# Latest papers in fluid mechanics

### Energy budget of a viscoelastic planar liquid sheet in the presence of gas velocity oscillations

This study investigates the energy budget of a viscoelastic planar liquid sheet in the presence of gas velocity oscillations. The energy budget is studied in different unstable regions, and the results are very different from those obtained for steady basic flow. The work done by surface tension and aerodynamic forces is periodic, leading to the growth of standing waves on liquid sheets. The positive work done by aerodynamic forces is the main cause of the instability, as for steady basic flow. However, treating the negative work of the surface tension as an increment in the surface energy is an effective means of determining the instability mechanisms. The unsteady basic flow causes the rate of change in the work done by viscosity and elasticity to vary periodically. An increase in elasticity and a decrease in deformation retardation promote the instability by increasing the work done by the gas medium, with reduced dissipation only as a secondary factor. This effect is more significant in parametric unstable regions than in the Kelvin–Helmholtz unstable region.

### Inertial migration of spherical particles in channel flow of power law fluids

The cross-stream inertial migration of neutrally buoyant particles in a power law fluid in a pressure-driven flow between two parallel walls is studied using three-dimensional numerical simulations. The particles are modeled as rigid and compliant spherical shells filled with a Newtonian fluid. Our simulations show that the particles in the flow equilibrate at stable off-center positions that depend on the particle size and fluid power exponent. In a shear thickening fluid, the equilibrium position is insensitive to the particle size. In a shear thinning fluid, an additional unstable off-center equilibrium position emerges for smaller particles, which leads to the accumulation of such particles at the channel centerline. We find that these equilibrium positions are insensitive to the magnitude of the channel Reynolds number and particle elasticity. The results of our study have applications to sorting, focusing, and separation of synthetic particles and biological cells.

### Enhanced stability of free viscous films due to surface viscosity

The stability of a thin liquid film bounded by two free surfaces is examined in the presence of insoluble surface-active agents. This study is broadly aimed at understanding enhanced stability of emulsions with the increasing surface concentration of surface-active agents. Surface-active agents not only cause gradients in surface tension but could also render surface viscosity to be significant, which could vary with surface concentration. We employ two phenomenological models for surface viscosity, a linear viscosity model and a nonlinear viscosity model. In the latter, surface viscosity diverges at a critical concentration, which is termed the “jamming” limit. We show that rupture can be significantly delayed with high surface viscosity. An analysis of the “jamming” limit reveals that [math] provides a simple criterion for enhanced stability, where [math], [math], and M are the normalized initial surfactant concentration, disjoining pressure number, and Marangoni number, respectively. Nonlinear simulations suggest that high surface viscosity renders free films remarkably stable in the jamming limit, and their free surfaces behave like immobile interfaces consistent with experimental observations. Furthermore, it is shown that rupture times can be arbitrarily increased by tuning the initial surfactant concentration, offering a fluid dynamical route to stabilization of thin films.

### Stability and transition on a Coandă cylinder

An experimental stability and transition investigation of a centrifugally unstable wall jet blown from a slot over a circular Coandă cylinder was conducted using flow visualization and particle image velocimetry. Clear and unambiguous observations of spontaneously generated stationary streamwise structures, never observed previously, were analyzed using standard image processing techniques. These structures ultimately exhibited a secondary time-dependent wavy instability that was followed by transition to turbulence. A modified Görtler number, based on the slot height, was used as a basis for comparison to linear stability theory and was directly related to the Reynolds number via geometric scaling. Direct observation of the vortices allowed the identification of an upper limit to the critical Görtler number of 6.3 that bracketed the value of 3.5 from the linear stability theory. The vortical shear layer grew exponentially along the azimuth and was characterized by a Reynolds number dependent growth rate parameter. Extrapolation of the growth rate parameter to zero furnished a critical Görtler number of 3.1 ± 1.25 (95% CI) that compared remarkably well with the linear stability theory. The shear layer separation angle did not vary monotonically with the Reynolds number: as the Reynolds number increased, the thicker boundary layer was more susceptible to separation, and thus, the separation angle, relative to the slot, decreased. However, following transition to turbulence at higher Reynolds numbers (≈400), the high-momentum fluid near the wall, resulting from turbulent mixing, produced a subsequent increase in the separation angle.

### Wakes of rotorcraft in advancing flight: A large-eddy simulation study

We perform the large-eddy simulation of the flow past a helicopter rotor to support the investigation of rotorcraft wake characteristics and decay mechanisms. A hybrid Lagrangian–Eulerian vortex particle–mesh method is employed to simulate the wake development with the blades modeled using immersed lifting lines. The validity of the numerical approach is first evaluated through a comparison of the rotor trim parameters with experimental results. Then, the rotor wake at low, medium, and high advance ratios is simulated up to 30 rotor diameters. The wake generation and roll-up are described (i) qualitatively using rotor polar plots and three-dimensional (3D) vortex dynamics visualizations and (ii) quantitatively using classical integral diagnostics in cross sections. The highly 3D unsteady near wake transitions to a system dominated by two parallel vortices over a distance that depends on the advance ratio. This process is accelerated by the multiple interactions between successive tip vortices, supporting the generation of self-induced turbulence and uncovering a mechanism of vorticity alignment along the streamwise axis. The vortices in the far wake are compared to typical aircraft ones and exhibit less compact cores and faster decaying energy. Finally, we illustrate the loss of time periodicity in the far wake using the power spectral density of the kinetic energy, and the backscattering of energy from high rotor harmonics to lower frequencies, as complementary evidence of the intense vortex interaction activity.

### 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.