattachment, recirculation, and streamline curvature of the flow through complex structures. In this study, the capability of turbulence models was estimated for predicting the flow in a butterfly valve. The explicit algebraic Reynolds stress model (EARSM) and nonlinear eddy viscosity model (NLEVM) were evaluated in terms of the velocity profile, turbulence intensity, and Reynolds stress, and their results were compared with those of the standard k–ε and renormalization group (RNG) models. A numerical validation was conducted with the flow past a backward-facing step as the benchmark test. Comparison with the validation test showed that the NLEVM accurately predicted the reattachment length. For the flow in a butterfly valve, the NLEVM and EARSM indicated a smaller velocity increase than the standard k–ε and RNG models in the recirculation area near the valve region. The NLEVM and EARSM demonstrated an ability to predict anisotropic stresses with a dominant stress value near the valve region.

### Explosion-driven interfacial instabilities of granular media

This paper investigates the evolution of a Richtmyer–Meshkov (RM)-like instability on the internal surface of particle rings impinged by divergent blast waves. Despite the signature spike–bubble instability structure analogous to the hydrodynamic RM instability, the growth of the perturbation amplitude in granular media undergoes an exponential phase followed by a linear phase, markedly differing from the hydrodynamic RM instability and indicating a fundamentally different mechanism. The granular RM-like instability arises from the incipient transverse granular flows induced by hydrodynamic effects upon the shock interaction. Substantial perturbation growth is initiated by the ensuing rarefaction dilation when the hydrodynamic effects are small. It is found that the interplay between the localized transverse and radial granular flows sustains the persistent perturbation growth and drives the corresponding morphological changes in the instability pattern.

### Two-temperature Navier-Stokes equations for a polyatomic gas derived from kinetic theory

Author(s): Kazuo Aoki, Marzia Bisi, Maria Groppi, and Shingo Kosuge

A polyatomic gas with slow relaxation of the internal modes is considered, and the Navier-Stokes equations with two temperatures, the translational and internal temperatures, are derived for such a gas on the basis of the ellipsoidal-statistical (ES) model of the Boltzmann equation for a polyatomic ...

[Phys. Rev. E 102, 023104] Published Mon Aug 10, 2020