# Latest papers in fluid mechanics

### Turbulent Rayleigh-Bénard convection under strong non-Oberbeck-Boussinesq conditions

Author(s): Hiufai Yik, Valentina Valori, and Stephan Weiss

Thermal convection experiments with strongly varying fluid properties, when the Oberbeck-Boussinesq (OB) condition is violated, are presented. By using compressed sulfur hexafluoride above its critical point, measurements with different degrees of fluid property variations are conducted, while keeping the Rayleigh and Prandtl number fixed. The vertical heat transport is significantly enhanced under non-OB conditions, which is explained with an increase of the density and heat capacity in the bulk due to asymmetries in the vertical temperature profile.

[Phys. Rev. Fluids 5, 103502] Published Tue Oct 20, 2020

### Wake symmetry impacts the performance of tandem hydrofoils during in-phase and out-of-phase oscillations differently

Author(s): Ahmet Gungor and Arman Hemmati

The hydrodynamics of two oscillating foils in side-by-side configuration is numerically investigated for in-phase and out-of-phase pitching at Reynolds number of 4000 and Strouhal numbers of St=0.25–0.5. The effects of phase difference (in-phase and out-of-phase) and Strouhal number on symmetric att...

[Phys. Rev. E 102, 043104] Published Mon Oct 19, 2020

### Hydrochemical interactions in dilute phoretic suspensions: From individual particle properties to collective organization

Author(s): T. Traverso and S. Michelin

In suspensions of self-propelled Janus phoretic colloids, chemically mediated interactions generate spontaneous collective dynamics. A kinetic model of such dilute phoretic suspensions demonstrates how these phenomena may be promoted, hindered, or even suppressed by the particles’ self-propulsion velocity, depending on their detailed surface properties. The long-term dynamics are characterized by the competition between the stirring effect of the flow field generated by the particles and the formulation of regular patterns resulting from chemical interactions.

[Phys. Rev. Fluids 5, 104203] Published Mon Oct 19, 2020

### Quantifying mixing of Rayleigh-Taylor turbulence

Author(s): You-sheng Zhang, Wei-dan Ni, Yu-cang Ruan, and Han-song Xie

A systematic model is established to quantitatively predict the evolution of Rayleigh-Taylor turbulence at three different mixing levels and density ratios. Our predictions show great correspondence with the previous experiments and simulations and make an appropriate explanation for the distinct differences existing in experiments.

[Phys. Rev. Fluids 5, 104501] Published Mon Oct 19, 2020

### Reactive convective dissolution with differential diffusivities: Nonlinear simulations of onset times and asymptotic fluxes

Author(s): M. Jotkar, L. Rongy, and A. De Wit

Convective dissolution, relevant to CO2 geological sequestration, occurs when a given species dissolves in a host phase and increases density. Chemical reactions have been shown to enhance this convection. If the chemical species involved diffuse at different rates, an additional convection zone due to double-diffusion processes can develop below the reaction front in addition to the dissolution-driven Rayleigh-Taylor instability below the interface. An analysis of the influence of the interaction between these various convective modes on the nonlinear dynamics and on the dissolution flux is presented.

[Phys. Rev. Fluids 5, 104502] Published Mon Oct 19, 2020

### Production and dissipation of kinetic energy in grid turbulence

Author(s): Wouter J. T. Bos

The origin of nonclassical behavior in grid turbulence is traced back to the mean flow induced by the wakes of the grid bars. A simple model captures and explains the main nonequilibrium features of the flow.

[Phys. Rev. Fluids 5, 104607] Published Mon Oct 19, 2020

### Roughness-induced secondary flows in stably stratified turbulent boundary layers

Spanwise heterogeneous roughness, more specifically, spanwise-adjacent strips of relatively high and low roughness, is known to cause large-scale secondary flows in the vertical domain in neutral turbulent boundary layers. In this work, we study the response of secondary vortices to thermal stratification with focus on the stably stratified case. We systematically vary the Monin–Obukhov (MO) length scale from L/h = 0.3, which corresponds to relatively strong stratification, to ∞, which corresponds to the neutral condition. Here, L is the MO length and h is an outer length scale. The results show that stable stratification suppresses the vertical motions and reduces the vertical size and strength of the first off-wall secondary vortex. Moreover, the reduced vertical extent of the first off-wall vortex and the shear near its top together give rise to a second vortex, and the second to a third vortex. This leads to a stack of secondary vortices in a stably stratified boundary layer flow with decreasing strength when moving away from the wall.

### Kinetic simulations of laser-induced plume expansion from a copper target into a vacuum or argon background gas based on ab initio calculation of Cu–Cu, Ar–Ar, and Ar–Cu interactions

The kinetic simulations of plume expansion induced by pulsed laser heating of a copper target in a vacuum or low-pressure argon background gas are performed based on the direct simulation Monte Carlo (DSMC) method and ab initio quantum mechanical calculation of interactions between copper and argon atoms. The potential energy curves (PECs) for Cu–Cu, Ar–Ar, and Ar–Cu interactions are obtained in density functional theory (DFT) calculations with the van der Waals (vdW) correction. The computed Cu–Cu PEC is strikingly different from the Lennard-Jones (LJ) potentials with semi-empirical parameters, which were previously suggested for kinetic simulations of the copper vapor flows. It is found that the Lorentz–Berthelot rule cannot reliably predict the parameters of the LJ potential for cross-species Ar–Cu interaction. The DFT-vdW PECs are fitted by the Morse long-range (MLR) potentials. The MLR potentials are used to compute the outcomes of binary collisions in the DSMC method based on the solution of the classical scattering problem and to parameterize the variable hard sphere (VHS) collision model. The results of the DSMC simulations based on DFT-vdW PECs are compared with the results obtained based on various parameterizations of the VHS model. It is shown that the previously developed parameterizations of the VHS model can either over- or underestimate the plume temperature and density compared to the results obtained based on the DFT-vdW PECs. The simulations also reveal the strong effect of the cross-species collision model parameters on the flow structure in the mixing layer, which is dominated by molecular diffusion.

### The effect of end-plate wetting and unpinned contact lines on the filament thinning of strain hardening fluids

The Filament Extension Atomizer™ (FEA) is a unique technology designed for highly viscous or strain-hardening fluids that are otherwise difficult to atomize. The fluid is processed as a thin film between the contact points of two counter-rotating rollers of different materials. As the film is processed beyond the contact point, it is subject to an extensional flow that creates numerous thin filaments. As the filaments are stretched, they thin, and eventually, surface tension causes them to break into tightly dispersed droplets. Certain fluids, particularly those of low to moderate viscosity and high surface tension, can present challenges to atomize in FEA. Due to the tendency of these fluids to coalesce, their wetting on the rollers has been critical in optimizing film formation, though the impact of surface wetting on filament formation and breakup is not well understood. Accordingly, we studied the role of end-plate wetting for a high surface tension, aqueous, strain-hardening polymer solution on filament formation, thinning, and breakup, and fluid transfer to the end-plates, using a modified Capillary Breakup Extensional Rheometer (CABER). We found that filament formation and evolution were dramatically affected by both the wetting and wetting imbalances between the two end-plates, leading to different behavior across different end-plate combinations. The highly imbalanced wetting scenarios (i.e., combining a highly wetting and a non-wetting end-plate) gave rise to the most extreme deviations from classic behavior in conventional CABER experiments, such as long persisting filaments.

### Variational derivation of thermal slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules and Cercignani–Lampis boundary conditions: Comparison with experimental results

In the present paper, a variational method is applied to solve the Boltzmann equation based on the true linearized collision operator for hard-sphere molecules and the Cercignani–Lampis boundary conditions. This technique allows us to obtain an explicit relation between the first- and second-order thermal slip coefficients and the tangential momentum and normal energy accommodation coefficients, defined in the frame of the Cercignani–Lampis scattering kernel. Comparing the theoretical results with the experimental data from the work of Yamaguchi et al. [“Mass flow rate measurement of thermal creep flow from transitional to slip flow regime,” J. Fluid Mech. 795, 690 (2016)], a pair of accommodation coefficients has been extracted for each noble gas considered in the experiments. Then, these values have been used to compute, by means of our variational technique, the temperature-driven mass flow rates, and the outputs have been compared with the measurements for helium, neon, and argon. Good agreement has been obtained between the theoretical and the experimental data, within the range of validity of the proposed second-order slip model. For all the gases analyzed, the tangential accommodation coefficient is found to be much larger than the normal energy coefficient. The general trend, according to which, by increasing the molecular weight of the different gases, the values of both accommodation coefficients also increase, is confirmed in this study.

### Investigation of the dielectric strength of supercritical carbon dioxide–trifluoroiodomethane fluid mixtures

We investigate the dielectric strength of supercritical carbon dioxide–trifluoroiodomethane (CO2–CF3I) fluid mixtures. Supercritical fluids (SCFs), as a novel dielectric medium, combine advantageous properties of gaseous and liquid dielectrics: most notably, low viscosity, high heat transfer capability, and high dielectric strength. To our knowledge, this supercritical mixture of substances has never been investigated with respect to its dielectric properties. Our results suggest that supercritical CO2–CF3I binary mixtures have the electrical breakdown behavior similar to what we had observed in pure SCFs near the critical point. Specifically, we present the first evidence that the density fluctuation in SCF binary mixtures has a direct impact on the mean free path of electrons. By adjusting the mixing ratio, we show that the region where the discontinuity of breakdown voltage occurs shifts based on the ratio of the two substances. In addition, the experiment result shows a dielectric strength of the supercritical CF3I–CO2 mixture reaching up to 350 kV/mm, which is comparable to solid insulating materials. This paper indicates the suitability of using the supercritical CF3I–CO2 mixture as a dielectric medium for high power density applications.

### Dynamic mode of viscoelastic capsules in steady and oscillating shear flow

Because capsules exhibit viscoelasticity and shear resistance, the study of their dynamic motion under external flow is vital for biomedical and industrial applications. Toward this end, the present study uses the finite-element method to delve into the motion and deformation of viscoelastic capsules under steady and oscillating shear flow. In the steady shear, the effect of membrane viscosity is not obvious enough, which only slows the phase angle of capsules, which is consistent with previous work. However, the effect of membrane viscosity is more significant in the oscillatory shear, and we find that the deformation of capsules is affected by both viscosity and elasticity and exhibits two modes: For shear amplitudes γ0 < 0.06 or frequencies f > 0.3 Hz, the capsules essentially return to their original shape after being deformed. For amplitudes γ0 ≥ 0.06 or frequencies f ≤ 0.3 Hz, the capsules are strongly deformed and cannot return to their original state, which easily leads to membrane wrinkles and stress concentration. The results of this study systematically illustrate the dynamic behavior of viscoelastic capsules, which is critical to expound a capsule for use in drug transport, cell screening, and physiological processes.

### Freezing of axisymmetric liquid bridges

Author(s): Weiqi Huang and Xinping Zhou

An experimental study of the supercooling solidification of an axisymmetric vertical liquid bridge under the influence of gravity is carried out. An ice ring is formed at the end of the freezing process because of the instability of the liquid bridge. A model considering gravity and the supercooling effect is developed to describe the freezing of liquid bridge.

[Phys. Rev. Fluids 5, 103601] Published Fri Oct 16, 2020

### Hidden microscopic life of the moving contact line of a waterlike liquid

Author(s): Juan Carlos Fernández-Toledano, Terence D. Blake, Joël De Coninck, and Matej Kanduč

Large-scale molecular dynamic simulations are used to investigate the velocity dependence of the dynamic contact angle of a waterlike liquid on a flat carbonlike solid surface and to extract the coefficients of contact-line friction. It is shown that the same coefficients are obtained from a Langevin model of contact-line fluctuations at equilibrium, without any additional theoretical interpretation or model. A mechanistic link between the coefficients of slip and contact-line friction is also confirmed.

[Phys. Rev. Fluids 5, 104004] Published Fri Oct 16, 2020

### Vector field solution for Brinkman equation in presence of disconnected spheres

Author(s): Bo Liu and S. Bhattacharya

A basis function expansion and transformation technique are generalized to find a vector variable solution around two separated spheres where the Brinkman equation governs the field. Addressing this problem can lead to a derivation of the flow field over many porous spheres and quantify how the unsteady dynamics of many Brownian particles cumulatively affects stochastic motion.

[Phys. Rev. Fluids 5, 104303] Published Fri Oct 16, 2020

### Fluid-particle suspension by gas release from a granular bed

Author(s): Tess Homan, Valérie Vidal, Clément Picard, and Sylvain Joubaud

Understanding and quantifying the ability of gas to entrain and maintain particles in a liquid is a challenge in many fields. Here, an experimental study of the formation of a suspension by injecting gas at the bottom of a submerged granular bed is presented. The suspension packing fraction in the stationary state results from the balance between particle entrainment by bubble rise and sedimentation and can be well captured by a simple model.

[Phys. Rev. Fluids 5, 104304] Published Fri Oct 16, 2020

### Spectral-scaling-based extension to the attached eddy model of wall turbulence

Author(s): Dileep Chandran, Jason P. Monty, and Ivan Marusic

An extension to the attached eddy model (AEM) of wall turbulence is presented, where, in addition to the self-similar wall-attached eddies (Type A), we include two new eddy types for better predictions of the total kinetic energy. The first eddy type (Type SS) represents the wall-coherent very-large-scale motions, and the second eddy type (Type CA) is representative of the wall-incoherent but self-similar small-scale energetic motions. The extended AEM better predicts the energy spectra of all three velocity components across a broad range of Reynolds numbers.

[Phys. Rev. Fluids 5, 104606] Published Fri Oct 16, 2020

### Analytical solution for two-dimensional displacement flow in a curved down-sloping duct

Exact solution of the Navier–Stokes equations is used in this study to get a closed form equation for the transient and the steady state displacement flow of two Newtonian iso-viscous fluids in a two-dimensional curved plane channel. First, the displacement flow in a straight plane channel is considered. An available analysis is adapted in order to enhance its capability in explaining more details of the flow as well as prepare an appropriate frame to study the flow in curved channels. The behavior of the interface is predicted qualitatively both immediately and a while after the gate valve separating the fluids opens. It is shown that with the aid of the derivative of the flux of the heavier fluid, the viscous dominated flow regime may be analyzed with less difficulty compared to the available explanations in the literature and can also describe the behavior of the interface over a wider range of variations of the imposed flow. For the case of curved channels, the evolution of the interface at different rates of the imposed flow is analyzed again by considering the rate of change of the flux of the heavier displacing fluid in the viscous dominated regime. The results of the current study suggest that introducing the curvature in a displacement channel flow can facilitate the removal of the lighter fluid.

### Feature selection and processing of turbulence modeling based on an artificial neural network

Data-driven turbulence modeling has been considered an effective method for improving the prediction accuracy of Reynolds-averaged Navier–Stokes equations. Related studies aimed to solve the discrepancy of traditional turbulence modeling by acquiring specific patterns from high-fidelity data through machine learning methods, such as artificial neural networks. The present study focuses on the unsmoothness and prediction error problems from the aspect of feature selection and processing. The selection criteria for the input features are summarized, and an effective input set is constructed. The effect of the computation grid on the smoothness is studied. A modified feature decomposition method for the spatial orientation feature of the Reynolds stress is proposed. The improved machine learning framework is then applied to the periodic hill database with notably varying geometries. The results of the modified method show significant enhancement in the prediction accuracy and smoothness, including the shape and size of separation areas and the friction and pressure distributions on the wall, which confirms the validity of the approach.

### Nonlinear dynamics of double-layer unstable interfaces with non-uniform velocity shear

The interaction of double-layer density stratified interfaces with initial non-uniform velocity shear is investigated theoretically and numerically, taking the incompressible Richtmyer–Meshkov instability as an example. The linear analysis for providing the initial conditions in numerical calculations is performed, and some numerical examples of vortex double layers are presented using the vortex sheet model. We show that the density stratifications (Atwood numbers), the initial distance between two interfaces, and the distribution of the initial velocity shear determine the evolution of vortex double layers. When the Atwood numbers are large, the deformation of interfaces is small, and the distance between the two interfaces is almost unchanged. On the other hand, when the Atwood numbers are small and the initial distance between two interfaces is sufficiently close (less than or equal to the half of the wavelength of the initial disturbance), the two interfaces get closer to each other and merge at the last computed stage due to the incompressibility. We confirm this theoretically expected fact numerically.