# Latest papers in fluid mechanics

### Droplet collision and jet evolution hydrodynamics in wetting modulated valley configurations

Droplet impact hydrodynamics on “V”-shaped valleys or grooves of variant wettability and geometric dimensions have been studied experimentally and probed theoretically. The groove geometry makes the hydrodynamics three-dimensional, as in addition to the droplet dynamics in the lateral direction, liquid jets are generated from the post-impact droplet along the axial direction of the groove. The effect of the impact Weber number (We) on the jet velocity, the non-dimensional spreading width (γ), and north-pole height (h*) has been studied. It has been observed that the inertial forces dominate over the surface forces for higher impact We and hence, the effect of wettability is not important. However, the wettability of the substrate has a significant role in lower impact We as recoiling of the droplet is observed for the impact on the superhydrophobic substrate in this case. It has been observed that the spreading width of the post-impact droplet decreases with the increase in groove steepness. The jetting hydrodynamics has been probed and instantaneously after the impact, the generated jets travel at high velocity, but quickly reduce to a steady value. Jet velocity is observed to increase with an increase in the hydrophobicity of the substrate as well as the impact We. A semi-analytical formalism has been proposed to predict the jet velocity evolution in terms of governing Weber (We) and capillary (Ca) numbers. The predictions from the proposed model are in good agreement with the experimental results.

### Flow destabilization and nonlinear solutions in low aspect ratio, corrugated duct flows

Flows through narrow, rectangular ducts, with width to height aspect ratio below the established linear stability threshold of 3.2 and modified with grooves on top and bottom walls, are investigated. The primary objective of the current work lies in reintroduction of the linear destabilization mechanism, which is not present for the case of low aspect ratio rectangular ducts, via geometrical modifications of boundaries. The flow is assumed periodic in the streamwise- and bounded by sidewalls in the spanwise-direction. Applied geometrical modifications consist of two wavelengths of sinusoidal grooves running parallel to the flow direction. The current analysis starts with a brief characterization of flows through rectangular ducts and recalls some canonical results on hydrodynamic stability in such flows. In the second part, we illustrate that grooved geometries may lead to the onset of unstable modes in the form of waves traveling downstream, in the case of narrow ducts, already at relatively low values of the Reynolds number. The work is concluded with a concise characterization of flow states resulting from amplification of unstable modes into the nonlinear regime.

### Two-relaxation time lattice Boltzmann models for the ion transport equation in electrohydrodynamic flow: D2Q5 vs D2Q9 and D3Q7 vs D3Q27

Two commonly used discrete velocity models [the linear discrete velocity model (LDVM) and the full discrete velocity model (FDVM)] are investigated using the two-relaxation time lattice Boltzmann method coupled to a fast Poisson solver in an electroconvection system. We derived analytically the LDVM, i.e., D2Q5 and D3Q7 and FDVM, i.e., D2Q9 and D3Q27, for the ion transport equation (convection–diffusion–drift equation) in both two- and three-dimensional systems. The analytical results indicate that the error terms in LDVM are higher orders and can be neglected in practical simulations. The numerical results of LDVM and FDVM are quantitatively compared, showing the differences between the models' prediction in charge density, velocity, and stability hysteresis loops. The numerical results are consistent with the theoretical analysis. We perform all the simulations using graphics processing units, and the computational efficiency is measured via the wall clock time. We find that the LDVM can substitute FDVM in certain conditions with a substantial saving in computational costs and a small sacrifice in accuracy.

### Off-wall boundary conditions for large-eddy simulation based on near-wall turbulence prediction

Wall-modeled large-eddy simulation (LES) is currently the only affordable technique toward the eddy-resolving simulation of high-Reynolds number wall turbulence. Treatment of near-wall region in LES has drawn much attention in recent studies of wall turbulence and computational fluid dynamics. Traditional wall models typically relate the wall stress to the velocity through prescribed algebraic relations or the thin boundary layer equation. In the present study, we developed a new method for the treatment of near-wall region in LES based on the off-wall boundary conditions. The method combines the minimum flow units [Yin et al., “Prediction of near-wall turbulence using minimal flow unit,” J. Fluid Mech. 841, 654–673 (2018)] and the predictive inner–outer (PIO) model for wall turbulence [Marusic et al., “Predictive model for wall-bounded turbulent flow,” Science 329, 193–196 (2010)]. Fluctuating near-wall velocity field is predicted in real time to supply boundary conditions on the off-wall boundary. This method does not assume any velocity profile of the flow, but rather exploits the well-established universality of near-wall turbulence, and incorporates turbulent structures in the boundary conditions. We derived the expressions of the velocity and the subgrid-scale (SGS) stress boundary conditions in combination with the PIO model, and proved that the modulation effect and the fluctuating part of the SGS stress are not necessary for the off-wall boundary conditions. Through comparisons with other wall models, the current method is found to induce a shorter transition zone in the wall-normal direction. The validity and robustness of the method are verified by the reasonable simulation results of channel flows under different computational parameters.

### Impact of the membrane viscosity on the tank-treading behavior of red blood cells

Author(s): P. Matteoli, F. Nicoud, and S. Mendez

Numerical simulations are used to compare the impact of the internal fluid viscosity and the membrane viscosity on an isolated tank-treading red blood cell. Both decrease the tank-treading frequency, with moderate changes in the deformation and inclination of the red blood cell. However, it is shown that tank-treading frequencies from existing experiments are only retrieved if membrane viscosity is accounted for, and with an apparent shear-thinning of the membrane.

[Phys. Rev. Fluids 6, 043602] Published Tue Apr 20, 2021

### Settling of a particle pair through a sharp, miscible density interface

Author(s): David Deepwell, Raphael Ouillon, Eckart Meiburg, and Bruce R. Sutherland

The settling of a pair of particles through a density interface is analyzed for various particle positions and stratifications. The particles decelerate through the interface as surface fluid remains attached to the particles. Heightened transport is found to occur for vertically aligned particles.

[Phys. Rev. Fluids 6, 044304] Published Tue Apr 20, 2021

### Effect of ${\text{Re}}_{λ}$ and Rouse numbers on the settling of inertial droplets in homogeneous isotropic turbulence

Author(s): Daniel Odens Mora, Martin Obligado, Alberto Aliseda, and Alain Cartellier

Turbulent particle-laden flows have a widespread presence in industrial and natural processes. In this context, when gravity is present a natural question that arises is how the particles will settle. In this work, we show that the Rouse and Reynolds numbers seem to describe the particles settling dynamics under homogeneous isotropic turbulence. Our claim is supported by ours as well as previous experimental datasets available in the literature.

[Phys. Rev. Fluids 6, 044305] Published Tue Apr 20, 2021

### Large eddy simulations of high Reynolds number turbulence based on interscale energy transfer among resolved scales

Author(s): J. Andrzej Domaradzki

We show that the task of subgrid scale (SGS) modeling can be split into computing the total SGS energy transfer and determining its distribution among scales of motion. The former can be computed from energy transfers involving only resolved scales, providing a physical constraint on any proposed SGS model. The latter can be prescribed through classical spectral SGS modeling expressions shown in the figure or computed directly from resolved fields, allowing self-contained large eddy simulations.

[Phys. Rev. Fluids 6, 044609] Published Tue Apr 20, 2021

### Spinning and tumbling of long fibers in isotropic turbulence

Author(s): Theresa B. Oehmke, Ankur D. Bordoloi, Evan Variano, and Gautier Verhille

We simultaneously measure both the spinning and the tumbling components of rotation for long inertial fibers in isotropic turbulence. The spinning rates of these fibers are higher than the tumbling rates, manifesting dynamics analogous to sub-Kolmogorov fibers in turbulent flows. Similar to how sub-Kolmogorov fibers preferentially align with the local vorticity, long fibers preferentially align with the large scale coherent vortex filaments that can be as long as the integral scale of the turbulent flow.

[Phys. Rev. Fluids 6, 044610] Published Tue Apr 20, 2021

### Numerical study of COVID-19 spatial–temporal spreading in London

A recent study reported that an aerosolized virus (COVID-19) can survive in the air for a few hours. It is highly possible that people get infected with the disease by breathing and contact with items contaminated by the aerosolized virus. However, the aerosolized virus transmission and trajectories in various meteorological environments remain unclear. This paper has investigated the movement of aerosolized viruses from a high concentration source across a dense urban area. The case study looks at the highly air polluted areas of London: University College Hospital (UCH) and King's Cross and St Pancras International Station (KCSPI). We explored the spread and decay of COVID-19 released from the hospital and railway stations with the prescribed meteorological conditions. The study has three key findings: the primary result is that the concentration of viruses decreases rapidly by a factor of 2–3 near the sources although the virus may travel from meters up to hundreds of meters from the source location for certain meteorological conditions. The secondary finding shows viruses released into the atmosphere from entry and exit points at KCSPI remain trapped within a small radial distance of < 50 m. This strengthens the case for the use of face coverings to reduce the infection rate. The final finding shows that there are different levels of risk at various door locations for UCH; depending on which door is used there can be a higher concentration of COVID-19. Although our results are based on London, since the fundamental knowledge processes are the same, our study can be further extended to other locations (especially the highly air polluted areas) in the world.

### Effect of the supporting disks shape on nonlinear flow dynamics in a liquid bridge

The stability of convective flows in a non-homogeneous temperature field is affected by the shape of the container hosting the fluid. We present a nonlinear two-phase computational study of convection in a liquid bridge that develops under the action of buoyancy and Marangoni forces. The hydrothermal instability is examined for three shapes of disks supporting liquid bridge: both disks flat, the upper (hot) disk tapered, and the lower (cold) disk tapered. Steady flow is also analyzed for the case that both disks are tapered. In all the cases of instability, the flow pattern comprises, but is not limited to, a hydrothermal wave with an azimuthal wavenumber m = 2. An intriguing flow pattern is observed in the case of flat disks when the nonlinear interaction between the modes m = 0 and m = 2 leads to quasiperiodic motion forming a torus in the phase space. The torus originates from two traveling waves (TW) with the same mode m = 2 but with distinct (close) frequencies. Note that this was not observed in the one-phase model. The case with a tapered cold disk reveals an oscillatory state with a single TW wave associated with m = 2 mode. In the case of a tapered hot disk, an axially symmetric TW with m = 0 is observed first and, at later times, is accompanied by a TW with m = 2.

### Experimental and numerical study of blood backspatter interaction with firearm propellant gases

Experiments are used to quantify the influence of propellant gases on blood backspatter and the numerical model presented in the first part of this work (G. Li, N. Sliefert, J. B. Michael, A. L. Yarin, Phys. Fluids, 33, 043318 (2021)) is compared with the experimental results, which stem from muzzle gas expansion. Experimental results with blood backspatter show the reversal of backspatter blood drops and also indicate the presence of secondary atomization induced by the high relative velocity of the oncoming muzzle gases and the backward propagating bullet-induced blood spatter. To characterize the degree of influence, the muzzle gases for a range of modified and unmodified rifle and pistol configurations are considered. These muzzle gas expansions are used to infer the parameters of the numerical model presented in the first part. The significant effects of muzzle gases on blood backspatter have important implications for the use of forensic analysis of deposited bloodstain patterns, where flow reversal and breakup may significantly alter the forensic evidence.

### Trajectory and attitude study of a skipping stone

Although skipping stones seems like a time-honored pastime, an in-depth study of this game is of vital importance for the understanding of the water landing of space flight re-entry vehicles and aircraft, hull slamming, antitorpedo and antisubmarine water entry, etc. This study is devoted to scrutinize the motion rules involved in stone skipping theoretically and experimentally. A new physical model of the skipping stones is first developed by the Lagrange equation, in which both the Magnus effect and gyro effect are taken into consideration. Then, based on the theoretical model, the motion mechanism of a disk under the coupling effect of translation and spinning is revealed. The physical mechanism of the “trout” regime and trajectory deflection are discussed during the continuous bounce. Motion rules of the attitude and trajectory involved in the stone-skipping phenomenon are also presented. Furthermore, an experimental setup is established to verify the theoretical analysis, where for convenience in analyzing, an aluminum disk is employed instead of a real stone. Finally, the theoretical and experimental results are analyzed synthetically. The results reveal that (a) appropriate attack angles and horizontal velocities are the key factors in generating sufficient hydrodynamic forces to satisfy the conditions of bounce ([math]); (b) the gyro effect can guarantee the stability of the attack angle, which creates favorable conditions for the continuous bounce of the stone; and (c) the trajectory deflection results from the combination of the gyro effect and the Magnus effect. In the low-spin zone ([math] rot s−1), the Magnus effect plays a dominant role in the trajectory deflection, while in the high-spin zone ([math] rot s−1), the gyro effect plays the vital role. Besides, the deflection direction of trajectory is controlled by the rotational direction of the stone (clockwise or counterclockwise).

### Blood backspatter interaction with propellant gases

The theoretical results of the present work reveal a significant interaction of the oncoming vortex ring of propellant muzzle gases with backward blood spatter. It is shown that there is even possibility that a blood droplet from the backspatter will fully turn around by a powerful vortex ring and land behind a victim. Such a predicted outcome is confirmed by experimental data of fully reversed drop trajectories observed in the experiments conducted in the second part of this work [N. Sliefert, G. Li, J. B. Michael, A. L. Yarin, “Experimental and numerical study of blood backspatter interaction with propellant gases,” Phys. Fluids 33, 043319 (2021)]. A parametric study is conducted here to investigate the totality of the outcomes of the vortex ring interaction with the backward blood spatter and the corresponding deflections and landing locations of blood drops. Furthermore, a secondary vortex ring is introduced here to reveal a continuous effect of the propellant gas.

### Lie group solutions of advection-diffusion equations

Transport phenomena in homogeneous and inhomogeneous media are commonly encountered in many practical and industrial applications, which are modeled by advection-diffusion equations (ADEs) with constant or variable diffusivities, respectively. This paper provides a new perspective on how to solve advection-diffusion equations that model different transport phenomena in low Reynolds number flows. A mathematical description of the Lie group method is conducted first and then its potential in solving advection-diffusion equations for passive scalars transport with no-slip and no-flux boundary conditions is explored. The key step is to recast advection-diffusion equations as homogeneous diffusion processes on unimodular matrix Lie groups. Consequently, an approximate solution can be obtained from mean and covariance propagation techniques developed for diffusion equations on these Lie groups. The motivation to transform the advection-diffusion equation from Euclidean space to Lie groups is to exploit the available solutions of diffusion equation on these Lie groups so that the original equation can be solved in a simple way. In this paper, methodological details have been illustrated in solving ADEs modeling three kinds of transport phenomena. Two of them govern homogeneous transport and the solutions from mean and covariance propagation on the Lie group agree well with available results in published papers. We also use this method to solve more complicated ADEs governing inhomogeneous transport in one-dimensional compressible flows with spatially varying diffusivity, which is beyond the capabilities of existing approaches. The three real problems solved by the Lie group method illustrate the potential of this method. Instead of numerical calculations, the proposed closed-form method provides a simple alternative to study mass transfer encountered in various complex physical and industrial processes.

### A general single-node second-order boundary condition for the lattice Boltzmann method

In this work, we propose a general single-node nonslip hydrodynamic boundary condition for the lattice Boltzmann method. The construction of the boundary scheme is the combination of the bounce back rule for the nonequilibrium part of the density distribution and linear interpolation. The proposed boundary condition is very simple, universal, stable, and accurate. The asymptotic analysis of the newly proposed boundary condition confirms that is of second-order accuracy. The numerical experiments demonstrate that the boundary condition is indeed second-order accurate for both straight and curved boundaries.

### How a rotating magnetic field causes ferrofluid to rotate

Author(s): Mark I. Shliomis

The spin-up effect - entrainment of a ferrofluid by a rotating magnetic field - is still poorly understood despite its 50-year history and many published works. This work shows that the generally accepted theory of spin diffusion can not explain this effect due to the completely insignificant value of the spin viscosity of real ferrofluids. Instead, it is shown that the heat generated in the micro-eddies that arise around the rotating magnetic particles makes the fluid magnetization inhomogeneous, and this is enough to explain the bulk flow in the fluid. The flow rate is proportional to the cubes of the field rotation frequency and the vessel radius.

[Phys. Rev. Fluids 6, 043701] Published Mon Apr 19, 2021

### Constant-energetics control-based forcing methods in isotropic helical turbulence

Author(s): Takuya Kitamura

A deterministic forcing method and stochastic forcing method are proposed to keep mean turbulence kinetic energy and mean helicity at ideal values. Using the proposed forcing methods, it is shown that characteristics common to energy and helicity dissipation rates, and results of direct numerical simulations, support the joint cascade scenario of energy and helicity.

[Phys. Rev. Fluids 6, 044608] Published Mon Apr 19, 2021

### Electron heating and cooling in hypersonic flows

Using recently developed advanced numerical methods for plasma flows and sheaths, the first detailed study of electron cooling and heating taking place within hypersonic non-neutral flows is presented here. The numerical simulations fully couple the Navier–Stokes equations for the neutrals to the drift–diffusion model for the electrons and ions and include a 11-species finite-rate chemical solver along with a transport equation for the electron temperature in non-equilibrium. Results for Mach 18 airflow around a wedge with a sharp leading edge show that at low flight dynamic pressure the electron temperature remains close to the freestream temperature in the stagnation region. Such is attributed to the product of the electric field and the electron current being dominantly negative within the plasma sheaths and acting as an electron energy sink. This cooling effect leads to a significant portion of the flow downstream of the shock exhibiting electron temperatures much lower than expected. This study is the first to show a large impact of the non-neutral plasma sheaths on the post-shock electron temperature. This study also shows that the common approach to set the electron temperature equal to the vibrational temperature can result in the electron temperature being over-predicted by one order of magnitude or more in hypersonic flows.

### Stress-gradient-induced migration effects on the elastic instabilities of wormlike micellar solutions in a cross-slot flow

Using the two-species VCM model, we report the effects of stress-gradient-induced migration on the elastic instabilities of a wormlike micellar solution flowing through a cross-slot microchannel. The model was solved using a mixed finite element method in the open-source platform FEniCS. The stress-gradient-induced migration due to the non-Fickian (conformation) fluxes changes the onset of the instability and symmetry breaking and the size of secondary flow patterns upstream of the cross-channel corner. Varying the chain scission and micellar extensibility parameter, we observed that the suppression of asymmetric flow instability occurs at a different rate with the effects of migration. These results suggest that conformation force-driven migration has an influence on the onset of flow instability and should not be neglected a priori.