# Latest papers in fluid mechanics

### Analysis of free surface oscillations of a droplet due to ultrasonic wave impingement

An analytical approach based on the linear potential theory is employed to enlighten the fundamental physics of atomization of droplets with an impinging sound wave, with a particular application in surface acoustic wave (SAW) atomization. When a plane sound wave, originated from the gas or the liquid side (resembling SAW), impinges on a liquid droplet, capillary waves are generated. It is shown that, for both cases, spatial phase-locking between the sound spherical modes and the free surface oscillations occurs. Hence, capillary waves will have the same spatial modes of the sound wave. The frequency spectrum analysis shows that the phase-locking causes two types of waves: the natural capillary waves with a wide range of frequencies, two to five orders of magnitude smaller than the impinging sound wave, and the forced wave, with a frequency equal to that of the sound wave. Since the instability of these surface waves leads to separation of droplets from the surface and the size of these droplets is correlated with the wavelength of the surface waves, this well explains the previous observations that droplets with a wide range of sizes are generated in the SAW experiments. Finally, a correlation is also proposed for predicting the atomized droplet size, which gives the size order for the generated droplets in SAW with good accuracy. The correlation could also suggest the possible size for remote atomization of the droplets by sound wave propagated in gas.

### Cross-stream migration of droplets in a confined shear-thinning viscoelastic flow: Role of shear-thinning induced lift

Shear-thinning viscoelastic (STVE) flows exhibit intriguing phenomena owing to their complex rheology and the coupling of various forces involved. Here, we present an understanding of the cross-stream migration of droplets in a confined STVE flow and unravel the role of a shear-thinning induced lift force (FSM) in their dynamical behavior. We perform experiments with popular STVE liquids of different molecular weights and concentrations (c) for Reynolds numbers Re < 1 and Weissenberg numbers Wi = 0.01–7.4. Our results reveal larger droplets (of drop-to-channel ratio β ≥ 0.28) that follow their original streamlines, whereas smaller droplets (β ≤ 0.2) exhibit center ward migration and the migration rates depend upon the drop-to-medium viscosity (k) and elasticity (ξ) ratios. The lateral displacement of droplets is tracked using high-speed imaging that is used to estimate the relevant forces using suitable correlations. We find that the migration dynamics of droplets is underpinned by the non-inertial lift (FNIL), viscoelastic lift (FVM, FVD), and shear-thinning induced lift (FSM) forces. We provide experimental evidence of the proposed FSM and, from analytical scaling and empirical modeling, develop an expression for FSM ∼ [math] (with R2 = 0.95) for an object at a distance h from the wall and with a drop in viscosity Δμ and strain rate [math] across its diameter D. Our study sheds light on the underlying dynamics on droplets in an STVE medium and opens up avenues for sorting and focusing of drops in an STVE medium at low Re.

### Two-phase flow boiling in a microfluidic channel at high mass flux

We report the experimental investigations of two-phase flow boiling heat transfer characteristics of a refrigerant in a microfluidic channel at a high mass flux (more than 1000 kg/m2 s). We investigate the heat transfer coefficients at a heat flux range of 7.63 kW/m2–49.46 kW/m2, mass flux range of 600 kg/m2 s–1400 kg/m2 s (high mass flux), and saturation temperature range of 23 °C–31 °C. We propose the new two-phase flow boiling heat transfer correlation of a refrigerant, which is used as the working fluid for the present experiments, at the microfluidic scale. We experimentally establish the functional relationship of two-phase flow boiling heat transfer correlation of the refrigerant during flow boiling in a rectangular microchannel with the Reynolds number, the boiling number, and the Weber number. We believe that the inferences of this study may provide a design basis for the micro-heat exchanger, typically used for thermal management in electronic devices, micro-electro-mechanical systems, and electric vehicle battery cooling system.

### Anomalous features in internal cylinder flow instabilities subject to uncertain rotational effects

We study the flow dynamics inside a high-speed rotating cylinder after introducing strong symmetry-breaking disturbance factors at cylinder wall motion. We propose and formulate a mathematically robust stochastic model for the rotational motion of the cylinder wall alongside the stochastic representation of incompressible Navier–Stokes equations. We employ a comprehensive stochastic computational fluid dynamics framework combining the spectral/hp element method and the probabilistic collocation method to obtain high-fidelity realizations of our mathematical model in order to quantify the propagation of parametric uncertainty for dynamics-representative quantities of interests. We observe that the modeled symmetry-breaking disturbances cause a flow instability arising from the wall. Utilizing global sensitivity analysis approaches, we identify the dominant source of uncertainty in our proposed model. We next perform a qualitative and quantitative statistical analysis on the fluctuating fields characterizing the fingerprints and measures of intense and rapidly evolving non-Gaussian behavior through space and time. We claim that such non-Gaussian statistics essentially emerge and evolve due to an intensified presence of coherent vortical motions initially triggered by the flow instability due to the symmetry-breaking rotation of the cylinder. We show that this mechanism causes memory effects in the flow dynamics in a way that noticeable anomaly in the time-scaling of enstrophy record is observed in the long run apart from the onset of instability. Our findings suggest an effective strategy to exploit controlled flow instabilities in order to enhance the turbulent mixing in engineering applications.

### Instability of natural convection of air in a laterally heated cube with perfectly insulated horizontal boundaries and perfectly conducting spanwise boundaries

Author(s): Alexander Yu. Gelfgat

Primary and secondary instabilities of buoyancy convection in a laterally heated cube with perfectly thermally insulated horizontal boundaries and perfectly thermally conducting spanwise boundaries are studied. It is revealed that en route to unsteadiness, the flow undergoes a steady symmetry-breaking pitchfork bifurcation. With a further increase of the Grashof number, the nonsymmetric flow bifurcates into an oscillatory state via a Hopf bifurcation.

[Phys. Rev. Fluids 5, 093901] Published Thu Sep 17, 2020

### Yield stress fluid behavior of foam in porous media

Author(s): Alexis Mauray, Max Chabert, and Hugues Bodiguel

Flow of foams is studied in a model porous medium, in a large range of capillary numbers, Ca, and relative gas flow rates, fg. Pressure measurements show that the effective viscosity is a decreasing power-law function of Ca, with the exponent ranging from −1 to −0.75. Direct observation reveals that the flow is heterogeneous and the fraction of preferential paths increases with both fg and Ca. In a straight channel of varying cross section, a bubble train behaves as a shear-thinning yield stress fluid, accounting quantitatively for the effective viscosity in the micromodel.

[Phys. Rev. Fluids 5, 094004] Published Thu Sep 17, 2020

### Drag enhancement in a dusty Kolmogorov flow

Author(s): A. Sozza, M. Cencini, S. Musacchio, and G. Boffetta

Particles suspended in a fluid exert feedback forces that can significantly impact the flow by altering turbulent drag. Flow modulation induced by small spherical heavy particles is studied by means of numerical simulations of an Eulerian two-way coupling model. The amplitude of the mean flow and the turbulence intensity are found to be reduced by increasing particle mass loading and fluid friction is enhanced. Surprisingly, these effects are stronger for particles of smaller inertia.

[Phys. Rev. Fluids 5, 094302] Published Thu Sep 17, 2020

### Correlation between linear and nonlinear material functions under large amplitude oscillatory shear

Fourier transform rheology is the most frequently used method to interpret the nonlinear rheological behavior of complex fluids under large amplitude oscillatory shear (LAOS). However, the unclear relationship between the higher harmonics and the fundamental harmonic obscures the physical meaning of the nonlinear functions. Here, we hypothesize that all the nonlinear oscillatory shear functions and normal stress functions can be expressed as linear combinations of linear viscoelastic functions or their derivatives at different frequencies under both strain-controlled LAOS (LAOStrain) and stress-controlled LAOS (LAOStress). We check this hypothesis using the time-strain separable Wagner model, Giesekus model, and modified Leonov model. We find such correlations between the nonlinear material functions and the linear material functions are intrinsic for viscoelastic liquids under LAOStrain, and for viscoelastic solids under LAOStress. Finally, these correlations are justified by a viscoelastic standard polydimethylsiloxane, an ethylene–octene multiblock copolymer melt, and a typical simple yield stress material (0.25 wt. % Carbopol).

### On determining the power-law fluid friction factor in a partially porous channel using the lattice Boltzmann method

In the present work, the power-law fluid flow in a channel partially filled with a porous medium is numerically investigated using the lattice Boltzmann method (LBM). The porous domain, placed in the lower half of the channel, is represented according to a heterogeneous approach by a matrix of solid square disconnected blocks. The apparent viscosity of the power-law fluid is computed by locally varying the LBM relaxation factor. The results show the influence of geometry (porosity, number of obstacles, and hydraulic diameter), inertia (Reynolds number), and fluid properties (power-law index) over the partially porous-to-impermeable channel friction factor ratio. In general, the higher the porosity and the lower the number of obstacles, Reynolds number, and power-law index, the lower the friction factor. Finally, a correlation for the friction factor ratio as a function of the free region hydraulic diameter, permeability, and power-law index is presented for a specific channel configuration.

### Validation of finite element analysis strategy to investigate acoustic levitation in a two-axis acoustic levitator

A two-axis acoustic levitator can be used to generate a standing pressure wave capable of levitating solid and liquid particles at appropriate input conditions. This work proposes a simulation framework to investigate the two-axis levitation particle stability using a commercial, computational fluid dynamics software based on the harmonic solution to the acoustic wave equation. The simulation produced predictions of the standing wave that include a strong “+” shaped pattern of nodes and anti-nodes that are aligned with the levitator axes. To verify the simulation, a levitator was built and used to generate the standing wave. The field was probed with a microphone and a motorized-scanning system. After scaling the simulated pressure to the measured pressure, the magnitudes of the sound pressure level at corresponding high-pressure locations were different by no more than 5%. This is the first time a measurement of a two-axis levitator standing pressure wave has been presented and shown to verify simulations. As an additional verification, the authors consulted high speed camera measurements of a reference-levitator transducer, which was found to have a maximum peak-to-peak displacement of 50 ± 5 μm. The reference-levitator is known to levitate water at 160 dB. The system for this work was simulated to match the operation of the reference-levitator so that it produced sound pressure levels of 160 dB. This pressure was achieved when the transducer maximum peak-to-peak displacement was 50.8 µm. The agreement between the two levitators’ displacements provides good justification that the modeling approach presented here produces reliable results.

### Comprehensive study of monatomic fluid flow through elliptical carbon nanotubes

To achieve a realistic model of a carbon nanotube (CNT) membrane, a good understanding of the effects associated with CNT deformations is a key issue. In this study, using molecular dynamics simulation, argon flow through elliptical CNTs is studied. Two armchair CNTs (6, 6) and (10, 10) were considered. The results demonstrated non-uniform dependency of the flow rate to eccentricity of the tube, leading to an unexpectedly increased flow rate in some cases. The effects of tube size, temperature, and pressure gradient are investigated, and longitudinal variations of the interatomic potential and average axial velocity in different segments of the cross section are presented to justify the abnormal behavior of the flow rate with eccentricity. The results showed a significant deviation from the macroscale expectations and approved elliptical deformation as a non-negligible change in the overall flow rate, which should be considered in predictive models of CNT membranes.

### Dynamics of large-scale circulation and energy transfer mechanism in turbulent Rayleigh–Bénard convection in a cubic cell

We present the characteristics and dynamics of large-scale circulation (LSC) in turbulent Rayleigh–Bénard convection (RBC) inside a cubic cell. The simulations are carried out for a Rayleigh number range of 2 × 106 ≤ Ra ≤ 109 and using air (at Prandtl number Pr = 0.7) as the working fluid. Using the Fourier mode analysis, the strength, orientation, and associated dynamics of LSC are characterized. Following previous two-dimensional studies in RBC, we propose a mechanism of flow reversals based on the dynamics of corner vortices, which is less attempted in three-dimensional counterparts. We observe that the plane containing LSC is generally aligned along one of the diagonals of the box accompanied by a four-roll structure in the other. In addition to the primary roll, two secondary corner-roll structures are also observed in the LSC plane, which grow in size and destabilize the LSC, resulting in partial (ΔΦ1 ≈ π/2) and complete (ΔΦ1 ≈ π) reversals. In addition to previously reported rotation-led reorientations, we also observe cessation events that are rare in cubic cells. We observe that as the Rayleigh number is increased from Ra = 2 × 106 to 107, the number of reorientations reduces by one third. With an increase in Ra, the strength of LSC (SLSC) increases and the corner rolls reduce in size, which leads to the reduction in the occurrence of reorientations. At higher Rayleigh numbers (Ra > 108), the strength saturates around SLSC ≈ 0.75. To connect the dynamics between different coherent structures, we evaluate the turbulent kinetic energy (TKE) budget. Notably, our novel approach to study the variation of TKE along the azimuthal direction helps in identifying the dynamical coupling between the LSC and non-LSC planes. The analysis suggests that TKE is generally produced in localized regions in both the planes, while its dissipation mainly happens in the vicinity of the plane that contains LSC. The transport mechanism redistributes the energy between these planes and thus sustains the LSC and other coherent structures.

### A comparative turbulent flow study of unconfined orthogonal and oblique slot impinging jet using large-eddy simulation

The incompressible turbulent flow field of the slot impinging jet has been studied numerically at a Reynolds number of 7900 and d = 6w using large-eddy simulation with the wall adapting local eddy-viscosity subgrid-scale model for the angles of impingement 70° and 90°. The validity of the computation is confirmed by reasonable comparisons of the wall shear stress, pressure variation over the impingement plate, jet-centerline velocity, and second-order turbulent properties with past experimental and numerical results. The turbulent stress, turbulent length scales, and turbulent structure sizes are observed to be increased in the oblique impingement. The appearance of the oblate spheroid-shaped, three-dimensional isotropic, and prolate spheroid-shaped turbulence has been marked in the wall-jet region using the anisotropy invariant map. The power spectra of the fluctuating field maintain the −5/3 slope in the inertial subrange, which as expected becomes steeper in the dissipation range, as stated by Kolmogorov. Both positively skewed and negatively skewed fluctuations are seen in the flow field, and their probability density functions suggest that the fluctuation range increases in the case of oblique impingement. The involvement of various shearing and swirling structures has been investigated employing the proper orthogonal decomposition, the Q- function, and the λ2- function, where the isosurface of vorticity components is used to represent the direction of rotations.

### Molecular transportation phenomena of simple liquids through a nanoporous graphene membrane

Author(s): Mohammad Rashedul Hasan and BoHung Kim

The mechanism of pressure-driven transport of simple liquid through a nanoporous graphene membrane has been analyzed using nonequilibrium molecular dynamics simulation. In this study, we investigate liquid dynamics properties such as local density, pressure variation, and local viscosity depending o...

[Phys. Rev. E 102, 033110] Published Tue Sep 15, 2020

### Time-averaged transport in oscillatory squeeze flow of a viscoelastic fluid

Author(s): Rui Yang, Ivan C. Christov, Ian M. Griffiths, and Guy Z. Ramon

An investigation of the Taylor–Aris dispersion in an oscillatory axisymmetric squeeze flow, driven periodically by the motion of one of the confining, parallel planes is presented. Using the method of multiple timescale homogenization, the mass-heat balance equation in this flow is reduced to a one-dimensional equation, indicating three effective mechanisms: diffusion, advection, and reaction. The results show that the transport in the oscillatory squeeze flow can be either enhanced or diminished, depending on the interplay of these three effective (homogenized) mechanisms.

[Phys. Rev. Fluids 5, 094501] Published Tue Sep 15, 2020

### Dynamics of bacterial deposition in evaporating drops

Evaporation of drops almost always deposits their suspended particles at the drop edge. The dynamics of this process and the resulting patterns depend upon various parameters related to the liquid, substrate, and particles. An interesting scenario is interactions among the particles leading to inhomogeneous depositions characterized by distinct edge-growth dynamics. Here, we study a more complex system with bacteria inside the evaporating drop. Bacteria interact like sticky particles forming inhomogeneous clusters, however, with edge-growth dynamics as that of non-interacting particles. We hypothesis that this contradicting behavior is due to the increased randomness introduced by bacteria–substrate interactions. Our findings have importance in understanding the patterns and their formation in growth systems of soft matter.

### Coupled radiative and convective heat transfer in enclosures: Effect of inner heater–enclosure wall emissivity contrast

The problem of thermal radiation in the presence of nonuniform emissivity arising through different types surfaces involved in thermal-control systems is addressed. In particular, its effect on natural convection driven by an inner hot plate kept inside a square enclosure is studied. The enclosure considered is either horizontally or vertically cooled, and two different primary orientations of the inner hot plate are considered. The corresponding governing partial differential equations were solved by the finite volume method on a uniform and regular grid system. While doing so, the net radiation method was used to determine the radiative surface fluxes. The effect of two opposing emissivity contrasts between the inner hot plate and enclosure walls is studied for the Rayleigh numbers Ra ≤ 107. The flow and heat transfer mechanisms at the resulting steady state are discussed via isotherms, streamlines, and average Nusselt number [math]. The findings arrived out of this comprehensive study shows that prominent heat transfer enhancement occurs when the emissivity of the inner hot plate is higher. Significant changes introduced by the emissivity contrast in the velocity and temperature fields can be seen for higher Rayleigh numbers. Moreover, better heat removal through the combined radiation and convection mechanism is observed invariably for the vertical hot plate in the presence of emissivity contrast. It is found that the heat transfer can be augmented up to around 35% through a good knowledge of the emissivity contrast.

### Statistical analysis of deformation of a shock wave propagating in a local turbulent region

Direct numerical simulation is performed for analyzing the interaction between a normal shock wave and turbulence. The shock wave is initially located in a quiescent fluid and propagates into a local turbulent region. This flow setup allows investigation of the initial transition and statistically steady stages of the interaction. Shock deformation is quantified using the local shock wave position. The root-mean-square (rms) fluctuation in the shock wave position increases during the initial stage of the interaction, for which the time interval divided by the integral time scale increases with [math], where Mt is a turbulent Mach number and Ms is a shock Mach number. In late time, the rms fluctuation in the shock wave position hardly depends on the propagation time and follows a power law, [math], whose exponent is similar to the power law exponent of the rms pressure-jump fluctuation reported in experimental studies. Fluctuations in the shock wave position have a Gaussian probability density function. The spectral analysis confirms that the length scale that characterizes shock wave deformation is the integral length scale of turbulence. The fluctuating shock wave position is correlated with dilatation of the shock wave, where the correlation coefficient increases with Mt/(Ms − 1). In addition, the shock wave that deforms backward tends to be stronger than average and vice versa. Mean pressure jumps across the shock wave are different between areas with forward and backward deformations. This difference increases with the rms fluctuation in the shock wave position and is well-represented as a function of [math].

### The effect of the geometric features of the turbulent/non-turbulent interface on the entrainment of a passive scalar into a jet

We consider the scalar concentration field in the proximity of the turbulent/non-turbulent interface (TNTI) of a round momentum-driven turbulent jet at Re = 10 600. Orthogonal cross sections of the jet are taken at 50 nozzle diameters from the nozzle exit using planar laser-induced fluorescence. The conditional scalar concentration is evaluated along the interface-normal direction, identifying the thickness of the TNTI region as 0.64λ (where λ is the Taylor microscale). Conditioning the scalar concentration within the TNTI revealed higher values of the passive scalar in the vicinity of the boundary elements shaped by large vorticity structures, i.e., isosurface points with low curvature (flat regions), small interface angle, and large radial distance from the jet centerline. In contrast, small vorticity structures near the boundary manifesting with high interface curvature, high interface angle, and small radial distance are associated with lower concentration values. Using the current experimental resolution, we find that high concentrations near the far boundary points persist up to a distance of 0.40λ–0.48λ into the TNTI region, after which boundary points closer to the jet centerline exhibit larger concentration values along the interface-normal direction, similar to the fully turbulent region. The cross correlation analysis showed that in regions characterized by low streamwise momentum, there are positive, albeit small, scalar correlations between the non-turbulent and the TNTI regions. The latter may imply local detrainment of the fluid particles containing the scalar at far radial positions.

### Influence of cell interaction forces on growth of bacterial biofilms

A hybrid computational method was proposed for simulation of biofilm growth processes using a continuum model for transport of water and extracellular polymeric substance (EPS) and a discrete model for simulation of bacterial cells. The current paper focuses on development of accurate models for different forces acting between bacterial cells, which are represented by spherocylinder particles. The major forces acting on the bacterial cells include drag from flow of EPS generated by the bacterial colony, adhesion forces (e.g., van der Waals adhesion and ligand–receptor binding) between colliding cell surfaces, lubrication force due to cell growth and EPS production, and tension from the fimbria appendages that project outward from many types of bacterial cells. The lubrication force and drag force act to separate the cells and expand the bacterial colony, whereas the adhesion and fimbria forces act to pull the bacterial colony together. Simulations are performed to examine the effect on biofilm development of each of these forces individually. The significance of different forces depends on the cell shape and other specifics of the given computation. However, there appears to be an opposing influence at the scale of the bacterial colony between the outward-oriented EPS drag on cells and the inward-oriented fimbria force. These two forces were particularly found to be important for determining the degree of orientation alignment of the cells. On the smaller scale of individual cells, the actions of the cell surface adhesion force and the lubrication force similarly oppose each other, with the balance influencing cell clustering and the degree of contact.