# Latest papers in fluid mechanics

### Modeling the effect of flow-induced mechanical erosion during coffee filtration

The espresso extraction process involves a complex transport inside a geometry-changing porous medium. Large solid grains forming the majority of the porous medium can migrate, swell, and consolidate, and they can also morphologically change during flow, i.e., being mechanically eroded by hydrodynamic forces. These processes can, in turn, have a significant back-effect on the flow and the related coffee extraction profiles. In this article, we devise a bottom–up erosion model in the framework of smoothed dissipative particle dynamics to consider flow-induced morphological changes of the coffee grains. We assume that the coffee grains are not completely wetted and remain brittle. We found that heterogeneity in both the filtration direction and the transverse direction can be induced. The former is controlled by the angle of internal friction while the latter is controlled by both the cohesion parameter and the angle of internal friction. Not restricted to the modeling of espresso extraction, our model can also be applied to other eroding porous media. Our results suggest that, under ideal porous flow conditions, we can control the heterogeneity (in both the pressure drop direction and the transverse direction) of an eroding medium by tuning the yield characteristics of the eroding material.

### Solenoidal linear forcing for compressible, statistically steady, homogeneous isotropic turbulence with reduced turbulent Mach number oscillation

This study investigates a solenoidal linear forcing scheme with reduced oscillation of a turbulent Mach number MT for direct numerical simulations (DNS) of statistically steady, homogeneous isotropic turbulence. A conventional linear forcing scheme results in a large temporal oscillation of MT, where the maximum MT reaches about 1.1 times the time-averaged MT. Therefore, strong shocklets are generated when MT becomes large although such strong shocklets hardly appear when MT is close to the time-averaged value. DNS with the proposed forcing scheme confirms that the temporal oscillation of MT is effectively reduced by adjusting a forcing coefficient with a ratio between velocity variance and its steady state value prescribed as a parameter. The time-dependent forcing coefficient results in the variation of the power input to kinetic energy. Therefore, the temporal oscillation of the Reynolds number for this forcing scheme is as large as that for the conventional linear forcing. The ratio between the solenoidal and dilatational kinetic energy dissipation rates increases with MT, and the MT dependence is consistent between the present solenoidal linear forcing and the low-wavenumber solenoidal forcing in wavenumber space. The skewness and flatness of the velocity derivative become large compared with incompressible turbulence when MT exceeds 0.6. Both average and root-mean-squared fluctuation of the shock Mach number of shocklets increase with MT. The most typical thickness of shocklets decreases with MT and asymptotically approaches about 1.5 times the Kolmogorov scale. The shocklet thickness normalized by the Kolmogorov scale hardly depends on the Reynolds number.

### Nonlinear behavior of electrohydrodynamic flow in viscoelastic fluids

Author(s): Zheng-Gang Su, Tian-Fu Li, Kang Luo, and Hong-Liang Yi

The nonlinear evolution of electrohydrodynamic flow subjected to unipolar injection in the dielectric liquid is extended from Newtonian fluids to viscoelastic fluids. The effect of viscoelasticity not only precipitates the onset of chaos but also leads to new transition sequences to chaos. Moreover, an asymmetric steady flow pattern is observed in a perfectly symmetric geometry. In viscoelastic fluids, the electric current transfer is reduced in most cases, but for weakly elastic fluid, it may be enhanced.

[Phys. Rev. Fluids 6, 093701] Published Tue Sep 07, 2021

### Numerical study of the McIntyre instability around Gaussian floating vortices in thermal wind balance

Author(s): Michael Le Bars

The viscodiffusive McIntyre instability has been suggested as a possible source for density layer formation around laboratory and oceanic floating vortices. This suggestion is here quantitatively addressed using idealized, axisymmetric, numerical simulations of a simple Gaussian-like vortex in thermal wind balance, floating in a rotating, stratified flow.

[Phys. Rev. Fluids 6, 093801] Published Tue Sep 07, 2021

### Surfactant-driven instability of a divergent flow

Author(s): G. Koleski, J.-C. Loudet, A. Vilquin, B. Pouligny, and T. Bickel

The flow of a submerged water jet directed toward the liquid interface is investigated both experimentally and theoretically. We find evidence that the presence of a small amount of surfactants can trigger an azimuthal instability. Our theoretical model reveals that surfactant advection in the Stokes regime contains the minimal ingredients to explain the instability.

[Phys. Rev. Fluids 6, 094001] Published Tue Sep 07, 2021

### Diffusive and capillary instabilities of viscous fluid threads in microchannels

Author(s): Thomas Cubaud, Bryan Conry, Xiaoyi Hu, and Thai Dinh

We experimentally investigate the flow behavior of viscous oil threads in a a variety of miscible and immiscible low-molecular weight alcohols in microchannels. A comparative study is conducted between diffusive and capillary regimes using simple functional relationships for the thread characteristics, including diameter and detachment length. We develop a comprehensive classification of immiscible and miscible fluid dynamics in square microfluidic channels and provide a quantitative analysis of the evolution of multiphase flow properties across flow patterns.

[Phys. Rev. Fluids 6, 094202] Published Tue Sep 07, 2021

### Onset of grain motion in eroding subaqueous bimodal granular beds

Author(s): Marios Galanis, Philip Wang, Mark D. Shattuck, Corey S. O'Hern, and Nicholas T. Ouellette

The effect of grain size on the critical shear stress required to initiate sediment transport in erodible granular beds is typically described by the Shields number which compares the hydrodynamic stress to the particle weight. Although this framework works well for beds composed of grains of the same size, we find that it does not capture the behavior of polydisperse beds. In particular, we find that larger grains are mobilized by nominally subcritical stresses when small grains are present. Our results highlight the importance of granular contact and force networks in controlling the onset of sediment transport.

[Phys. Rev. Fluids 6, 094301] Published Tue Sep 07, 2021

### Promoting global stability in data-driven models of quadratic nonlinear dynamics

Author(s): Alan A. Kaptanoglu, Jared L. Callaham, Aleksandr Aravkin, Christopher J. Hansen, and Steven L. Brunton

Modeling realistic fluid and plasma flows is computationally intensive, motivating the use of reduced-order models for a variety of scientific and engineering tasks. However, it is challenging to characterize, much less guarantee, the global stability (i.e., long-time boundedness) of these models. In this work, we illustrate how to modify the objective function in machine learning algorithms to promote globally stable data-driven models of fluid and plasma flows. This innovation significantly extends the applicability of sparse system identification for complex dynamics, such as models of turbulent boundary layers.

[Phys. Rev. Fluids 6, 094401] Published Tue Sep 07, 2021

### Taylor dispersion of elongated rods

Author(s): Ajay Harishankar Kumar, Stuart J. Thomson, Thomas R. Powers, and Daniel M. Harris

In many complex fluids, the geometry of particles in suspension can be complex, prompting the need to understand how shape influences their bulk transport. We consider the Taylor dispersion of passive, elongated Brownian rods subject to a background Poiseuille flow. Monte-Carlo simulations demonstrate that elongated particles exhibit enhanced longitudinal dispersion compared to their spherical counterparts, in excellent agreement with integral expressions derived from asymptotic analysis. For particles of high aspect-ratio, the dispersion coefficient can be collapsed along a single curve, providing a simple correction factor that extends Taylor’s seminal results to elongated particles.

[Phys. Rev. Fluids 6, 094501] Published Tue Sep 07, 2021

### Nonlinear shallow water dynamics with odd viscosity

Author(s): Gustavo M. Monteiro and Sriram Ganeshan

The concept of an “odd” coefficient of viscosity appears in some fluid mechanical contexts, including quantum fluids, electron fluids in mesoscopic systems, as well as some classical systems. Here we study the shallow depth limit of weakly nonlinear surface dynamics with odd viscosity and gravitational effects and obtain an integrable Kortweg-de Vries equation, the solution of which admits right- and left-moving disturbances with some differences. The odd viscosity term plays a role similar to surface tension.

[Phys. Rev. Fluids 6, L092401] Published Tue Sep 07, 2021

### Elastic-plastic Rayleigh-Taylor instability at a cylindrical interface

Author(s): A. R. Piriz, S. A. Piriz, and N. A. Tahir

The boundaries of stability are determined for the Rayleigh-Taylor instability at a cylindrical interface between an ideal fluid in the interior and a heavier elastic-plastic solid in the outer region. The stability maps are given in terms of the maximum dimensionless initial amplitude ξth* that can...

[Phys. Rev. E 104, 035102] Published Tue Sep 07, 2021

### Statistical properties of two-dimensional elastic turbulence

Author(s): Himani Garg, Enrico Calzavarini, and Stefano Berti

We numerically investigate the spatial and temporal statistical properties of a dilute polymer solution in the elastic turbulence regime, i.e., in the chaotic flow state occurring at vanishing Reynolds and high Weissenberg numbers. We aim at elucidating the relations between measurements of flow pro...

[Phys. Rev. E 104, 035103] Published Tue Sep 07, 2021

### Black tea interfacial rheology and calcium carbonate

An interfacial phenomenon can be observed in the kitchen in a cup of black tea. When tea is left to cool after steeping, a thin film at the air–water interface can form. In certain conditions, this film is observable by naked eye and, when disturbed, cracks visibly like sea ice. The mechanical properties of this interfacial film are assessed using bicone interfacial rheometry. Water hardness, acidity, the presence of sugar or milk, tea concentration, and brewing temperature all affect the formation of this film. Interfaces formed in hard water (200 mg CaCO3/L) exhibit increased elastic modulus vs those in moderately hard water (100 mg CaCO3/L), soft water (50 mg CaCO3/L), and Milli-Q water. All films formed in chemically hardened water exhibit yielding point behavior in the interfacial oscillatory shear. Film physical thickness shows no correlation with measured physical strength. Conditions forming the strongest film, chemically hardened water, may be industrially useful in packaged tea beverages for preferable shelf stability and for emulsion stabilization of milk tea products. Conditions forming weakened films, addition of citric acid, may be useful for dried tea mixes. In lab conditions, the film visibility is obscured due to purity of tea ingredients and careful washing. However, the film physically forms and can still be measured through interfacial rheometry.

### Visualization of the interaction of water aerosol and nanofiber mesh

Face masks play a critical role in reducing the transmission risk of COVID-19 and other respiratory diseases. Masks made with nanofibers have drawn increasingly more attention because of their higher filtration efficiency, better comfort, and lower pressure drop. However, the interactions and consequences of the nanofibers and microwater droplets remain unclear. In this work, the evolution of fibers made of polymers with different contact angles, diameters, and mesh sizes under water aerosol exposure is systematically visualized. The images show that capillarity is very strong compared with the elasticity of the nanofiber. The nanofibers coalesce irreversibly during the droplet capture stage as well as the subsequent liquid evaporation stage. The fiber coalescence significantly reduces the effective fiber length for capturing aerosols. The nanofiber mesh that undergoes multiple droplet capture/evaporation cycles exhibits a fiber coalescing fraction of 40%–58%. The hydrophobic and orthogonally woven fibers can reduce the capillary forces and decrease the fiber coalescing fraction. This finding is expected to assist the proper design, fabrication, and use of face masks with nanofibers. It also provides direct visual evidence on the necessity to replace face masks frequently, especially in cold environments.

### A direct numerical simulation study of flow modulation and turbulent sedimentation in particle-laden downward channel flows

Fully resolved direct numerical simulations of turbulent downward channel flow laden with finite-size spherical particles are performed using the lattice Boltzmann method. Unlike upward particle-laden channel flows, the potential energy of settling particles serves as the driving force in the downward channel flows. Furthermore, the particles have an overall positive slip velocity at the center which causes the lateral hydrodynamic force to drive particles away from the center region. Both changes in the flow driving mechanism and the particle distribution affect the details of turbulence modulation in the downward channel, when compared to the upward channel flow. In this study, we focus on the effect of different particle terminal velocities, i.e., different particle settling Reynolds numbers, on the turbulent modulation of particle-laden downward channel flows. Indeed, the simulation results for downward channel flow show larger local particle concentration in the near-wall region, relative to the upward channel. It is also found that the level of particle near-wall accumulation increases with the particle terminal velocity. Opposite to the upward channel flows, the fluid-phase mean velocity in the downward channel flows is increased by heavy particles in the channel center, but reduced in the buffer layer. The reduction of mean velocity in the buffer layer is caused by the particle accumulation in low-speed streak regions. For the largest particle settling Reynolds number case (ReT = 30) investigated, strong accumulation of particles in the buffer layer interrupts the near-wall turbulence structures and thus leads to the reductions of fluid turbulence intensity and Reynolds stress.

### A direct numerical simulation study of flow modulation and turbulent sedimentation in particle-laden downward channel flows

Fully resolved direct numerical simulations of turbulent downward channel flow laden with finite-size spherical particles are performed using the lattice Boltzmann method. Unlike upward particle-laden channel flows, the potential energy of settling particles serves as the driving force in the downward channel flows. Furthermore, the particles have an overall positive slip velocity at the center which causes the lateral hydrodynamic force to drive particles away from the center region. Both changes in the flow driving mechanism and the particle distribution affect the details of turbulence modulation in the downward channel, when compared to the upward channel flow. In this study, we focus on the effect of different particle terminal velocities, i.e., different particle settling Reynolds numbers, on the turbulent modulation of particle-laden downward channel flows. Indeed, the simulation results for downward channel flow show larger local particle concentration in the near-wall region, relative to the upward channel. It is also found that the level of particle near-wall accumulation increases with the particle terminal velocity. Opposite to the upward channel flows, the fluid-phase mean velocity in the downward channel flows is increased by heavy particles in the channel center, but reduced in the buffer layer. The reduction of mean velocity in the buffer layer is caused by the particle accumulation in low-speed streak regions. For the largest particle settling Reynolds number case (ReT = 30) investigated, strong accumulation of particles in the buffer layer interrupts the near-wall turbulence structures and thus leads to the reductions of fluid turbulence intensity and Reynolds stress.

### Turbulent flow characteristics over an abrupt step change in bed roughness

Turbulent flow characteristics over an abrupt step change in bed roughness from smooth to rough are studied measuring the flow field by a Particle Image Velocimetry (PIV) system. The smooth and rough beds are referred to as the upstream and downstream beds, respectively. The velocity color maps and profiles show that an abrupt step change in bed roughness causes flow retardation in the downstream bed owing to the combined effects of roughness-induced and separated flows. The results of the Reynolds stresses reveal that the profiles in the downstream bed exhibit discriminable bulges, whose size increases with an increase in the streamwise distance. The stress color maps illustrate the creation of a roughness-induced layer that grows over the downstream bed as the streamwise distance increases. The bed shear stress evidences an overshooting behavior immediate downstream of the abrupt step change in bed roughness to reach its peak magnitude. The third-order correlations indicate that the effects of the abrupt step change in bed roughness produce an inrush of rapidly moving fluid streaks in the near-bed flow and arrival of slowly moving fluid streaks in the away-bed flow. Regarding the turbulent kinetic energy (TKE) budget, the enhanced magnitudes of the TKE budget terms within the roughness-induced layer are prevalent. The TKE dissipation rate lags the production rate, and the negative TKE diffusion rate implies an addition in the TKE production. Bursting analysis endorses that the sweeps govern the near-bed flow on the downstream bed and the ejections prevail far from the bed.

### Turbulent flow characteristics over an abrupt step change in bed roughness

Turbulent flow characteristics over an abrupt step change in bed roughness from smooth to rough are studied measuring the flow field by a Particle Image Velocimetry (PIV) system. The smooth and rough beds are referred to as the upstream and downstream beds, respectively. The velocity color maps and profiles show that an abrupt step change in bed roughness causes flow retardation in the downstream bed owing to the combined effects of roughness-induced and separated flows. The results of the Reynolds stresses reveal that the profiles in the downstream bed exhibit discriminable bulges, whose size increases with an increase in the streamwise distance. The stress color maps illustrate the creation of a roughness-induced layer that grows over the downstream bed as the streamwise distance increases. The bed shear stress evidences an overshooting behavior immediate downstream of the abrupt step change in bed roughness to reach its peak magnitude. The third-order correlations indicate that the effects of the abrupt step change in bed roughness produce an inrush of rapidly moving fluid streaks in the near-bed flow and arrival of slowly moving fluid streaks in the away-bed flow. Regarding the turbulent kinetic energy (TKE) budget, the enhanced magnitudes of the TKE budget terms within the roughness-induced layer are prevalent. The TKE dissipation rate lags the production rate, and the negative TKE diffusion rate implies an addition in the TKE production. Bursting analysis endorses that the sweeps govern the near-bed flow on the downstream bed and the ejections prevail far from the bed.

### Dynamics of a single free-settling spherical particle driven by a laser-induced bubble near a rigid boundary

Author(s): Shengji Wu, Bo Li, Zhigang Zuo, and Shuhong Liu

We systematically investigate the dynamics of a free-settling particle driven by a laser-induced bubble near a rigid boundary. Two types of particle-bubble interaction are identified, in terms of the intensity of the influence of the boundary on the particle-bubble dynamics. Two important phenomena where the particle ends up impacting on the boundary at a relatively high velocity are discovered, which provide a potential mechanism for enhanced cavitation erosion in sand-laden water.

[Phys. Rev. Fluids 6, 093602] Published Fri Sep 03, 2021

### Splash of impacting nanodroplets on solid surfaces

Author(s): Yi-Bo Wang, Yi-Feng Wang, Xin Wang, Ben-Xi Zhang, Yan-Ru Yang, Duu-Jong Lee, Xiao-Dong Wang, and Min Chen

Using molecular dynamics simulations we study the splash of water nanodroplets (ND) on hydrophilic to hydrophobic surfaces. Mechanisms for internal breakup and prompt splash are found to be different from those of macroscale (MS) impacting droplets. Breakup is attributed to initial air holes on solid surfaces for MS, but to vibration of a nanometer spreading film for ND. The prompt splash is initiated by air bubbles under spreading lamella at MS, but for ND by Rayleigh-Taylor instability of ejected rims from rapidly decelerated spreading lamella. ND internal breakup depends on surface wettability because vibration attenuation is larger on hydrophilic than hydrophobic surfaces.

[Phys. Rev. Fluids 6, 094201] Published Fri Sep 03, 2021