# Latest papers in fluid mechanics

### Dynamic arrest during the spreading of a yield stress fluid drop

Author(s): Grégoire Martouzet, Loren Jørgensen, Yoann Pelet, Anne-Laure Biance, and Catherine Barentin

We study the spreading of drops made of yield-stress fluids. In contrast to what is observed in Newtonian fluids, the final contact angle reached by the drop depends on the drop size, on its yield stress, and on the liquid/solid hydrodynamic boundary condition. This highlights the crucial role of dynamic history. We then extend the classical Young’s law to the case of yield stress fluids. In particular, by considering that the final shape of the drop is set by a dynamical arrest, we predict the observed final contact angle.

[Phys. Rev. Fluids 6, 044006] Published Fri Apr 30, 2021

### Teaching the incompressible Navier–Stokes equations to fast neural surrogate models in three dimensions

Physically plausible fluid simulations play an important role in modern computer graphics and engineering. However, in order to achieve real-time performance, computational speed needs to be traded-off with physical accuracy. Surrogate fluid models based on neural networks (NN) have the potential to achieve both fast fluid simulations and high physical accuracy. However, these approaches rely on massive amounts of training data, require complex pipelines for training and inference, or do not generalize to new fluid domains. In this work, we present significant extensions to a recently proposed deep learning framework, which addresses the aforementioned challenges in two dimensions (2D). We go from 2D to three dimensions (3D) and propose an efficient architecture to cope with the high demands of 3D grids in terms of memory and computational complexity. Furthermore, we condition the neural fluid model on additional information about the fluid's viscosity and density, which allows for simulating laminar as well as turbulent flows based on the same surrogate model. Our method allows us to train fluid models without requiring fluid simulation data beforehand. Inference is fast and simple, as the fluid model directly maps a fluid state and boundary conditions at a moment t to a subsequent fluid state at t + dt. We obtain real-time fluid simulations on a 128 × 64 × 64 grid that include various fluid phenomena such as the Magnus effect or Kármán vortex streets and generalize to domain geometries not considered during training. Our method indicates strong improvements in terms of accuracy, speed, and generalization capabilities over current 3D NN-based fluid models.

### Mathematical model and analysis method for flowfield separation and transition

Transition and separation are difficult but important problems in the field of fluid mechanics. Hitherto, separation and transition problems have not been described accurately in mathematical terms, leading to design errors and prediction problems in fluid machine engineering. The nonlinear uncertainty involved in separation and transition makes it difficult to accurately analyze these phenomena using experimental methods. Thus, new ideas and methods are required for the mathematical prediction of fluid separation and transition. In this article, after an axiomatic treatment of fluid mechanics, the concept of an excited state is derived by generating a fluctuation velocity, and it is revealed that fluid separation and transition are special forms of this excited state. This allows us to clarify the state conditions of fluid separation and transition. Mathematical analysis of the Navier–Stokes equations leads to a general excited state theorem suitable for flowfields. Finally, the conditions of separation and transition are derived, and the corresponding general laws are established. The results presented in this article provide a foundation for future research on the mechanism of turbulence and the solution of engineering problems.

### Rheology and morphology of Pluronic F68 in water

We investigated the morphological transitions of aqueous solutions of Pluronic F68 induced by temperature and polymer concentration by means of rheological and x-ray measurements. We adopted a rheological method to evaluate the characteristic equilibrium temperatures associated with the transition from unimers to spherical micelles and from disordered spherical micelles to a body-centered cubic phase. We used the transition temperatures to build the phase diagram water/F68. Based on a paracrystalline model for hard spheres, we extracted the characteristic size of the micellar core as a function of temperature from small-angle x-ray scattering (SAXS) data. We compared the microstructural information obtained via SAXS with the rheological response, and we developed a consistent link between the microstructural evolution of the system and the macroscopic flow properties.

### Experimental study of horizontal heated buoyant jets in a linearly stratified ambience

Horizontal warm buoyant jets injecting into a linearly stratified ambience are common in lakes, estuaries, and oceans. Dynamic features and potential surface temperature signatures of heated buoyant jets are experimentally investigated using particle image velocimetry and an infrared camera. Results reveal that when heated jets are completely underwater, the flow evolution can be classified into the horizontal regime, ascending regime, and collapsing regime, respectively. The maximum rise height and the neutral height both increase linearly with the increasing jet length scale. Based on this relationship, an equation is developed to predict the surface impingement of a horizontal heated buoyant jet. If the surface impingement occurs, staggered vortexes and large meanders caused by mixing between the jet and the free surface are observed on the surface temperature maps. Furthermore, surface temperature fluctuation fields are decomposed using the Karhunen-Loeve method, the first four eigenmodes appear to capture the root mean square temperature fluctuations and the features correlated with the swirling vortexes. In the turbulent kinetic energy budget, mean-flow convection is found to be mainly balanced by turbulent transport. As the heated jet propagates downstream, more kinetic energy is transferred into potential energy rather than into turbulent energy.

### Computational study of gaseous cellular detonation diffraction and re-initiation by small obstacle induced perturbations

A gaseous detonation wave that emerges from a channel into an unconfined space is known as detonation diffraction. If the dimension of the channel exit is below some critical value, the incident detonation fails to re-initiate (i.e., transmit into a self-sustained detonation propagating) in the unconfined area. In a previous study, Xu et al. [“The role of cellular instability on the critical tube diameter problem for unstable gaseous detonations,” Proc. Combust. Inst. 37(3), 3545–3533 (2019)] experimentally demonstrated that, for an unstable detonable mixture (i.e., stoichiometric acetylene–oxygen), a small obstacle near the channel exit promotes the re-initiation capability for cases with a sub-critical channel size. In the current study, two-dimensional numerical simulations were performed to reveal this obstacle-triggered re-initiation process in greater detail. Parametric studies were carried out to examine the influence of obstacle position on the re-initiation capability. The results show that a collision between a triple-point wave complex at the diffracting shock front and the obstacle is required for a successful re-initiation. If an obstacle is placed too close or too far away from the channel exit, the diffracting detonation cannot be re-initiated. Since shot-to-shot variation in the cellular wave structure of the incident detonation results in different triple-point trajectories, for an obstacle at a fixed position, the occurrence of re-initiation is of a stochastic nature. The findings of this study highlight that flow instability generated by a local perturbation is effective in enhancing the re-initiation capability of a diffracting cellular detonation wave in an unstable mixture.

### Explicit wall models for large eddy simulation

Algebraic explicit wall models covering the entire inner region of the turbulent boundary layer are proposed to reduce the computational effort for large eddy simulation of wall-bounded turbulent flows. The proposed formulas are given in closed forms with either logarithmic- or power-function-based laws of the wall, allowing straightforward evaluation of the friction velocity on near wall grids independent of their locations in the turbulent boundary layer. The performance of the proposed models is demonstrated by the wall modeled large eddy simulation of a turbulent plane channel flow.

### Oscillatory flow of Koo–Kleinstreuer and aggregate nanofluids in cylindrical annuli: Toward an innovative solution to deal with nanofluids instability

This paper exhibits the oscillatory characteristics of a free convective flow of nanofluids in horizontal concentric annuli of pilot dimensions to provide a mechanical solution against their particles settling which occurs by aggregation. These nanofluids are generated according to each class of particles that may exist with four types of industrial base liquids. Koo–Kleinstreuer semi-empirical models are used to generate databases of ideal suspended particles with Brownian motion. Meanwhile, Maxwell–Bruggeman and Kreiger–Dougherty semi-empirical models are used to incorporate the aggregation mechanism. A hybrid lattice Boltzmann/finite-difference approach is adopted to provide the space-time solutions. The accuracy of this numerical tool is inspected by providing over nine validations based on literature data. Hence, an improved flow pattern chart is accomplished to expand the open literature, depending on the flow nature of the base liquids in the annuli. Next, the oscillatory nature is fully revealed for each nanofluid processed. Following the frontiers toward the non-settling of aggregates, three main regimes are identified depending on the annulus size and the combination between ideal and aggregate mechanisms. Owing to this, a new settling chart is established to emerge the sheer limit of the annulus size for a non-settling process.

### Diffraction of weakly unstable detonation through an obstacle with different sizes and shapes

Author(s): Yuan Wang, Zheng Chen, and Haitao Chen

Two-dimensional simulations considering detailed chemistry are conducted to investigate the weakly unstable detonation diffracting through an obstacle. Subcritical, critical, and supercritical regimes are identified and their distributions are significantly affected by the obstacle size and shape. In contrast, the mixtures with different nitrogen dilution have little influence on the regime distributions.

[Phys. Rev. Fluids 6, 043201] Published Thu Apr 29, 2021

### Large-eddy simulation of bubble plume in stratified crossflow

Author(s): Shuolin Xiao, Chen Peng, and Di Yang

Bubble-driven plume in stratified crossflow is modeled using Eulerian-Eulerian large-eddy simulation. Various bubble sizes and crossflow velocities are considered, and noticeable differences in the plume characteristics and material transport are observed. Statistical analysis of the simulation results provides insights on how the crossflow affects the exchanges of momentum and mass between the bubble-driven plume and the surrounding water.

[Phys. Rev. Fluids 6, 044613] Published Thu Apr 29, 2021

### Air-cushioning effect and Kelvin-Helmholtz instability before the slamming of a disk on water

Author(s): Utkarsh Jain, Anaïs Gauthier, Detlef Lohse, and Devaraj van der Meer

A solid plate about to slam onto a water surface makes it presence felt before the actual contact by squeezing out a mediating air cushioning layer. This air cushioning layer has regions of low and high pressures. At the point of high (stagnation) air pressure, the water surface is deflected away from the impactor. While in the low pressure region, a Kelvin-Helmholtz instability initiates the suction of the water surface towards the impactor. Using a new measuring technique we measure such deflections, of the order of 10-300 microns, and explain the mechanisms driving them.

[Phys. Rev. Fluids 6, L042001] Published Thu Apr 29, 2021

### A benchmark study on the axial velocity profile of wave propagation in deformable blood vessels

Wave propagation models in the time domain have been extensively used in the available literature to study the flow characteristics in blood vessels. Most of the wave propagation models have considered flat or parabolic velocity profile functions to estimate the nonlinear convection and diffusion terms present in the conservation of momentum equation. There are only a few works available on the wave propagation analysis in which the velocity profile is approximated using different polynomial functions. In this study, a computationally efficient nonlinear axisymmetric formulation is presented without a priori assumed velocity profile function across the cross section to model the blood flow. Such a formulation in terms of axial velocity (u), pressure (p), and domain radius (R) facilitates the evolution/development of axial velocity profile as the flow progresses with time. The arterial mechanical behavior is modeled using a linear elastic constitutive relation. Partial differential equations are discretized using the finite element method and the Galerkin time integration technique in space and time domains, respectively. This study finds a phase difference between the shear stress at the wall and the flow rate. The flow characteristics and the velocity profile function are found to be in good agreement with the three-dimensional computational results available in the literature. The detailed investigation of the axial velocity across the cross section reveals neither flat nor parabolic profiles, as previously assumed in the literature.

### Uniform breaking of liquid-jets by modulated laser heating

We report a theoretical and experimental study of the breaking of liquid jets under external periodic heating by laser pulses. In this case, jet breaking is controlled by the competition between the growth of the initial disturbances, which possess a wide wavenumber spectrum and result in the classical Rayleigh–Plateau (RP) unstable modes, and the growth of the disturbance caused by the surface tension perturbation corresponding to the periodic temperature modulation by pulsed laser heating, which appears as the thermocapillary (TC) unstable modes driven by the Marangoni flow. Our linear stability analysis shows that both the RP modes and the TC modes obey the same dispersion relation. We obtain analytical results on the range of the laser pulsing frequency that produces uniform jet breaking, at which the principal TC mode dominates the RP modes and the jet breaks at exactly the laser heating frequency, and the resulting liquid drops are uniform in size. Our theoretical prediction agrees well with experimental observations. In the uniform jet breaking range, our stability analysis also gives the growth rates of the TC modes and the jet breakup length, both of which are supported by experimental measurements. In the experiments, we also observed the growth of higher-order modes, which can again be explained quantitatively by our stability analysis.

### Internal circulation and mixing within tight-squeezing deformable droplets

Author(s): Jacob R. Gissinger, Alexander Z. Zinchenko, and Robert H. Davis

The internal flow and mixing properties inside deformable droplets, after reaching the steady state within two types of passive droplet traps, are visualized and analyzed as dynamical systems. The first droplet trap (constriction) is formed by three spheres arranged in an equilateral triangle, while...

[Phys. Rev. E 103, 043106] Published Wed Apr 28, 2021

### Droplet splashing on rough surfaces

Author(s): Thijs de Goede, Karla de Bruin, Noushine Shahidzadeh, and Daniel Bonn

Drop splashing on surfaces is important for a wide variety of processes ranging from inkjet printing to pollination by rain and forensic blood pattern analysis. The critical impact velocity beyond which the drop disintegrates is well understood for smooth surfaces, but remained a puzzle for rougher ones that are often encountered in practice. We find that the splashing threshold on rough surfaces is lower, which can be understood as an interplay between the surface roughness and the viscous, inertial, and capillary forces on the drop.

[Phys. Rev. Fluids 6, 043604] Published Wed Apr 28, 2021

### Electrical voltage by electron spin-vorticity coupling in laminar ducts

Author(s): Hamid Tabaei Kazerooni, Georgy Zinchenko, Jörg Schumacher, and Christian Cierpka

A tiny electrical voltage can be generated by the collective coupling of the electron spins to the flow vorticity in laminar and turbulent liquid metal flows. Here, we demonstrate a linear scaling law between electrical voltage and pressure drop for laminar flows through capillaries with different cross sections, both, analytically and experimentally.

[Phys. Rev. Fluids 6, 043703] Published Wed Apr 28, 2021

### When the doorbell rings in COVID-19 times: Numerical insights into some possible scenarios

As ongoing Corona virus disease 2019 pandemic is ravaging the world, more and more people are following social distancing norms, avoiding unnecessary outings and preferring online shopping from the safety of their home over visiting brick and mortar stores and neighborhood shops. Although this has led to a significant reduction in chances of exposure, human-to-human interaction at the doorstep of the customer might be involved during the delivery of the ordered items. This human-to-human doorstep interaction arises in some other situations also. There is a finite probability that the person standing in front of the door coughs or sneezes during such an interaction. In this work, a three dimensional (3D) Euler–Lagrangian computational fluid dynamic model is used to understand the transmission and evaporation of micrometer-size droplets generated due to a coughing event in this setting. Different possible scenarios varying in wind direction, wind velocity, ventilation in the vicinity of door, and extent of door opening have been postulated and simulated. The results obtained from numerical simulations show that in the presence of wind, the dynamics of transmission of droplets is much faster than the dynamics of their evaporation. Thus wind velocity and direction have a significant impact on the fate of the droplets. The simulation results show that even if the door is opened by a very small degree, cough droplets enter through the door. Having open windows in the vicinity of the door on a windy day is expected to reduce the chance of the exposure significantly.

### Effect of adiabatic index on Richtmyer–Meshkov flows induced by strong shocks

Richtmyer–Meshkov Instability is an instability that develops at the interface between fluids of distinct acoustic impedance when impacted by a shock wave. Its applications include inertial confinement fusion, supernovae explosions, and the evolution of blast waves. We systematically study the effect of the adiabatic index of the fluids on the dynamics of strong-shock-driven flows, particularly the amount of shock energy available for interfacial mixing. Only limited information is currently available about the dynamic properties of matter at these extreme regimes. We employ smooth particle hydrodynamics simulations to ensure accurate shock capturing and interface tracking. A range of adiabatic indexes is considered, approaching limits which, to the best of the author's knowledge, have never been considered before. We analyze the effect of the adiabatic indexes on the interface speed and growth rate immediately after the shock passage. The simulation results are compared wherever possible with rigorous theories, achieving good quantitative and qualitative agreement. We find that the more challenging cases for simulations arise where the adiabatic indexes are further apart, and that the initial growth rate is a non-monotone function of the initial perturbation amplitude, which holds across all adiabatic indexes of the fluids considered. The applications of these findings on experiment design are discussed.

### Water interaction with dielectric surface: A combined ab initio modeling and experimental study

A combined ab initio modeling and experimental study of water adsorption on a dry hydrophobic dielectric surface is presented. This is an important phenomenon for controlled droplet deposition in various technological applications. The ab initio density functional theory calculations are performed to reveal the dominant water adsorption sites, energetics, and the electron density profile on Teflon and parafilm surfaces. Several surface states such as stretched, nondefective, and defective are considered for water adsorption studies. It is revealed that stretching of nondefective surface leads to weaker water adsorption compared to an unstretched surface. Accordingly, such stretching makes the surface more hydrophobic as revealed by the electron density profile. The introduction of random defects into Teflon and parafilm surfaces results in an increase in water adsorption energy leading, in some cases, to practically hydrophilic interactions. These findings are in good agreement with the present measurements of static contact angle on prestretched Teflon and parafilm samples, where stretching not only elongates interatomic bonds but also changes the surface roughness. Thus, the present combined modeling and experimental study allows for a mechanistic interpretation of the reasons behind the change of wettability of dry hydrophobic surfaces.

### Kinetic theory models for granular mixtures with unequal granular temperature: Hydrodynamic velocity

Kinetic theory for granular mixtures with a separate granular temperature for each solid phase is considered. The particle phases are assumed to follow a Maxwellian distribution with zero-order approximation of the Boltzmann equation. A solution strategy for solving the integrals of the collisional closure relations is presented. The present analysis enables the solution of these integrals without neglecting the solid particle hydrodynamic velocities in the distribution function. However, the solution strategy limits the validity of the closure relations to relatively small and moderate hydrodynamic velocity differences. Dependent on the magnitude of the hydrodynamic velocity difference, the present closure relations can differ significantly from the simplified models where such velocity difference is traditionally neglected.