# Latest papers in fluid mechanics

### Squeezing multiple soft particles into a constriction: Transition to clogging

Author(s): Clément Bielinski, Othmane Aouane, Jens Harting, and Badr Kaoui

We study numerically how multiple deformable capsules squeeze into a constriction. This situation is largely encountered in microfluidic chips designed to manipulate living cells, which are soft entities. We use fully three-dimensional simulations based on the lattice Boltzmann method to compute the...

[Phys. Rev. E 104, 065101] Published Fri Dec 03, 2021

### Single-shot wideband active microrheology using multiple-sinusoid modulated optical tweezers

Author(s): Avijit Kundu, Raunak Dey, Shuvojit Paul, and Ayan Banerjee

Optically trapped colloidal probes have been widely used for active microrheology of viscoelastic fluids over the last decade. A significant issue which arises is measurement of complex viscoelastic parameters over a wide frequency range and a short time. We use a combination of square and sinusoidal waves to spatially modulate the trapped probe over a frequency range spanning five decades, and use the phase response to calculate complex viscoelastic parameters with high signal to noise in a little over three minutes. We test our method over a wide variety of linear viscoelastic samples at different concentrations, and find good agreement of the measured parameters with known values.

[Phys. Rev. Fluids 6, 123301] Published Fri Dec 03, 2021

### Real-time reactive control of stochastic disturbances in forced turbulent jets

Author(s): Igor A. Maia, Peter Jordan, André V. G. Cavalieri, Eduardo Martini, Kenzo Sasaki, and Flávio J. Silvestre

In this work we perform reactive control of axisymmetric disturbances in turbulent jets. The disturbances are produced by an external forcing and possess stochastic phases and amplitudes, akin to turbulent fluctuations found in unforced jets. The control law is based on an existing inverse feedforward scheme developed for transition control. Here we apply it to control convective growth mechanisms in fully turbulent jets and we build on previous works that considered control of harmonic disturbances. We demonstrate the successful implementation of real-time reactive control of the disturbances and achieve order-of-magnitude attenuations of velocity fluctuations.

[Phys. Rev. Fluids 6, 123901] Published Fri Dec 03, 2021

### Initial solidification dynamics of spreading droplets

Author(s): Robin B. J. Koldeweij, Pallav Kant, Kirsten Harth, Rielle de Ruiter, Hanneke Gelderblom, Jacco H. Snoeijer, Detlef Lohse, and Michiel A. J. van Limbeek

An experimental study is performed to investigate the influence of crystal growth on the contact line behavior of a droplet on an undercooled surface. We show the effect that the growing nucleus has on the arrest of the contact line and the underlying dependence on nucleation rate. Finally, based on classical nucleation theory and scaling relations for droplet spreading, we calculate the temporal evolution of the solidifying area.

[Phys. Rev. Fluids 6, L121601] Published Fri Dec 03, 2021

### Suppression of Leidenfrost effect on superhydrophobic surfaces

The Leidenfrost phenomenon entails the levitation of a liquid droplet over a superheated surface, cushioned by its vapor layer. This vapor layer can obstruct boiling heat transfer in heat exchangers, thereby compromising energy efficiency and safety. For water, superhydrophobic surfaces are believed to reduce the Leidenfrost point (TL)—the temperature at which this phenomenon occurs. Therefore, superhydrophobic surfaces are not commonly utilized in thermal machinery despite their benefits such as reducing frictional drag. Here, we demonstrate that it is possible to achieve superhydrophobicity without lowering TL by surface engineering and fine-tuning liquid–solid adhesion. We demonstrate that TL of water on superhydrophobic surfaces comprising doubly reentrant pillars (DRPs) can exceed that on hydrophilic and even superhydrophilic surfaces. Via theory and computation, we disentangle the contributions of microtexture, heat transfer, and surface chemistry on the onset of the Leidenfrost phenomenon. Remarkably, coating-free and superhydrophobic DRP architecture can facilitate ∼300% greater heat transfer to water droplets at 200 °C in comparison with conventional superhydrophobic surfaces. These findings advance our understanding of the Leidenfrost phenomenon and herald technological applications of superhydrophobic surfaces in thermal machinery.

### A method for long-time integration of Lyapunov exponent and vectors along fluid particle trajectories

Finite-time Lyapunov exponents (FTLEs) and Lyapunov vectors (LVs) are powerful tools to illustrate Lagrangian coherent structures (LCSs) in experiments and numerical simulations of fluid flows. To obtain the FTLEs and LVs with the flow simulation simultaneously, we computed the eigenvectors and eigenvalues of the left Cauchy–Green tensor along the trajectories of fluid particles separately instead of computing deformation gradient tensor directly. The method proposed in the present study not only avoids solving the eigenvalue problem of the singular matrix at each time step but also guarantees a stable simulation for a long time. The method is applied in the computation of FTLEs and LVs in two-/three-dimensional (2D/3D) compressible/incompressible cases. In 2D cases, we found that LCSs are folded as fine filaments induced by vortices, while LCSs are sheet-like structures among the vortices for 3D cases. Meanwhile, the directions of stretching and compression of LVs are tangent and normal to the FTLE ridges (2D)/iso-surfaces (3D), respectively.

### Propagation of cylindrical shock waves in rotational axisymmetric dusty gas with magnetic field: Isothermal flow

In this article, the effect of the dust particles is studied on the propagation of a cylindrical shock wave in rotational axisymmetric ideal gas under isothermal flow conditions with the magnetic field. Here, magnetic pressure, azimuthal fluid velocity, and axial fluid velocity are supposed to vary according to a power law in the undisturbed medium. With the help of Sakurai's technique, we obtain approximate solutions analytically by expanding the flow parameters in the form of a power series in [math]. The power series method is used to derive the zeroth and the first-order approximations. The solutions for the zeroth-order approximation are constructed in analytical form. Distributions of the hydrodynamical quantities are analyzed graphically behind the shock front. Also, the effects of shock Cowling number [math], mass fraction of the solid particles in the mixture [math] adiabatic exponent [math], and rotational parameter (L) on the flow variables are discussed. It is investigated that the density and pressure near the line of symmetry in the case of isothermal flow become zero, and hence a vacuum is formed at the axis of symmetry when the flow is isothermal. The present work may be used to verify the correctness of the solution obtained by self-similarity and numerical methods. Furthermore, the results obtained in the present work are found to be in good agreement with those obtained from the study by Nath and Singh [Can. J. 98, 1077 (2020)].

### Nonlinear stability of regular vortex polygons in a Bose–Einstein condensate

The problem of stability of rotating regular vortex N-gons (Thomson's configurations) in a Bose–Einstein condensate in a harmonic trap is considered. A reduction procedure on the level set of the momentum integral is proposed. The dependence of the velocity of rotation ω of vortex polygon about the center of the trap is obtained as a function of the number of vortices N and the radius of the configuration, R. The analysis of the orbital linear and nonlinear stability of the motion of such configurations is carried out. For [math], regions of orbital stability of configurations in the parameter space are constructed. It is shown that vortex N-gons for [math] are unstable for any parameters of the system. In this paper, we study the stability of rotating regular vortex N-gons in a Bose–Einstein condensate in a harmonic trap. The analysis of the orbital linear and nonlinear stability of motion is carried out. The dependence of the stability of regular vortex N-gons on the number of vortices N and the parameters of the system is given.

### Transcritical transition of the fluid around the interface

In this paper, fundamental insights into the dynamic transcritical transition process were provided using molecular dynamics simulations. A transcritical region, which covers three different fluid states, was discovered as a substitute for the traditional interface. The physical properties, such as temperature and density, exhibited a highly nonlinear distribution in the transcritical region. Meanwhile, the surface tension was found to exist throughout the transcritical region, and the magnitude was directly proportional to [math].

### Features of surface physical quantities and temporal-spatial evolution of wall-normal enstrophy flux in wall-bounded flows

This paper presents a concise derivation of the temporal-spatial evolution equation of the wall-normal enstrophy flux on a no-slip flat wall. Each contribution to the evolution is explicitly expressed using the two fundamental surface quantities: skin friction (or equivalently surface vorticity) and surface pressure which are coupled through the boundary enstrophy flux (BEF). The newly derived relation is then used to explore, in a preliminary manner, the physical features of surface quantities and their dynamical roles in wall-bounded laminar and turbulent flows. It is confirmed that the BEF usually changes its sign near the separation and attachment lines in the skin friction field. For the simulated incompressible turbulent channel flow at [math], violent variations of different terms in the derived formulation are observed in the regions below the strong wall-normal velocity events (SWNVEs) when compared to other common regions. Near the SWNVEs, the evolution of the wall-normal enstrophy flux is found to be dominated by the wall-normal diffusion of the vortex stretching term which is relatively weak or negligible for laminar flows. Combined with our previous research results, it is conjectured that the strong interaction between the quasi-streamwise vortex and the channel wall intensifies the temporal-spatial evolution of the wall-normal enstrophy flux on the wall, which accounts for the highly intermittent feature of the viscous sublayer.

### Characteristics of flow past elongated bluff bodies with underbody gaps due to varying inflow turbulence

An experimental study was performed on two elongated bluff bodies with underbody gaps, a square-back Ahmed body and a cuboid, to investigate the effects of geometry and the approach flow conditions on the time-averaged and temporal characteristics. The flow fields produced from two approach turbulent boundary layers with moderate (∼4%) and high (∼7%) turbulence levels were studied using time-resolved and double-frame particle image velocimetry systems. With the moderate turbulence, the wake topology and the loci of the centroid of vortices exhibit the well-known toroidal structure behind the Ahmed body, though it is skewed away from the wall. Also, the regions of elevated Reynolds stresses are considerably larger in the upper shear layer compared to the lower shear layer due to the reduced underbody velocity. The dominant frequencies obtained from the velocity fluctuations, reverse flow area, and the coefficient of the first proper orthogonal decomposition (POD) mode are identical. The flow structures are more complex behind the cuboid and the Ahmed body mounted in the high turbulent flow due to the enhanced interaction between the lower and upper shear layers, which is also evident from the shape of the turbulent structures in these shear layers. Consequently, the dominant vortex shedding frequencies varied as the streamwise distance from the bodies increased. The probability density function of the reverse flow area and the POD analysis performed in the spanwise plane revealed that the bi-stability phenomenon is absent in the present study due to the significant modification of the wake topology.

### Effects of nutrient depletion on tissue growth in a tissue engineering scaffold pore

In a tissue engineering scaffold pore lined with cells, nutrient-rich culture medium flows through the scaffold and the cells proliferate. In this process, both environmental factors—such as flow rate and shear stress—as well as cell properties have significant effects on tissue growth. Recent studies have focused on the effects of scaffold pore geometry on tissue growth, while in this work, we focus on the nutrient depletion and consumption rate by the cells, which cause a change in the nutrient concentration of the feed and influence the growth of cells lined downstream. In this paper, our objectives are threefold: (i) design a mathematical model for the cell proliferation describing fluid dynamics, nutrient concentration, and tissue growth; (ii) solve the models and then simulate the tissue proliferation process; (iii) design a “reverse algorithm” to find the initial configuration of the scaffold with the knowledge of the desired property of the final tissue geometry. Our model reduces the numerical burdens and captures the experimental observations from the literature. In addition, it provides an efficient algorithm to simulate the cell proliferation and determine the design of a tissue engineering scaffold given a desired tissue profile outcome.

### Effect of weak solute advection on a chemically active particle under the influence of an external concentration gradient

Author(s): Prathmesh M. Vinze and S. Pushpavanam

A Janus particle is an example of a micro swimmer which converts chemical energy present in the environment to its mechanical energy using surface reaction. In this work, we theoretically study the weak effect of solute advection on the swimming velocity of an active particle. Using the method of matched asymptotic expansion we provide a general framework for calculating first order corrections to the concentration field and the swimming velocity of an active particle in terms of Peclet number relative strength of advection to diffusion. The O(Pe) corrections reduce the magnitude of swimming velocity independent of other parameters

[Phys. Rev. Fluids 6, 124201] Published Thu Dec 02, 2021

### High-fidelity simulation of a hydraulic jump around a surface-piercing hydrofoil

For a surface-piercing hydrofoil traveling at high speed, a turbulent hydraulic jump may arise at the intersection of the body with the free surface. This hydrodynamic phenomenon involves violent wave breaking, bringing great challenges for experimental analysis. In this work, a high-fidelity large eddy simulation is performed to study the turbulent air-entraining flow near foil. One advantage of the present simulation is that a quantitative analysis can be implemented even in the turbulent two-phase mixing region containing a large amount of entrained air, which is difficult for traditional experimental and theoretical approaches. We employ a conservative coupled level set/volume-of-fluid scheme to capture the free surface. A highly robust scheme is introduced to guarantee stability in simulating large density ratio two-phase flows. The present method is implemented based on a block-structured adaptive mesh, by which the efficiency of the high-fidelity simulation can be improved. The main flow features of the wedge-shaped hydraulic jump, including the wave patterns, free surface elevation, and frequency spectra, are compared with experimental data. We find that the flow structures show clear differences from those found in the canonical hydraulic jump, owing to the presence of the foil surface. Shoulder wave breaking starts at the trough of the mid-body, develops in a wedge shape, depends strongly on Froude number, and is responsible for most of the large-scale air entrainment. The properties of the turbulent hydraulic jump and some of the key quantities characterizing the air-entraining flow, including the spatial distribution of the bubble cloud, the void fraction, and the bubble/droplet size spectrum, are fully investigated for typical Froude numbers.

### Multiphase flow simulation with three-dimensional weighted-orthogonal multiple-relaxation-time pseudopotential lattice Boltzmann model

In this paper, based on two lattice models (D3Q19 and D3Q27), two three-dimensional weighted-orthogonal multiple-relaxation-time pseudopotential lattice Boltzmann (WMRT-PLB) models with tunable thermodynamic consistency and surface tension are developed in which the high-order terms of the equilibrium density distribution function and discrete forcing term in moment space are eliminated, and thus, the implementation of the collision process is simplified. The Chapman–Enskog analysis shows that the WMRT-PLB models can correctly recover the macroscopic Navier–Stokes equations in the low Mach number limit. Then, six classical multiphase flows benchmark cases are performed to validate the performance of the proposed model. The numerical results of the first three cases indicate that the developed WMRT-PLB models effectively weaken the non-physical coupling between kinetic viscosity and density, enhance the numerical stability because of the low spurious velocity, improve the computational efficiency by about 25% because of the simplification of the collision process, and increase the numerical accuracy in the dynamic problems. Meanwhile, the numerical results of the last three cases with the density ratio of 857.7 and the kinetic viscosity ratio of 1/15 agree well with the analytical solutions and experimental results reported in the literature. Note that it is also found that the simulation of droplet bouncing is still stable even when the Reynolds number is more than 3000, which shows the good numerical stability of the proposed model. It has the potential to be applied to the simulation of the complex multiphase flows with large density ratio and large Reynolds number.

### Numerical study on the effects of modulated ventilation on unsteady cavity dynamics and noise patterns

Supercavitating flow is accompanied by significant unsteady characteristics, and it is therefore very important to find methods to control this multiphase flow phenomenon. Ventilation is an important method for creating supercavitation and it affects the evolution, load, and noise characteristics. In this paper, cavity flows with and without modulated ventilation (i.e., the imposition of a sinusoidal component on the ventilation rate) are investigated using computational fluid dynamics techniques incorporating large eddy simulation, coupled with the Ffowcs Williams–Hawkings (FW–H) method. The effects of modulated ventilation on cavity shedding, vortex structure, and the noise characteristics of the cavity are compared and analyzed. The results show that modulated ventilation can change the shedding period of the ventilated cavity and can slightly improve its lift and drag performance. It can also promote the formation and growth of hairpin vortices and impose a periodicity on the evolution of the vortex structure. Furthermore, although modulated ventilation cavitation enhances pressure fluctuations near the vent and increases the self-noise of ventilation, it has little impact on far-field noise while reducing the turbulence of the far field, which decreases the total sound pressure level in the wake of the cavitator.

### Evaporation flow characteristics of airborne sputum droplets with solid fraction: Effects of humidity field evolutions

The continuance of the COVID-19 pandemic largely depends on the spread of virus-carrying aerosols in ambient air. The mechanism of virus transmission and infection remains under intense investigation. In this study, an evaporation flow model of airborne sputum droplets is proposed which considers the evolution effects of the humidity field under different particle distributions and solid/salt fraction interactions. The incompressible Navier–Stokes equations characterize a stream of airflow jets, and the convection-diffusion-evaporation process is used to account for the inhomogeneous humidity field caused by the respiratory tract. Momentum equations for droplet dynamics which involve the effects of drag, gravity, and Brownian motion on sputum droplets are introduced to quantify the transport of droplets in a humidity field. The Lattice Boltzmann method is used to track the evolution of the aerosol in space and time under different ambient temperature and relative humidity conditions. The results of the simulation demonstrate that airborne humidity accelerates the evaporation rate of droplet, while supersaturated humid air forms a vapor mass in front of the respiratory tract. Despite the short lifespan of this phenomenon, it significantly hinders the evaporation of the droplets. Besides, the droplet vortex dynamics in a humidity field are sensitive to the droplet size.

### Electrohydrodynamic behavior of polyelectrolyte vesicle accompanied with ions in solution through a narrow pore induced by electric field

We use finite element numerical simulations to study the electrohydrodynamic behavior of a polyelectrolyte vesicle passing through a narrow pore in an electrically neutral system. We systematically explain the deformation and migration of the vesicle, including the motion of ions in the solution, the strain energy and stress distribution of the vesicle under electric drive, and the minimum potential difference (critical potential difference) that allows the vesicle to pass through the narrow pore. The migration of the vesicle into the pore drives ion motion, causing rapid changes in the ion flux and potential difference in the pore, which may provide an important means to determine whether the vesicle passes through the pore. In addition, the changes in ion concentration and potential difference in the pore will not disappear when the radius of the vesicle is smaller than the pore diameter. We also find that the critical potential difference is independent of the pore diameter, but it does depend strongly on the vesicle's radius. When the vesicle's radius becomes larger than the pore diameter, the critical potential difference increases by an order of magnitude, which provides an effective method for separation of vesicles.

### Flow over a hydrofoil at incidence immersed within the wake of a propeller

The flow over a hydrofoil in the wake of a marine propeller is studied using large-eddy simulation on a cylindrical grid composed of 3.8 billion points. Four angles of incidence of the downstream hydrofoil are considered, ranging from [math] to [math]. The impact of the propeller wake on the flow within the boundary layer of the hydrofoil is substantial, increasing the skin-friction and producing significant spanwise flows, associated especially with the deflection of the tip and hub vortices. This deflection is strongly influenced by the incidence angle of the hydrofoil, producing an overall expansion of the propeller wake on its pressure side and a contraction on its suction side. The tip and hub vortices are also the major source of pressure fluctuations on the surface of the hydrofoil, affecting this way its unsteady lift and drag coefficients. On the pressure side, the most significant pressure fluctuations are due to the hub vortex, while on the suction side, their maxima originate from the overlapping effects by the tip vortices and the adverse streamwise pressure gradient, promoting the instability of the boundary layer. Pressure fluctuations are an increasing function of the incidence of the hydrofoil on both its pressure and suction sides.

### Onset of submerged granular collapse in densely packed condition

Granular materials are widespread in nature, and understanding their transport is important in geophysics. This study investigated the initiation of submerged granular collapse and collapse types, which affect transport processes. Laboratory experiments and failure analysis were performed; four particles and five liquids were experimentally examined. The experimental results reveal that the failure angle increases with decreasing particle size and increasing liquid viscosity. As the failure angle approaches [math], the breaching collapse dominates; otherwise, sliding collapse occurs. Furthermore, the failure analysis indicated that the failure angle depends on the dimensionless parameter Darcy number; this was validated experimentally. The critical value of the Darcy number to distinguish between breaching and sliding collapse was devised on the basis of the experimental results.