# Latest papers in fluid mechanics

### Strong shear flows release gaseous nuclei from surface micro- and nanobubbles

Author(s): Zibo Ren, Shuhong Liu, Beng Hau Tan, Fabian Denner, Fabien Evrard, Berend van Wachem, Zhigang Zuo, and Claus-Dieter Ohl

Surface attached micro- and nanobubbles are long-lived gaseous domains which are remarkably difficult to move or destroy. By creating a localized shear flow of sufficient shear rate from jets of cavitation bubbles, we observe that surface attached micro- and nanobubbles form long gaseous tethers, leading to the pinch-off and release of submicroscopic daughter bubbles, i.e. streaming gaseous nuclei. Detailed three-dimensional simulations and theoretical analysis show that the condition for pinch-off is dependent on the capillary number coupled with the Rayleigh-Plateau instability.

[Phys. Rev. Fluids 6, 043601] Published Fri Apr 16, 2021

### Transport of large particles through the transition to turbulence of a swirling flow

Author(s): Nathanaël Machicoane and Romain Volk

In inhomogeneous turbulent flows particles whose size are close to the flow integral length scale do not sample the flow homogeneously. Instead they explore preferentially regions of low velocity fluctuations. We study how this preferential sampling becomes more and more accentuated when the flow fluctuations decrease as the Reynolds number is lowered. In the absence of fluctuations, the large particles are trapped in the vicinity of the islands of the laminar flow, due to a shear-induced lift force, for times several order of magnitude longer than those associated with the flow forcing.

[Phys. Rev. Fluids 6, 044303] Published Fri Apr 16, 2021

### Modeling the deformation of a surfactant-covered droplet under the combined influence of electric field and shear flow

A surfactant-covered droplet subject to both electric field and shear flow is studied using a lattice Boltzmann and finite difference hybrid method, which breaks the limitation of asymptotic approaches that allow only small droplet deformation. It is found that in the electric system where electric field induces circulating flows directed from equator to poles, the presence of surfactants promotes droplet deformation for each electric capillary number (CaE), whereas in the electric system where droplets exhibit a prolate shape and circulating flows are directed from poles to equator, the presence of surfactants hinders droplet deformation at high CaE. We also for the first time show that in the electric system where droplet exhibits an oblate shape, the presence of surfactants almost has no effect on droplet deformation at high CaE. Regardless of electric properties and CaE, the inclination angle of surfactant-covered droplets is always smaller than that of clean droplets.

### Three-dimensional wake transition behind an elliptic cylinder near a moving wall

Three-dimensional flow past an elliptic cylinder with an aspect ratio of 0.5 near a moving bottom wall is investigated numerically for gap ratios of [math] and 0.4 (where G denotes the gap between the cylinder bottom and the moving wall, and D is the major-axis length of the cylinder) with Reynolds numbers (Re) ranging from 100 to 200 (based on a constant inlet velocity and the major-axis length of the cylinder); the transition between two- and three-dimensional flow regimes is described in detail. For [math], the flow is first two-dimensional with a Kármán vortex street followed by a two-layered wake, then it evolves into a three-dimensional flow regime with near-wake and far-wake elliptic instabilities of vortex pairs; for [math], the near-wake elliptic instability disappears (i.e., the near wake becomes two-dimensional) while the far-wake elliptic instability persists. For [math], the flow is first two-dimensional without the development of the two-layered wake, then it evolves into a three-dimensional flow regime with streamwise vorticity pairs propagating periodically in the spanwise direction; this propagation becomes irregular for [math]. For [math] the flow is first two-dimensional as for [math], then it becomes three-dimensional, exhibiting a behavior of modified mode C instability; for [math], this flow exhibits a chaotic behavior. For [math], the flow is first three-dimensional and steady without vortex shedding, and then develops into an unsteady flow with a dominating upper shear layer in the near-wake and a chaotic wake structure farther downstream.

### Study on boiling heat transfer in a shear flow through the lattice Boltzmann method

The liquid–vapor phase change and the boiling heat transfer induced by a microheater in a fluid are numerically studied through a two-phase lattice Boltzmann method. The fluid is subjected to simple shear. The effects of the gravity force, flow strength, and wall wettability are taken into account. A direct comparison between the cases of pool boiling and flow boiling is made in terms of the bubble release period, flow features, and the temperature of the microheater. In particular, it is shown that the flow motion has a negligible effect on the bubble release period for hydrophilic surfaces. By contrast, the bubble departure is considerably accelerated by the shear flow for hydrophobic surfaces which is associated with the formation of “bubble neck.”

### Transported and presumed probability density function modeling of the Sandia flames with flamelet generated manifold chemistry

The first modeling results for Sandia flames D, E, and F using the flamelet generated manifold reduced chemistry model with a transported probability density function (TPDF) closure model are presented. The micro-mixing is modeled with the simple “interaction by exchange with the mean” model and mean molecular diffusion is accounted for through a mean drift term. By accounting for mean molecular diffusion, stable burning flames D, E, and F could be predicted using the standard value for the mixing rate constant [math]. The TPDF results are used in an a priori analysis of the main simplifying assumptions typically used in presumed PDF (PPDF) models. A new PPDF model that accounts for the correlation between mixture fraction and progress variable in the joint PDF through a Gaussian copula is presented and included in the analysis. The analysis reaffirmed earlier findings: the marginal PDF of the progress variable is not well approximated by a β-PDF and the mixture fraction and progress variable are not statistically independent. The Gaussian copula PPDF model did show a qualitative improvement over the models that invoke the statistical independence assumption. Quantitative analysis showed that the mean progress variable source term could not be predicted accurately by any of the PPDF models. The PPDF models were then applied in actual simulations of flames D and E. The erroneous predictions of the mean progress variable source term cause relative errors in the PPDF simulation results for the conditional mean temperature exceeding 20%.

### An a priori analysis of the structure of local subfilter-scale species surrounding flame fronts using direct numerical simulation of turbulent premixed flames

An a priori analysis of subfilter-scale (SFS) species structure important to estimate chemical reaction rates in large-eddy simulation (LES) is performed using direct numerical simulation (DNS) of a turbulent premixed flame at a turbulence Reynolds number [math] and Karlovitz number [math] with semi-detailed finite-rate chemistry. Differences between the complete chemical reaction rates extracted from DNS and those estimated from LES-filtered variables are quantified. The spatial distributions of these differences are found to be localized in regions surrounding the flame front for representative reactions. Within these regions, variations in the localization relative to the flame, scale, and magnitude of the SFS species concentrations are quantified, and mean SFS structure is determined. SFS species structure is found in two groupings: “single-banded” structure characterized by one distinct peak and “double-banded” structure characterized by two peaks of opposite signs. Species that are produced and consumed within the flame such as [math] and HCO are observed to have single-banded structure, and species displaying a frontal behavior such as n-C7H16 and OH are found to have double-banded structure, on average. The local SFS structure surrounding the flame is impacted by neighboring flame-flame interactions as well as by variations in flame curvature. The impacts of the flame-flame interactions are strong when the SFS species structure has “large” length scales with concentration peaks significantly displaced from the flame front. Curvature effects are shown to be strong in high curvature regions of the flame.

### Criterion for the linear convective to absolute instability transition of a jet in crossflow: The countercurrent viscous and round mixing-layer analogy

Author(s): Davi B. de Souza, Rômulo B. Freitas, and Leonardo S. de B. Alves

An inviscid and planar mixing-layer analogy has been recently developed to qualitatively identify the transverse jet transition from convectively to absolutely unstable. We have shown that introducing Reynolds number effects on the disturbance behavior as well as evaluating the entire problem in cylindrical instead of Cartesian coordinates leads to significant improvements. This novel viscous and round mixing-layer analogy can accurately identify the transverse jet transition.

[Phys. Rev. Fluids 6, L041901] Published Thu Apr 15, 2021

### A three-dimensional phase-field lattice Boltzmann method for incompressible two-components flows

In this paper, a lattice Boltzmann model for the coupled Allen–Cahn–Navier–Stokes equations in three dimensions is presented. Two equations are solved: one for the fluid velocity and one for the order parameter. Both are written within the general multiple-relaxation-time framework, where all the equilibrium and forcing terms are described by using the full set of Hermite polynomials. The resultant practical implementation is compact. The gradient of the order parameter can be computed by the non-local finite differences or the local central moments. The latter suffers from grid-scale oscillations. The very good accuracy properties are demonstrated against nine well-consolidated benchmark tests. Specifically, two groups of tests are tackled. In the former, the velocity field is superimposed. Hence, only the equation for the evolution of the order parameter is solved. These numerical experiments demonstrate the ability of the proposed scheme to capture the correct evolution of the interface. In the latter, two immiscible fluids are considered and the two equations are solved. Simulations of the vertical penetration of a wedge-shaped body, two- and three-dimensional Rayleigh–Taylor instability prove that two-fluids systems can be successfully simulated by our approach.

### Airfoil flow receptivity to simulated tonal noise emissions

On airfoils at low to moderate Reynolds numbers, trailing edge sound can have a feedback effect on the development of instability waves resulting in strongly periodic vortex shedding and tonal noise. This complex problem is decoupled in this study to investigate the flow response to deterministic noise emissions. The flow receptivity and response to tonal noise are examined using controlled steady and transient acoustic excitation. Experiments are performed on a NACA 0018 airfoil at a Reynolds number of [math] and an angle of attack of 5°, with a separation bubble on the suction side. Controlled acoustic perturbations are introduced via a loudspeaker. A combination of mean and time-resolved surface pressure and simultaneous high-speed particle image velocimetry measurements provides insight into the response of the bubble to simulated acoustic forcing. Amplification of shear layer perturbations in the fore portion of the separation bubble is observed only after some time delay from the onset of acoustic forcing. This places the receptivity region within the boundary layer upstream of the separation bubble, extending from the leading edge to just downstream of the suction peak. The acoustically excited perturbations in the receptivity region attain higher amplitudes than natural disturbances and are amplified significantly in the separation bubble, leading to a transient reduction in the separation bubble size. Results elucidate the ensuing transient response of the separation bubble, illustrating the flow dynamics expected during the initiation of the acoustic feedback loop during natural tonal noise emissions on an airfoil.

### Assessment of a flamelet approach to evaluating mean species mass fractions in moderately and highly turbulent premixed flames

Complex-chemistry direct numerical simulation (DNS) data obtained from lean methane-air turbulent flames are analyzed to perform a priori assessment of predictive capabilities of the flamelet approach to evaluating mean concentrations of various species in turbulent flames characterized by Karlovitz numbers [math], 74.0, and 540. Six definitions of a combustion progress variable [math] are probed and two types of probability density functions (PDFs) are adapted: (i) actual PDFs extracted directly from the DNS data or (ii) presumed [math]-function PDFs obtained using the DNS data on the first two moments of the [math]-field. Results show that the mean density, the mean temperature, and the mean mass fractions of CH4, O2, H2O, CO2, CO, CH2O, CH3, and HCO are very well predicted using the temperature-based combustion progress variable [math] and the actual PDF. For other considered species, the quantitative predictions are worse but still appear to be encouraging (with the exception of CH3O at [math]). The use of the flamelet library obtained from the equidiffusive laminar flame improves results for H2, HO2, and H2O2 at the highest Karlovitz number. Alternative definitions of the combustion progress variable perform worse and the reasons for this are explored. The use of the [math]-function PDF yields worse results for intermediate species such as OH, O, H, CH3, and HCO, with this PDF being significantly different from the actual PDF. Application of the flamelet approach to rates of production/consumption of various species is also addressed and implications of obtained results for modeling are discussed.

### An integral model based on slender body theory, with applications to curved rigid fibers

We propose a novel integral model describing the motion of both flexible and rigid slender fibers in viscous flow and develop a numerical method for simulating dynamics of curved rigid fibers. The model is derived from nonlocal slender body theory (SBT), which approximates flow near the fiber using singular solutions of the Stokes equations integrated along the fiber centerline. In contrast to other models based on (singular) SBT, our model yields a smooth integral kernel which incorporates the (possibly varying) fiber radius naturally. The integral operator is provably negative definite in a nonphysical idealized geometry, as expected from the partial differential equation theory. This is numerically verified in physically relevant geometries. We discuss the convergence and stability of a numerical method for solving the integral equation. The accuracy of the model and method is verified against known models for ellipsoids. Finally, we develop an algorithm for computing dynamics of rigid fibers with complex geometries in the case where the fiber density is much greater than that of the fluid, for example, in turbulent gas-fiber suspensions.

### Nano-confinement effects on liquid pressure

In this study, molecular dynamics simulations are performed to estimate the equilibrium pressure of liquid confined in nanopores. The simulations show that pressure is highly sensitive to the pore size and can significantly change from absolute positive to absolute negative values for a very small (0.1 nm) change in the pore size. The contribution from the solid–liquid interaction always dominates the pressure in the first liquid layer adjacent to the surface and the sensitiveness of pressure on the pore size is dependent on the atom distribution in the liquid layers. A surface influence number [math] is introduced to quantitatively characterize the degree of the confinement. At constant system temperature, the [math] number decreases with increasing pore size based on a power-law function. In nanopores with large S number, the pore liquid pressure is found to be independent of bulk liquid pressure, whereas in nanopores with small S number, the pore pressure is dependent and increases with bulk pressure.

### Extended lattice Boltzmann model for gas dynamics

We propose a two-population lattice Boltzmann model on standard lattices for the simulation of compressible flows. The model is fully on-lattice and uses the single relaxation time Bhatnagar–Gross–Krook kinetic equations along with appropriate correction terms to recover the Navier–Stokes–Fourier equations. The accuracy and performance of the model are analyzed through simulations of compressible benchmark cases including Sod shock tube, sound generation in shock–vortex interaction, and compressible decaying turbulence in a box with eddy shocklets. It is demonstrated that the present model provides an accurate representation of compressible flows, even in the presence of turbulence and shock waves.

### External pressure dependence of granular orifice flow: Transition to Beverloo flow

In this paper, we have designed and employed a suspended-wall silo to remove the Janssen effect in order to explore directly the local pressure dependence of granular orifice flow (GOF) systematically. We find that as the Janssen effect is removed, the flow rate Q changes linearly with the external pressure. The slope α of the linear change decays exponentially with the ratio of the silo size and the size of the orifice Φ/D, which suggests the existence of a characteristic ratio λ (∼2.4). When Φ/D > λ, α gradually decays to zero, and the effect of external pressure on the GOF becomes negligible, where the Beverloo law retrieves. Our results show that the Janssen effect is not a determining factor of the constant rate of GOF, although it may contribute to shield the top load. The key parameter in GOF is Φ/D. In small Φ/D, the flow rate of GOF can be directly adjusted by the external pressure via our suspended-wall setup, which may be useful to the transportation of granules in microgravity environment where the gravity-driven Beverloo law is disabled.

### Special topic on Drops and Flows in Acoustic Levitation

### Effect of surface contact angle on the wall impingement of a power-law liquid jet

This study theoretically investigated the impinging liquid sheet, formed by a power-law liquid jet obliquely encroaching on a wall surface. Based on the control volume method, the governing equations of the liquid sheet were established through force balance analysis at the curved edge. To solve the governing equations, energy conservation in the theoretical model was also considered throughout the impinging process. Typical working conditions were selected to validate the theoretical predictions. The results showed that the theoretical inner counter of liquid sheet agreed well with experimental data. Based on the theoretical model, influence of rheological parameters, surface contact angle, and surface tension coefficient are discussed, respectively. It is concluded that the surface contact angle could affect liquid sheet size by changing the total surface tension force at the rim, as well as the surface energy variation in the energy conservation equation.

### Antibubble formation by a single drop impact on a free surface

An experimental study of the antibubble formation by a single drop impact on an identical liquid bath is presented. With the increase in the impact velocity, different phenomena are observed and classified into four regimes: No droplet, Single droplet, Double droplets, and Antibubble formation. In fact, the Antibubble formation is part of the Double droplets regime. A high-speed drop impact leads to the formation of a thick jet, which subsequently pinches into two main droplets named as the primary droplet and the secondary droplet. The secondary droplet first impacts on the liquid surface, while the primary droplet then falls back and pushes it into the liquid bath, generating an antibubble. The detailed dynamics is presented, and the critical conditions for antibubble formation are introduced. This work should benefit the controllable generation of antibubbles and stimulate the future applications in practice.

### Mixing and transport enhancement in microchannels by electrokinetic flows with charged surface heterogeneity

Electrokinetic flow in a microchannel driven by charged surface heterogeneity in the presence of an external electric field is investigated by three-dimensional simulations. A computational framework is developed coupling a two-relaxation-time lattice Boltzmann solver for the transport equations of fluids, charged species, and passive tracing scalars and a fast Poisson solver for the electric potential. The two-relaxation-time lattice Boltzmann method is used to resolve the spatiotemporal distribution of flow field, ion concentration, and two passive tracing scalars. The fast Poisson solver is used to solve the electric potential at every time step. Three charged surface patterns together with various external electric fields are investigated. The induced electrokinetic vortices contribute to the mixing and transport enhancement of the passive scalars, depending on the surface patterns and the external electric field. The transport enhancement is found to follow a power law with respect to the magnitude of the external electric field.

### A near-wall predictive model for passive scalars using minimal flow unit

In the present study, direct numerical simulations (DNSs) are performed to the passive scalar transport in minimal flow units (MFUs) at [math], 2000, and 4000 and in a full-sized channel at [math] for comparison. The molecular Prandtl number ranges from 0.2 to 2.0. At each Prandtl number, the scalar intensities in MFUs at different Reynolds numbers agree well with each other, and with those at MFU-contained scales in the full-sized channel. This suggests that scalar transport in MFUs is Reynolds number independent and is able to represent that at small scales in the full-sized channel. A near-wall predictive model for passive scalars based on MFU data is proposed in the framework of superposition and modulation of the outer large-scale motions. The modulation coefficients at different Prandtl numbers are collapsed together under the presently proposed transforming. Both the scalar intensities and the joint probability density functions of the predicted results agree well with those of the DNS results. Furthermore, a predictive model for wall scalar-flux based on MFU data and the quasi-steady hypothesis is put forward and validated against the DNS results.