# Latest papers in fluid mechanics

### Dynamics of a buoyant pulsating bubble near two crossed walls

The dynamics of a buoyant pulsating bubble near two crossed perpendicular rigid boundaries (a horizontal and a vertical wall) are studied using the boundary element method combined with the method of mirror images. The Kelvin impulse and the elastic mesh velocity method are used to calculate the direction and volume of the liquid jet generated during bubble collapse. The numerical results show good agreement with experiments. An increase in buoyancy causes a local high-pressure zone at the root of the jet to move toward the bottom of the bubble, causing the jet to rotate upward toward the vertical wall. At a certain position, with the change in buoyancy, the dimensionless bubble volume at the instant of jet impact reaches a minimum when the jet direction is horizontal, with a peak in the dimensionless jet velocity occurring. A comprehensive parametric study of jet characteristics, including jet direction, velocity, and relative volume (the volume ratio of the jet to the bubble at the instant of jet impact), is carried out in terms of buoyancy and the standoff distances to the two walls. The Blake criterion can be used to judge whether a bubble jet is pointing obliquely upward or downward, provided that it deviates significantly from the horizontal direction. Depending on the buoyancy, the jet characteristics at different standoff distances are found to exhibit three distinct patterns of behavior. Finally, we discuss the changes in the jet velocity and relative volume as the buoyancy is varied.

### Slippery surfaces: A decade of progress

Slippery surfaces have received great attention for more than a quarter-century. In particular, during the last decade, interest has increased exponentially, resulting in thousands of articles concerning three types of slippery surfaces: superhydrophobic, superoleophobic, and omniphobic. This review focuses on recent developments and significant findings in naturally inspired slippery surfaces. Superhydrophobicity can be characterized by water droplets beading on a surface at significantly high static contact angles and low contact-angle hystereses. Microscopically rough hydrophobic surfaces could entrap air in their pores, resulting in a portion of a submerged surface with an air–water interface, which is responsible for the slip effect and drag reduction. Suberhydrophobicity enhances the mobility of droplets on lotus leaves for self-cleaning purposes, the so-called lotus effect. Surface hydrophobicity can be advanced to repel low-surface-tension liquids, i.e., become superoleophobic. Another kind of slippery coating is the slippery liquid-infused porous surfaces (SLIPS), which are omniphobic coatings. Certain plants such as the carnivorous Nepenthes pitcher inspired SLIPS. Their interior surfaces have microstructural roughness, which can lock in place an infused lubricating liquid. The lubricant is then utilized as a repellent surface for other liquids or substances such as water, blood, crude oil, ice, insects, and bio-fouling. In this review, we discuss different slippery mechanisms in nature. We also cover recent advances in manufacturing, texturing, and controlling slippery surface at the micro- and nanoscales. We further discuss the performance, sustainability, and longevity of such surfaces under different environmental conditions. Very-recent techniques used to characterize the surfaces are also detailed.

### Flow near porous media boundaries including inertia and slip: A one-domain approach

This work addresses the macroscopic modeling of flow near porous media boundaries. This includes the vicinity with a fluid channel (i.e., a fracture), another rigid porous medium, or an impervious non-deformable solid. The analysis is carried out for one-phase, steady, incompressible, inertial, and isothermal flow of a Newtonian fluid, considering slip effects at the solid–fluid interfaces. A one-domain approach is proposed, employing a simplified version of the volume averaging method, while conceiving the system as two homogeneous regions separated by an inter-region. The upscaling procedure yields a closed macroscopic model including a divergence-free average (filtration) velocity for the mass balance equation and a unique momentum equation having a Darcy structure. The latter involves apparent permeability tensors that are constant in the homogeneous regions and position-dependent in the inter-region. All the permeability tensors are determined from the solution of coupled closure problems that are part of the developments. The derived model is validated by comparisons with direct numerical simulations in several two-dimensional configurations, namely, two porous media of contrasted properties in direct contact or separated by a fracture, the boundaries being either flat or wavy and a porous medium in contact with a flat or corrugated solid wall or separated from the latter by a fluid layer. The simplicity and versatility of the derived model make it an interesting alternative to existing one- and two-domain approaches developed so far.

### Tonal noise of voluteless centrifugal fan generated by turbulence stemming from upstream inlet gap

Volutes for radial-flow turbomachines (e.g., centrifugal fans and pumps) are spiral funnel-shaped casings that house rotors. Their function is to guide the flow from rotors to outlets and maintain constant flow speeds. Under specific conditions, however, volutes are removed (termed voluteless) to reduce flow losses and noise. In this paper, a generic voluteless centrifugal fan is investigated for the tonal noise generation at an off-design operation point. In contrast to typical tonal noise sources induced by the fan blades, we find out that another predominant source is the turbulence stemming from the clearance gap between the fan front shroud and the inlet duct. The turbulence evolves along with the front shroud and is swept downstream to interact with the top side of the blade leading edge. An obvious additional tone is observed at [math] other than the blade passing frequency ([math]) and relevant harmonic frequencies. By coarsening the mesh resolution near the inlet gap and front shroud in the simulations, we artificially deactivate the gap turbulence. Consequently, the tone at [math] disappears completely. The finding indicates that the interaction between the gap turbulence and blades accounts for the tone. As the gap turbulence exists near the front shroud, this rotating wall introduces rotational momentum into the turbulence due to skin friction. Hence, this tonal interaction frequency is smaller than [math] with a decrement of the fan rotation frequency. To the authors' knowledge, this is the first time that voluteless centrifugal fans are studied for the gap-turbulence noise generation.

### Heat transfer mechanism driven by acoustic body force under acoustic fields

Author(s): Varun Kumar, Mohammed Azharudeen, Charish Pothuri, and Karthick Subramani

We demonstrate a heat transfer (HT) mechanism based on the relocation of an inhomogeneous fluid under acoustic fields. The proposed HT mechanism is studied under gravity and microgravity conditions. When differentially heated fluid is subjected to ultrasonic waves perpendicular to the HT direction, HT is found to be enhanced up to one order. Depending on acoustic properties, different flow patterns are observed for different fluids. A modified Rayleigh number is proposed for HT characterization that accounts for both gravity and acoustic effects. Furthermore, suppression of natural convection HT is observed when acoustic waves are applied parallel to the HT direction.

[Phys. Rev. Fluids 6, 073501] Published Thu Jul 15, 2021

### Experimental investigation of flow around a ${45}^{∘}$ oriented cube for Reynolds numbers between 500 and 50 000

Author(s): Majid Hassan Khan, P. Sooraj, Atul Sharma, and Amit Agrawal

Particle imaging velocimetry (PIV) measurements were performed for flow around an oriented cube, to study the wake at various Reynolds numbers. The wake shows numerous small eddies and the velocity profiles have multiple peaks. At higher Reynolds number the streamwise to transverse root mean square velocity ratio Urms/Vrms ~ 1 indicates homogenizing and better mixing ability of an oriented cube as compared to a normal cube. Proper orthogonal decomposition (POD) has been used to examine the energy content of the flow and the evolution of coherent structure.

[Phys. Rev. Fluids 6, 074606] Published Thu Jul 15, 2021

### Energy harvesting from passive oscillation of inverted foil

A numerical study is carried out to investigate the energy harvesting from an inverted foil undergoing flow-induced pitching oscillation for reduced velocity Ur = 1–45 and damping ratio ζ = 0–0.295. The benchmark results with undamped foil (ζ = 0) indicate that the foil does not oscillate for Ur ≤ 27 but does oscillate with increasing amplitude for 27 < Ur < 34 and with constant amplitude for Ur ≥ 34. Lissajous diagrams of moment coefficient against the foil displacement are linked to the energy harvesting, showing how Ur and ζ affect the oscillating amplitude, reduced frequency, wake structures, and power exchange between the foil and the flow. The energy harvesting efficiency η up to 15.06% is achieved at Ur = 37 and ζ = 0.130 with a reduced frequency f* = 0.151 that is used by the cruising aquatic animals. The foil oscillation with negative power enhances the growth of vortices while that with positive power weakens the growth.

### Construction and evolution of knotted vortex tubes in incompressible Schrödinger flow

We propose a theoretical method for constructing an initial two-component wave function that can be transformed into a knotted velocity field with finite kinetic energy and enstrophy. The wave function is constructed using two complex-valued polynomials, with one determining the desired shape of the knotted central axis and the other encoding the twisting nature of vortex lines, which facilitates the study of helicity conversions. We construct six knotted vortex fields with various centerline and twist helicity as initial conditions for direct numerical simulation of incompressible Schrödinger flow (ISF) in a periodic box. Although the evolution of morphological structure is similar for ISF and classical viscous flow, with all the knots becoming untied after a short time to form one or more separate vortex rings, their statistics are quite different. During the critical period of vortex reconnection, the increase in enstrophy is much more moderate in ISF than in viscous flow, indicating that the Landau–Lifshitz term in ISF inhibits the energy cascade from large to small scales. We also find that the centerline helicity changes dramatically during reconnection, which is consistent with the evolution of the geometrical shape of vortex lines.

### Lattice Boltzmann investigation of the influence of slip distributions on the flow past a diamond cylinder at low-Reynolds-number

Two-dimensional flow past a diamond cylinder with varying slip distributions is numerically investigated using the lattice Boltzmann method at a Reynolds number of 100. Nine slip distributions, namely, fore-up (FU), after-up (AU), fore-up + fore-down (FU–FD), after-up + after-down (AU–AD), FU–AU, FU–AD, FU–FD–AU, FU–AU–AD, and full-slip, are examined and compared with the no-slip case. Fore-side and after-side slip were found to have opposite effects on the friction drag of the diamond cylinder, and the combination of the fore-up and after-up (FU–AU) slip is beneficial for pressure reduction. A maximum drag reduction of 13.6% is achieved by the full-slip case mainly contributed by the pressure reduction. Furthermore, comparison of two typical slip distributions with a non-uniform slip length is investigated. A uniform slip length for the FU and AU (or the FD and AD) is found to be very helpful for pressure reduction. The asymmetric slip distributions could also result in torque on the cylinder, which can be utilized to achieve flow control by adjusting the slip length and the slip length difference between different locations of the cylinder edges.

### Unsteady flow structures behind a shark denticle replica on the wall: Time-resolved particle image velocimetry measurements

Experiments were performed to determine the unsteady flow structures of a shark denticle replica with three longitudinal ridges of different elevations and sharp trailing edges. Time-resolved particle image velocimetry measurements were conducted to capture the time-varying flow fields behind a shark denticle replica and contoured denticle, using the latter as a benchmark configuration for comparison. The flow fields in the streamwise and spanwise planes were obtained experimentally to determine the highly three-dimensional flow behavior. The flow dynamics of the unsteady superimposed flow structures behind the denticle replica are illustrated in terms of the time-averaged flow fields, statistical flow quantities, dominant vortex structures, and their phase-dependent evolution processes. The findings demonstrate that the denticle replica reduces the size and stability of the recirculation zone, suppressing flow separation. The velocity fluctuations and Reynolds shear stresses of the denticle replica are higher than those of the contoured denticle. Proper orthogonal decomposition analysis on the fluctuating velocity fields reveals alternating clockwise and counterclockwise vortices that convect along the streamwise direction, which correspond to decomposed flow structures, such as counter-rotating vortex pairs in the spanwise plane. These aspects are considered to be signatures of a hairpin-shaped vortex based on the phase-averaging analysis of the unsteady three-dimensional behavior. A hairpin-shaped vortex makes a concerted contribution to fluid mixing between the central wake region and surrounding area. As the fluid flows downstream, fast detachment of the hairpin-shaped vortex is recognized away from the wall to the main stream, which in turn attenuates the flow structure signatures in the spanwise plane. A low-frequency swinging motion of the fluid is also identified in the central wake region, which enhances fluid mixing on the two sides of the wake.

### Three-dimensional single framework multicomponent lattice Boltzmann equation method for vesicle hydrodynamics

We develop a three-dimensional immersed boundary chromodynamic multicomponent lattice Boltzmann method capable of simulating vesicles, such as erythrocytes. The presented method is encapsulated in a single framework, where the application of the immersed boundary force in the automatically adaptive interfacial region results in correct vesicle behavior. We also set down a methodology for computing the principal curvatures of a surface in a three-dimensional, physical space which is defined solely in terms of its surface normal vectors. The benefits of such a model are its transparent methodology, stability at high levels of deformation, automatic-adaptive interface, and potential for the simulation of many erythrocytes. We demonstrate the utility of the model by examining the steady-state properties, as well as dynamical behavior within shear flow. The stability of the method is highlighted through its handling of high deformations, as well as interaction with another vesicle.

### Direct numerical simulation of forced turbulent round jet: Effect of flow confinement and varicose excitation

Direct numerical simulation of a turbulent round jet subjected to varicose excitation has been carried out. The effect of domain size and waveform used for providing varicose excitation have been studied with the help of time-averaged mean, fluctuating quantities, and instantaneous isosurfaces of the Q-criterion. Initial evolution of the jet suggests that the secondary instability is delayed in time with an increase in the domain size irrespective of the waveform. It has also been observed that the secondary instability manifests stronger for the square wave based excitation as compared to sinusoidal excitation for the smaller and medium domains. In addition, simulations demonstrate that the aforementioned secondary instability is sustained in the long term for small and medium domains. In the case of a confined domain, simulations indicate that square wave based excitation leads to greater enhancement in mixing and entrainment characteristics of the jet when compared to sinusoidal excitation. We demonstrate that sine pulsing at the inlet excites energy up to the second harmonic of the preferred mode while square pulsing excites energy (at least) up to the fifth harmonic which results in more energetic small-scales structures in the far field which in turn augment the mixing characteristics of jet. Qualitative assessment of vortical structures indicates that differently excited jets gradually become similar in the far field of large domains owing to the availability of sufficient amounts of fluid for entrainment. This behavior has also been quantitatively established by means of axial and lateral profiles of both time-averaged as well as fluctuating quantities characterizing the pulsed jet.

### Dynamics of buoyancy driven miscible iso-viscous flows in heterogeneous layered porous media

Buoyancy-driven instabilities in horizontally layered heterogeneous porous media are investigated using numerical simulations. The analysis is conducted for two different permeability distributions, where the permeability attains its maximum (minimum) at the initial interface. The effects of the frequency of layers ([math]) and variance of the permeability distribution ([math]) under different scenarios of density mismatches were analyzed and characterized both qualitatively and quantitatively. Results revealed that heterogeneity induces undulated more diffuse finger structures compared to the homogeneous case. In cases where the permeability at the initial interface is maximum, it is found that the larger the [math] the less unstable the flow. It is shown that the onset time of the instability increases with increasing number of layers and decreases with increasing heterogeneity variance. Moreover, it is revealed that flow mixing increases (decreases) with increasing heterogeneity variance before (after) a critical flow time. The trends observed are, however, reversed in the case of shifted permeability heterogeneity where the smallest permeability is at the initial interface. Interestingly, it was found that for the shifted permeability distribution, an unstable flow in a homogeneous medium can be fully stabilized when a small number of layers are used in the heterogeneous case.

### Droplet breakup of a high-viscosity-ratio system in a nonuniform temperature field under laser irradiation

This study conducted experimental and simple numerical studies to investigate the effect of change in viscosity ratio on the dispersion progress in a two-phase immiscible fluid. The viscosity ratio of the fluid was successfully modified by supplying direct heat radiation from an infrared laser. In the experiment, polybutenes and polydimethylsiloxane silicone oils were used as the dispersed droplet and matrix phases, respectively, and the radiation from an infrared laser with an intensity ranging from 10.9 to 87.3 W/cm2 was applied. The results show that the selective radiation-heating method using different radiation absorption coefficients against the infrared laser wavelength caused significant deformation of the droplet phase, reaching even the breakup point of the droplet. We further performed a numerical simulation of three-dimensional thermal conduction, including radiation heating, to estimate the temperature changes in the droplet phase. The results show that the droplet size significantly affects the heat absorption and temperature distribution of the system. Finally, we discuss a suitable radiation intensity on a nondimensional chart using the modified viscosity ratio and critical capillary number.

### Effect of insoluble surfactants on a thermocapillary flow

The thermocapillary effect, arising flow due to a temperature gradient along a fluid interface, is the dominant effect in some industrial and microfluidic processes and must be studied in order to optimize them. In this work, we analyze how insoluble surfactants adsorbed at the interface can affect such a flow. In particular, we analyze the case where the thermocapillary flow is induced at the air–water interface by locally heating it with an infrared laser, setup that is used to manipulate floating particles through the generated flow. Since water is a polar fluid, the air–water interface is easily polluted by surfactants. We developed a numerical model considering the uncontrolled presence of surfactants, which evidences that the effect of the surface contamination cannot be neglected, even for small surfactants concentration. The results of this numerical model were compared with different experimental measurements: particle tracking velocimetry, convection cell radius measurements, and thermography of the surface. All the experimental observations agree with the numerical model with the initial surface contamination being a fitting parameter. The model was then validated comparing its results with measurements for which a known quantity of surfactant was added to the interface. Finally, an analytical model was developed to explain the effects of the governing parameters, which agrees with the simulations and the experimental results. The developed models give us insight toward the miniaturization of the manipulation platform.

### Water wave scattering by impermeable and perforated plates

In the field of offshore renewable energy, impermeable plates are used as underwater lenses to amplify the wave amplitude, and perforated plates can harness wave energy as a power takeoff device. Within the framework of the linear potential-flow theory, the water wave scattering by impermeable and perforated horizontal plates is investigated in the present study, and both circular and elliptical plates are considered. The hypersingular integral equation is constructed to model the interaction between water waves and plates of small thickness. For wave scattering by impermeable plates with the focus on wave amplification, wave interference effects due to multiple plates can be utilized to achieve large wave amplification. For perforated plates used for harnessing wave energy, deploying an array of elliptical plates is promising if the deployment line coincides with the major axis and the incident wave propagates along the minor axis. The study gives insight into harnessing energy from water waves by horizontal plates.

### Dielectrophoresis-driven jet impingement heat transfers in microgravity conditions

In this paper, the ability of a pair of triangular electrodes to generate the steady dielectrophoresis-driven thermal convection of a dielectric liquid in a differentially heated cavity is investigated in microgravity conditions. A non-uniform electric field is created on purpose, which, together with a temperature gradient, gives rise to an internal convective flow essentially based on the presence of a pair of counter-rotating vortices. A numerical study is developed to investigate the subsequent benefits on heat transfers. The results seem to be in agreement with a background scaling analysis and demonstrate a significant increase in the Nusselt number for increasing voltages, provided that the dielectric liquid of interest is characterized by a moderate-to-large Prandtl number. The triangular electrodes yield a significant heat transfer enhancement when the same voltage is being used, by comparison with planar electrodes. This benefit is essentially due to jet impingement heat transfers that take place within the cavity.

### Rheological signatures of gel–glass transition and a revised phase diagram of an aqueous triblock copolymer solution of Pluronic F127

In this work, we study temperature-induced state change of an aqueous solution of triblock copolymer composed of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide), PEO-PPO-PEO (Pluronic F127), at different concentrations using rheology. While this temperature-dependent state change visually appears like a liquid–soft solid transition, and the soft solid state has been termed as a gel in the literature, there is a debate regarding the precise microstructure of the soft solid state. We observe that over a concentration domain of interest, an aqueous solution of F127 overwhelmingly demonstrates all the characteristic rheological features of not just a sol–gel–glass transition at low temperatures and glass–liquid transition at high temperatures, but also that associated with the individual states, such as sol, post-gel, and glass. The temperature at which the gel–glass transition is observed decreases while the temperature associated with glass–liquid transition increases with an increase in the concentration of F127. Based on the observed behavior, we propose a mechanism that considers the change in micelle volume fraction and alteration of the hydrophilicity of PEO corona as a function of temperature. Finally, we construct a phase diagram and discuss the similarities and differences with respect to various phase diagrams of F127 solution available in the literature.

### Flow regime mapping for a two-phase system of aqueous alginate and water droplets in T-junction geometry

Microfluidic systems are an interesting topic for investigation due to their wide-spreading applications. Nowadays, polymeric solutions are used mainly for the generation of microparticles in biomedical engineering, food, and pharmaceutical industries. Droplet-based microfluidic devices have proposed an extensive interest in many applications such as chemical/biological/nanomaterial preparation to understand deeply the droplet size and formation in microchannels. However, numerous experimental and numerical studies have been done for oil–water combination, polymeric solutions behavior in the presence of oil has not been investigated widely. Therefore, it is important to understand the droplet formation mechanisms in a microfluidic device for both water and polymeric solutions to determine the flow regime mapping in order to control the characteristic of the produced droplets. Also, in many studies, the length of the droplets as a parameter to investigate the droplet size was studied. In this study, droplet generation in the T-shaped microfluidic junction with an enlarged horizontal outlet channel was studied to have opportunity to determine the diameter of spherical droplets. The water and the alginate 1% (w/v) solutions were used separately as a dispersed phase, and the mineral oil was used as the continuous phase in which the solution's flow rates were varied over a wide range. To perform numerical simulations of the droplet formation, a two-phase level set method was used which is a suitable method for the investigation and simulation of immiscible fluids. The flow regime mapping for the two different aqueous solutions was obtained. Furthermore, the influences of flow rates on droplet size, droplet generation frequency was quantified. In this study, flow regime, droplet size, and droplet frequency were studied. In general, flow rates of the oil and aqueous fluids readily control five main flow regimes including backflow, laminar flow, dripping flow, squeezing flow, jetting flow, and fluctuated flow. It was observed that generated droplets with alginate solution as dispersed phase were more in the region of the jetting flow regime while water droplets were more in the region of the dripping flow regime, this can be due to the difference in characteristics of polymeric solution and water. For both aqueous phases, larger droplets were obtained when flow rates of oil were decreased and aqueous phases were increased. Also, the frequency of droplet generation increases and decreases by increasing oil phase flow rate and increasing aqueous phase flow rate, respectively. In the same flow rates of aqueous phase and oil, the sizes of water droplets are larger than the alginate droplets and also water has a higher frequency of droplet generation compared to alginate. Finally, we characterized all the obtained data for flow regimes due to the capillary number (Ca) of the continuous phase. The findings of this study can help for better understanding of the detailed process of droplet generation of water and alginate solution as dispersed phase separately with mineral oil as the continuous phase in a T-junction geometry microfluidic and know the effect of characteristics of solutions as a dispersed flow in flow regimes.

### Changes in the hydrodynamic stability of plane porous-Couette flow due to vertical throughflow

A detailed study on the linear stability of plane porous-Couette flow in the presence of a uniform vertical throughflow using the Brinkman–extended Darcy equation has been presented. The equivalent of the Orr–Sommerfeld eigenvalue problem is formulated and solved numerically using the Chebyshev collocation method. The throughflow introduces an asymmetry in the basic flow amounting to the existence of a different set of onset modes. The contributions of the throughflow dependent modified Reynolds number and the modified porous parameter on the critical values defining the threshold for the onset of instability are presented. It is found that the stability characteristics of plane Couette flow in a porous medium in the presence of throughflow are remarkably different from no throughflow and non-porous cases.