# Latest papers in fluid mechanics

### Net fluid flow and non-Newtonian effect in induced-charge electro-osmosis of polyelectrolyte solutions

Author(s): Huicheng Feng and Teck Neng Wong

This paper reports an interesting net fluid flow in the induced-charge electro-osmosis (ICEO) of poly(sodium 4-styrenesulfonate) (NaPSS) solutions measured through microparticle image velocimetry (μPIV). The net fluid flow is attributed to the significantly unequal cations and poly-anions of NaPSS. ...

[Phys. Rev. E 100, 013105] Published Fri Jul 12, 2019

### Inverse cascade of hybrid helicity in $B\mathrm{Ω}$-MHD turbulence

Author(s): Mélissa D. Menu, Sébastien Galtier, and Ludovic Petitdemange

An inverse cascade of hybrid helicity is observed in direct numerical simulations of 3D magnetohydrodynamics with both an imposed magnetic field and a rotation rate. The impact of the tilt angle between the two axes and of the polarized forcing is discussed.

[Phys. Rev. Fluids 4, 073701] Published Fri Jul 12, 2019

### Evaluation of particle-based continuum methods for a coupling with the direct simulation Monte Carlo method based on a nozzle expansion

This paper investigates three different particle-based continuum methods, the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) and Fokker-Planck (ESFP) methods and the Low Diffusion (LD) method, for a coupling with the direct simulation Monte Carlo (DSMC) method. After a short description of the methods and their implementation, including the coupling concept for the LD-DSMC, simulation results of a nozzle expansion are compared with available experimental measurements and a DSMC simulation. Excellent agreement between ESBGK, ESFP, and DSMC can be observed in the throat of the nozzle, while the LD method fails to predict the correct velocity, temperature, and density profile. Further downstream, only the DSMC and the coupled ESBGK/ESFP-DSMC simulations are able to reproduce the measured rotational temperature profiles. A performance comparison shows the possible computational savings of a coupled ESBGK/ESFP-DSMC simulation, where a speedup of four orders of magnitude can be observed compared to a regular DSMC simulation.

### Effect of chordwise wing flexibility on flapping flight of a butterfly model using immersed-boundary lattice Boltzmann simulations

Author(s): Kosuke Suzuki, Takaaki Aoki, and Masato Yoshino

Wing flexibility is one of the important factors not only for lift and thrust generation and enhancement in flapping flight but also for development of micro-air vehicles with flapping wings. In this study, we construct a flexible wing with chordwise flexibility by connecting two rigid plates with a...

[Phys. Rev. E 100, 013104] Published Thu Jul 11, 2019

### On the particle discretization in hypersonic nonequilibrium flows with the direct simulation Monte Carlo method

To help understand the discrete molecular behaviors in a nonequilibrium state, this work investigated the statistical and physical features of particle discretization for the direct simulation Monte Carlo method with no time counter collision scheme in hypersonic flows. Different functionals, particle discretization errors of four macroscopic quantities, were studied by averaging their values throughout four flow regions. Specifically, a linear convergence behavior [math], an independence of Nc, and an inverted V-type variation of discretization errors were observed for different functionals and in different regions, where Nc is the particle number per cell. The magnitude of discretization error was found to be positively related to the degree of local nonequilibrium effect. Further microscopic analyses indicated that the mean collision separation is independent of Nc even if ⟨Nc⟩ < 10. Instead, the variation of collision frequency with a turning point of ⟨Nc⟩ ≈ 10 was found to be responsible for the observed convergence behaviors. An overestimation of collision frequency with decreased Nc appeared when ⟨Nc⟩ > 10 because of a reduced maximal relative velocity. Meanwhile, an underestimation of collision frequency with decreased Nc appeared when ⟨Nc⟩ < 10 because of repeated collisions. In addition, the effect of repeated collisions was enhanced by a strong kinetic and thermodynamic nonequilibrium in such a way that the mixed and inverted V-type trend of particle discretization errors inside the shock wave was observed.

### Simple multi-sections unit-cell model for sound absorption characteristics of lotus-type porous metals

This paper presents a simple multisection unit-cell model (UCM) with which to investigate the sound absorption characteristics of lotus-type porous metals (LTPMs). This model is inspired by analyzing micrographs of the LTPMs and by considering the relationship between the average pore diameter and the porosity. The multisection UCM is used to establish the analytical relationships between the basic nonacoustic parameters (namely, flow resistivity, tortuosity, and porosity) and the sound absorption characteristics of the LTPMs. The analytical predictions are compared with existing experimental data and with analytical results from a uniform UCM. Good agreement is found between the multisections UCM and the existing experimental results. The comparative relationships of the sound absorption coefficients of the LTPMs and uniform and graded open-cell foam aluminum are plotted as well.

### Inertial instabilities in a microfluidic mixing-separating device

Combining and separating fluid streams at the microscale has many scientific, industrial, and medical applications. This numerical and experimental study explores inertial instabilities in so-called mixing-separating micro-geometries. The geometry consists of two straight square parallel channels with flow from opposite directions and a central gap that allows the streams to interact, mix, or remain separate (often also referred to as the H-geometry). Under creeping-flow conditions (the Reynolds number tending to zero), the flow is steady, two-dimensional, and produces a sharp interface between fluid streams entering the geometry from opposite directions. When Re exceeds a critical value, one of two different supercritical, inertial instabilities appears which leads to significant changes in the flow pattern and an increased level of interaction between the two streams, although the flow remains steady. The exact form of the instability is dependent on the gap size and the Reynolds number, and we identify two distinct instabilities, one of which appears in devices with large gaps and another which appears in devices with small gaps. At intermediate gap sizes, both instabilities can occur in the same device (at different onset Re). The experimental results for one gap size are used to validate our numerical method, which is then applied to a wider range of gap sizes. The results suggest that the gap size is of primary importance in determining the type of instability that occurs. With a judicious choice of gap size, the instabilities can be exploited (or avoided) in scientific, medical, or other microfluidic applications.

### Experimental and numerical studies on the flow characteristics and separation properties of dispersed liquid-liquid flows

The local dynamics of spatially developing liquid-liquid dispersed flows at low superficial velocities, ranging from 0.2 to 0.8 m s−1, are investigated. The dispersions are generated with an in-line static mixer. Detailed measurements with laser-based diagnostic tools are conducted at two axial pipe locations downstream of the mixer, namely, at 15 and 135 equivalent pipe diameters. Different flow patterns are recorded, and their development along the streamwise direction is shown to depend on the initial size and concentration of the drops as well as the mixture velocity. The drop size is accurately predicted by an empirical formula. The variations in drop concentration over the pipe cross-section along the pipe result in local changes of the physical properties of the mixture and consequently in asymmetrical velocity profiles, with the maxima of the velocity located in the drop-free region. Computational fluid dynamics simulations based on a mixture approach predict the experimental results close to the experimental uncertainties for the majority of the cases. The simulation results reveal that gravity and lift forces, as well as shear-induced diffusion are the most important mechanisms affecting the drop migration. It is found that the drops behave as suspensions of rigid spheres for the conditions investigated, despite the deformation effects, which are found experimentally to be stronger at the densely packed region.

### Phase field lattice Boltzmann model for air-water two phase flows

Two phase flows occur in different forms with liquid and gas in general, among which, the interaction of the flow of air and water is a common scenario. However, modeling the two phase flow still remains a challenge due to the large density ratio between them and different space-time scales involved in the flow regimes. In the present work, the lattice Boltzmann (LB) model capable of handling large density ratio (1000) and high Reynolds number (104) simultaneously is proposed. The present model consists of two sets of LB equations, one for the flow field in terms of normalized pressure-velocity formulation and the other for the solution of the conservative Allen-Cahn equation to capture the interface. The numerical tests such as stationary drop, bubble coalescence, and capillary wave decay have been performed, and the results exhibit excellent mass conservation property. The capability of the present model to handle complex scenarios has been tested through test cases, for example, rise of an air bubble, splash of a water droplet on a wet bed, and Rayleigh-Taylor instability. In all test cases, the simulation results agree well with the available reference data. Finally, as an application of the present model, the breaking of a deep water wave with high Reynolds number (104) is simulated. The plunging breaker with wave overturning and the generation of secondary jet and splashes are well described by the present LB model. The evolution of wave energy dissipation during and after breaking is in agreement with the reference data.

### Modeling and verification of the Richtmyer–Meshkov instability linear growth rate of the dense gas-particle flow

The multiphase Richtmyer–Meshkov instability (RMI) often occurs in supernova events and inertial confinement fusion processes, where it plays a critical role. In the evolution of the RMI process, the particle phase may have either a dilute or a dense pattern. Previous studies have mainly focused on the dilute pattern. Currently, there is no published research on the theoretical growth model of the dense gas-particle flow. In this work, a new Atwood number model was developed with the assumption of a small Stokes number and shown to be effective for the RMI of the dense gas-particle flow. The Atwood number model was characterized by the moment coupling parameters and the ratio of the volume fractions of the two phases. Further derivation showed that it was consistent with the original Richtmyer’s model and the dilute gas-particle flow model. In addition, the theoretical growth rate was modeled to predict the evolution law of the mix zone width for the dense gas-particle flow. The presence of the particle phase inhibited the growth rate of the RMI, which emphasized the effect of the solid phase. The corresponding numerical simulations were also performed based on the compressible multiphase particle-in-cell method for different cases of the particle volume fraction. The numerical results demonstrated the accuracy of the theoretical growth rate model. Additionally, a brief analysis of the flow structures and cloud motion during the RMI process was performed.

### On vortex intensification due to stretching out of weak satellites

The interaction of two essentially unequal vortices is studied for the two-dimensional inviscid model. The curved stretching out of a weak satellite, localized at the periphery of the main vortex, is described analytically in the passive scalar approximation. The rate of energy transfer from the satellite to the main vortex is shown to increase with the curvature of the satellite orbit characterized by the ratio of the satellite size to its distance from the main vortex center. Such a mechanism of the energy cascade is distinct from previously considered symmetric deformations by external flows with a uniform strain rate when the energy is preserved for localized vortices with zero circulation in an unbounded domain. Therefore, asymmetric stretching out of satellites along curved orbits with the finite circumference is crucial for the vortex intensification and can serve as an important ingredient of inverse energy cascade in the two-dimensional turbulence.

### A micropolar-Newtonian blood flow model through a porous layered artery in the presence of a magnetic field

In this work, we present a two-phase model of blood flow through a porous layered artery in the presence of a uniform magnetic field. The characteristic of suspensions in blood allows us to assume blood as a micropolar fluid in the core region and plasma as a Newtonian fluid in the peripheral region of a blood vessel. The wall of a blood vessel is porous and composed of a thin Brinkman transition layer followed by a Darcy porous layer of different permeabilities. A magnetic field of uniform strength is transversally applied to the direction of blood flow. The authors obtained an analytical solution of the problem of blood flow through the composite porous walled artery. Analytical expressions for the flow velocity, microrotational velocity, flow rate, and stresses at the wall have been obtained in the closed form using the modified Bessel function. The effects of various flow parameters on the two-fluid model of blood flow are analyzed graphically. An important conclusion which is drawn from the solution of the present problem is that the different permeabilities of Darcy and Brinkman regions of the porous layered artery have a significant effect on the flow. The present work is validated from the previously published literature studies.

### Marangoni instability in a heated viscoelastic liquid film: Long-wave versus short-wave perturbations

Author(s): Rajkumar Sarma and Pranab Kumar Mondal

We investigate the Marangoni instability in a thin layer of viscoelastic fluid, confined between its deformable free surface and a substrate of low thermal conductivity. Following a theoretical analysis, we study the stability of the present system for the case when the fluid layer is subjected to h...

[Phys. Rev. E 100, 013103] Published Wed Jul 10, 2019

### Coarse graining the dynamics of immersed and driven fiber assemblies

Author(s): David B. Stein and Michael J. Shelley

We develop a coarse-grained Brinkman-type model for the dynamics of ordered arrays of immersed fibers. This approach provides a simple framework for the mathematical analysis and efficient numerical solution of problems including fiber-fluid rheology, soft valves, and waves within driven fiber beds.

[Phys. Rev. Fluids 4, 073302] Published Tue Jul 09, 2019

### Forced three-wave interactions of capillary-gravity surface waves

Author(s): Annette Cazaubiel, Florence Haudin, Eric Falcon, and Michael Berhanu

Two surface waves are forced in a cylindrical tank. Their nonlinear interaction generates a third wave not obeying the dispersion relation, whose presence is shown using a laser vibrometer or a three-dimensional free-surface reconstruction. We explain this result as a forced three-wave interaction.

[Phys. Rev. Fluids 4, 074803] Published Tue Jul 09, 2019

### Efficiency limits of the three-sphere swimmer

Author(s): Babak Nasouri, Andrej Vilfan, and Ramin Golestanian

The efficiency of the three-sphere swimmer is studied and the optimal actuation sequences determined. By accounting for full hydrodynamic interactions in the low Reynolds number regime, it is shown that, surprisingly, the swimmer with unequal spheres can be more efficient than the equally sized one.

[Phys. Rev. Fluids 4, 073101] Published Mon Jul 08, 2019

### Filament formation via the instability of a stretching viscous sheet: Physical mechanism, linear theory, and fiber applications

Author(s): Bingrui Xu, Minhao Li, Feng Wang, Steven G. Johnson, Yoel Fink, and Daosheng Deng

Liquid sheets are essential for industrial applications, and during thermal drawing, a stretching viscous sheet breaks up into filaments. A theory is proposed to elucidate the underlying mechanism, shedding light on the sophisticated structures for functional devices in fibers, fabrics, or textiles.

[Phys. Rev. Fluids 4, 073902] Published Mon Jul 08, 2019

### Dipolar thermocapillary motor and swimmer

Author(s): Valeri Frumkin, Khaled Gommed, and Moran Bercovici

A circular opening in a Hele-Shaw-type confinement gives rise to thermocapillary dipole flow, which can be used to drive flow in microfluidic configurations. The same mechanism can also be leveraged for the propulsion of light-actuated surface swimmers.

[Phys. Rev. Fluids 4, 074002] Published Mon Jul 08, 2019

### Experimental and numerical investigation of phase separation due to multicomponent mixing at high-pressure conditions

Author(s): C. Traxinger, M. Pfitzner, S. Baab, G. Lamanna, and B. Weigand

Mixture-induced phase separation of an initially supercritical fluid due to the interaction with its surrounding is studied. Three different injection temperatures are investigated and qualitative characteristics of the formation process agree well between experiments and simulations.

[Phys. Rev. Fluids 4, 074303] Published Mon Jul 08, 2019

### Dynamics and wakes of freely settling and rising cubes

Author(s): Arman Seyed-Ahmadi and Anthony Wachs

Direct numerical simulations of settling and rising cubes show the prevalence of distinct helical motions, the onset of which are accompanied by a significant jump in the drag coefficient. This enhancement is associated with a combined effect of the vortex-induced drag and the cube orientation.

[Phys. Rev. Fluids 4, 074304] Published Mon Jul 08, 2019