# Latest papers in fluid mechanics

### Retarding spreading of surfactant drops on solid surfaces: Interplay between the Marangoni effect and capillary flows

Author(s): Parisa Bazazi and S. Hossein Hejazi

Early time spreading of a water drop on a hydrophilic surface is characterized by the wetted radius which grows linearly in time. We report the unexpected result that the initial spread of surfactant-laden drops is impeded by Marangoni stresses, leading to a large increase in total spreading time. The nonuniform distribution of surfactants at the interface generates Marangoni stresses before the drop-solid contact suppresses film drainage and droplet expansion. Our experiments show that, remarkably, surfactants delay the initial fast motion of the three-phase contact lines.

[Phys. Rev. Fluids 5, 084006] Published Thu Aug 27, 2020

### Dynamics of retracting surfactant-laden ligaments at intermediate Ohnesorge number

Author(s): Cristian R. Constante-Amores, Lyes Kahouadji, Assen Batchvarov, Seungwon Shin, Jalel Chergui, Damir Juric, and Omar K. Matar

Three-dimensional direct numerical simulations of the ligaments retraction process over a range of system parameters that account for surfactant solubility, sorption kinetics, and Marangoni stresses are presented. The presence of surfactant inhibits the “end-pinching” mechanism and promotes neck reopening through Marangoni flow induced by the formation of surfactant concentration gradients that drive flow reversal toward the neck.

[Phys. Rev. Fluids 5, 084007] Published Thu Aug 27, 2020

### Physical modeling of the dam-break flow of sedimenting suspensions

Author(s): Laurence Girolami and Frédéric Risso

This paper develops a physical model able to describe the dam-break flow of particulate suspensions that sediment progressively during propagation at a constant velocity that solely depends on the mixture properties. The model considers the suspension as an equivalent fluid of constant density and negligible viscosity and leads to a good prediction of the flow duration and deposits shape. These findings allow the formulation of consistent shallow-water equations that can be used to compute the dense basal layer of small-volume pyroclastic flows.

[Phys. Rev. Fluids 5, 084306] Published Thu Aug 27, 2020

### Dynamics of nonisothermal two-thin-fluid-layer systems subjected to harmonic tangential forcing under Rayleigh–Taylor instability conditions

The stability of a nonisothermal system consisting of two superimposed fluid layers: a thin liquid film layer and a gas layer sandwiched between differentially heated horizontal solid plates in the gravity field, is investigated. The system is assumed to be subjected to the Rayleigh–Taylor instability (RTI) with the Marangoni effect that either enhances the RTI or opposes it and to the tangential harmonic vibration of the upper substrate. A set of reduced evolution equations is derived based on the weighted-residual integral boundary layer approach, and the investigation is carried out in the framework of this set. The base state of the system represents a time-periodic flow, and its linear stability analysis is carried out using the Floquet theory in the large-time limit. The nonlinear dynamics of the system is investigated numerically in the case of either a static or vibrating substrate. Among the possible outcomes of the nonlinear dynamics, there is the emergence of ruptured states of the liquid film with rupture taking place at either the upper or lower substrate and also the emergence of saturated continuous flows of the liquid film. We also find that the nonlinear dynamics of the system is consistent with the results of the linear stability analysis in terms of enhancement or attenuation of interfacial distortion.

### Interplay of Kelvin–Helmholtz instability with acoustics in a viscous potential flow

Among the hydrodynamic instabilities influencing the evolution, stabilization, and control of flows, the Kelvin–Helmholtz (KH) instability mode is a profound trigger to induce unsteadiness and turbulence—either within a single fluid, by means of a velocity shear, or along the interface of multiple fluids. This mechanism has been analytically studied by Funada and Joseph [“Viscous potential flow analysis of Kelvin–Helmholtz instability in a channel,” J. Fluid Mech. 445, 263 (2001)], for the surface separating two fluids within the approximation of inviscid and viscous potential flows. The present investigation extends the Funada–Joseph formulation to incorporate the effect of imposed acoustic waves on the system under consideration. Specifically, the KH–acoustic interaction is studied by employing a modification of the Bychkov approach [V. Bychkov, “Analytical scalings for flame interaction with sound waves,” Phys. Fluids 11, 3168 (1999)], which has been originally derived for the acoustic coupling to the combustion instability. The analytic formulae for the dispersion relations, growth rates, and neutral curves describing the perturbed interface of the KH instability/acoustic region are derived. Specifically, the limits for stable/unstable regimes as a function of hydrodynamic and acoustic parameters are identified. Two interacting modes are of particular interest: resonant and parametric modes, characterized by acoustic fields having the same frequency (resonant) and twice the frequency (parametric) of the instability oscillations. It is shown that while relatively weak acoustics provide a promising contribution to stabilize the KH instability, those of higher strength can excite the parametric instability. Overall, a comprehensive parametric study of the KH–acoustic coupling and stability limits shows that a global stability region may exist between that of the resonant and parametrically unstable regimes.

### Global eigenmodes of thin liquid sheets by means of Volume-of-Fluid simulations

The unsteady dynamics of planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, is numerically investigated by means of the Volume-of-Fluid (VOF) technique for supercritical regimes. The global behavior of the non-parallel flow is analyzed by perturbing the initial steady configuration by means of a Gaussian bump in the transverse velocity component of relatively small amplitude, thereby exciting sinuous modes. To gain more physical insights into the fluid system, a theoretical linear one-dimensional model is also developed. A physical interpretation of this model relates the sheet dynamics to transverse vibrations of tensional string forced by terms containing the lateral velocity and subjected to a total damping coefficient, which can assume negative values. The VOF simulation satisfactorily confirms that the velocity impulse perturbation splits into two wave fronts traveling downstream with the theoretical wave velocities. A good agreement is found in comparing the crossing times over the entire domain length of such waves with the almost constant spacing between the frequencies of the eigenvalue spectrum. Surface tension plays a stabilizing role, and for relatively high values of density ratio rρ of gaseous-to-liquid phases, the sheet becomes unstable. It is argued that the distribution of transverse velocity component of the gaseous phase represents the forcing term, which leads the system toward the instability when, for relatively high rρ, the total damping becomes negative. An analogy seems to exist between the global unstable behavior exhibited by the liquid sheet as rρ increases and the shear-induced global instability found by Tammisola et al. [Surface tension-induced global instability of planar jets and wakes,” J. Fluid Mech. 713, 632–658 (2012)] in the presence of surface tension. However, for the gravitational sheet, the surface tension is stabilizing.

### Modeling drug delivery from multiple emulsions

Author(s): G. Pontrelli, E. J. Carr, A. Tiribocchi, and S. Succi

We present a mechanistic model of drug release from a multiple emulsion into an external surrounding fluid. We consider a single multilayer droplet where the drug kinetics are described by a pure diffusive process through different liquid shells. The multilayer problem is described by a system of di...

[Phys. Rev. E 102, 023114] Published Wed Aug 26, 2020

### Interaction of wave-driven particles with slit structures

Author(s): Clive Ellegaard and Mogens T. Levinsen

Just over a decade ago Couder and Fort [Phys. Rev. Lett. **97**, 154101 (2006)] published a provocative paper suggesting that a classical system might be able to simulate the truly fundamental quantum mechanical single- and double-slit experiment. The system they investigated was that of an oil droplet ...

[Phys. Rev. E 102, 023115] Published Wed Aug 26, 2020

### Specific features of the gas-dynamic structure of supersonic axisymmetric microjets of a nonequilibrium $\mathrm{S}{\mathrm{F}}_{6}$ gas

Author(s): Vladimir Aniskin, Nikolay Maslov, Sergey Mironov, Elena Tsybulskaya, and Ivan Tsyryulnikov

The effect of vibrational nonequilibrium of SF6 molecules on the gas dynamic structure of microjets is revealed, manifesting in a decrease in the longitudinal cell size of the wave structure and weakening of variations in flow parameters along the axis of the microjet compared to the equilibrium flow. The physical justification is found for the diameter of the nozzle, which is the boundary value between the macro- and microjets of vibrationally relaxing gases.

[Phys. Rev. Fluids 5, 083401] Published Wed Aug 26, 2020

### Behavior of the square-back Ahmed body global modes at low ground clearance

Author(s): Baptiste Plumejeau, Laurent Keirsbulck, Sébastien Delprat, Marc Lippert, and Wafik Abassi

A study of the evolution of the wake flow of a square-back Ahmed body is presented. Various ground clearance configurations around the critical case associated with the onset of the lateral bistability are investigated. The oscillation modes vary between stable and bistable states, the corresponding Strouhal numbers for the horizontal (respectively, vertical) evolve from 0.16 (respectively, 0.27) to 0.13 (respectively, 0.18).

[Phys. Rev. Fluids 5, 084701] Published Wed Aug 26, 2020

### 3-dimensional particle image velocimetry based evaluation of turbulent skin-friction reduction by spanwise wall oscillation

The reduction of turbulent skin-friction drag and the response of vortical structures in a zero-pressure gradient, turbulent boundary layer subjected to spanwise wall oscillation is investigated using planar and tomographic particle image velocimetry (PIV). The experiments are conducted at a momentum based Reynolds number of 1000, while the range of spanwise oscillation amplitude and frequency is chosen around the optimum reported in previous studies. A high-resolution planar PIV measurement is employed to determine the drag reduction directly from wall shear measurements and to analyze the accompanying modifications in the turbulent vortical structures. Drag reduction of up to 15% is quantified, with variations following the trends reported in the literature. The analysis of the turbulence structure of the flow is made in terms of Reynolds shear stresses, turbulence production, and vortex visualization. A pronounced drop of turbulence production is observed up to a height of 100 wall units from the wall. The vorticity analysis, both in the streamwise wall-normal plane and in the volumetric results, indicates a reduction of vorticity fluctuations in the near-wall domain. A distortion of the hairpin-packet arrangement is hypothesized, suggesting that the drag-reduction mechanism lies in the inhibition of the hairpin auto-generation by the spanwise wall oscillations.

### Elliptic supersonic jet morphology manipulation using sharp-tipped lobes

Elliptic nozzle geometry is attractive for mixing enhancement of supersonic jets. However, jet dynamics, such as flapping, gives rise to high-intensity tonal sound. We experimentally manipulate the supersonic elliptic jet morphology by using two sharp-tipped lobes. The lobes are placed on either end of the minor axis in an elliptic nozzle. The design Mach number and the aspect ratio of the elliptic nozzle and the lobed nozzle are 2.0 and 1.65. The supersonic jet is exhausted into ambient under almost perfectly expanded conditions. Time-resolved schlieren imaging, longitudinal and cross-sectional planar laser Mie scattering imaging, planar Particle Image Velocimetry (PIV), and near-field microphone measurements are performed to assess the fluidic behavior of the two nozzles. Dynamic Mode Decomposition (DMD) and proper orthogonal decomposition analyses are carried out on the schlieren and the Mie scattering images. Mixing characteristics are extracted from the Mie scattering images through the image processing routines. The flapping elliptic jet consists of two dominant DMD modes, while the lobed nozzle has only one dominant mode, and the flapping is suppressed. Microphone measurements show the associated noise reduction. The jet column bifurcates in the lobed nozzle enabling a larger surface contact area with the ambient fluid and higher mixing rates in the near-field of the nozzle exit. The jet width growth rate of the two-lobed nozzle is about twice that of the elliptic jet in the near-field, and there is a 40% reduction in the potential core length. PIV contours substantiate the results.

### Non-autoregressive time-series methods for stable parametric reduced-order models

Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant interest in the use of techniques borrowed from machine learning to reduce the computational expense and/or improve the accuracy of predictions for these systems. These rely on the identification of a basis that reduces the dimensionality of the problem and the subsequent use of time series and sequential learning methods to forecast the evolution of the reduced state. Often, however, machine-learned predictions after reduced-basis projection are plagued by issues of stability stemming from incomplete capture of multiscale processes as well as due to error growth for long forecast durations. To address these issues, we have developed a non-autoregressive time series approach for predicting linear reduced-basis time histories of forward models. In particular, we demonstrate that non-autoregressive counterparts of sequential learning methods such as long short-term memory (LSTM) considerably improve the stability of machine-learned reduced-order models. We evaluate our approach on the inviscid shallow water equations and show that a non-autoregressive variant of the standard LSTM approach that is bidirectional in the principal component directions obtains the best accuracy for recreating the nonlinear dynamics of partial observations. Moreover—and critical for many applications of these surrogates—inference times are reduced by three orders of magnitude using our approach, compared with both the equation-based Galerkin projection method and the standard LSTM approach.

### On the role of surface grooves in the reduction of pressure losses in heated channels

Pressure-gradient-driven flows in grooved horizontal channels were investigated. The results show that a significant reduction in pressure losses can be achieved by exposing such channels to spatially distributed heating. The system response strongly depends on the characterization of both patterns and on their relative position, leading to a pattern interaction problem. Mismatch and misplacement of both patterns may result in a significant increase in pressure losses or may have no effect on such losses. The reduction in pressure loss is associated with the formation of convection rolls on the bounding surfaces due to spatially distributed buoyancy along the streamwise direction. The pressure-gradient-reducing effect is active only in small Reynolds number flows. Explicit results are given for fluids with the Prandtl number Pr = 0.71, representing air.

### Statistical transition to turbulence in plane channel flow

Author(s): Sébastien Gomé, Laurette S. Tuckerman, and Dwight Barkley

The subcritical route to turbulence in shear flows is characterized by metastable localized turbulent-laminar patterns. In plane channel flow, these take the form of intermittent oblique turbulent bands, which either proliferate or decay on timescales that depend on the Reynolds number. A statistical study via direct numerical simulations in a narrow tilted domain leads to the determination of a crossing Reynolds number of around 965, above which the probability for a band to split outpaces its probability to disappear.

[Phys. Rev. Fluids 5, 083905] Published Tue Aug 25, 2020

### Universal trends in human cough airflows at large distances

Coughs are one of the primary means of transmission of diseases such as influenza and SARS-CoV-2 (COVID-19). Disease spreading occurs by the expulsion of pathogen containing aerosol droplets. Fine droplets can pass through layers of masks and are carried away by the exhaled airflow unlike larger droplets that settle down due to gravity. Hence, it is important to quantitatively assess the maximum distance of travel of typical human coughs with and without different types of masks. Even though near field data are available near the mouth, far field data are scarce. In this study, the schlieren method that is a highly sensitive, non-intrusive flow visualization technique is used. It can directly image weak density gradients produced by coughs. An assessment of different methods of covering the mouth while coughing is arrived at by using observations from high speed schlieren images. The effectiveness of coughing into the elbow is examined. The velocity of propagation of coughs and the distance of propagation with and without masks are quantified. It is also found that normalizing the distance–velocity profiles causes all the data to collapse onto a universal non-dimensional curve irrespective of the usage of different types of masks or test subjects. Visualization of cough flow fields and analysis of experimental data reveal that the flow physics is governed by the propagation of viscous vortex rings.

### Reopening dentistry after COVID-19: Complete suppression of aerosolization in dental procedures by viscoelastic Medusa Gorgo

The aerosol transmissibility of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has impacted the delivery of health care and essentially stopped the provision of medical and dental therapies. Dentistry uses rotary, ultrasonic, and laser-based instruments that produce water-based aerosols in the daily, routine treatment of patients. Abundant aerosols are generated, which reach health care workers and other patients. Viruses, including SARS-CoV-2 virus and related coronavirus disease (COVID-19) pandemic, continued expansion throughout the USA and the world. The virus is spread by both droplet (visible drops) and aerosol (practically invisible drops) transmission. The generation of aerosols in dentistry—an unavoidable part of most dental treatments—creates a high-risk situation. The US Centers for Disease Control and The Occupational Safety and Health Administration consider dental procedures to be of “highest risk” in the potential spreading of SARS-CoV-2 and other respiratory viruses. There are several ways to reduce or eliminate the virus: (i) cease or postpone dentistry (public and personal health risk), (ii) screen patients immediately prior to dental treatment (by appropriate testing, if any), (iii) block/remove the virus containing aerosol by engineering controls together with stringent personal protective equipment use. The present work takes a novel, fourth approach. By altering the physical response of water to the rotary or ultrasonic forces that are used in dentistry, the generation of aerosol particles and the distance any aerosol may spread beyond the point of generation can be markedly suppressed or completely eliminated in comparison to water for both the ultrasonic scaler and dental handpiece.

### Parameter space mapping of the Princeton magnetorotational instability experiment

Author(s): Himawan W. Winarto, Hantao Ji, Jeremy Goodman, Fatima Ebrahimi, Erik P. Gilson, and Yin Wang

Extensive simulations of the Princeton Magnetorotational Instability (MRI) Experiment with the Spectral/Finite Element code for Maxwell and Navier-Stokes Equations (SFEMaNS) have been performed to map the MRI-unstable region as a function of inner cylinder angular velocity and applied vertical magne...

[Phys. Rev. E 102, 023113] Published Mon Aug 24, 2020

### Linear analysis of dewetting instability in multilayer planar sheets for composite nanostructures

Author(s): Bingrui Xu and Daosheng Deng

Dewetting instability of multilayer planar sheets are studied by linear analysis. Several unstable modes are identified, while the maximum growth rate depends on fluid properties. These results provide theoretical guidance to enhance or suppress the dewetting instability via material selection and structure design, enabling fabrication of sophisticated nanostructures for functional fibers and wearable textiles.

[Phys. Rev. Fluids 5, 083904] Published Mon Aug 24, 2020

### Explicit algebraic relation for calculating Reynolds normal stresses in flows dominated by bubble-induced turbulence

Author(s): Tian Ma, Dirk Lucas, and Andrew D. Bragg

Two new algebraic turbulence models for flows dominated by bubble-induced turbulence (BIT) are presented. The first model, referred to as the algebraic Reynolds normal stress model, is derived from a differential Reynolds stress model for bubbly flows. The second model utilizes one two-equation turbulence model to achieve algebraic expressions for k and ϵ in the BIT dominated cases. If both models are combined, it results in a purely algebraic, explicit relation for the Reynolds normal stresses.

[Phys. Rev. Fluids 5, 084305] Published Mon Aug 24, 2020