# Latest papers in fluid mechanics

### Effect of geometric parameters on synthetic jet: A review

A synthetic jet actuator is a fluidic device that produces a jet flow by the periodic ingestion of fluid into and expulsion of fluid out of a cavity across an orifice. Since such a mechanism transfers linear momentum to the fluid without introducing a net mass into the system over an actuation cycle, the synthesized jet is also termed a zero-net-mass-flux jet. Over the last two decades, synthetic jets have been the subject of intense research. It has been shown that the geometric parameters of a synthetic jet actuator can strongly influence the flow characteristics and performance of synthetic jets. The aim of this paper is to provide a comprehensive review of the influence of the geometric parameters of a synthetic jet actuator on the characteristics and performance of synthetic jets. These parameters include the height and diameter of the cavity and the orifice and the shape and edge configuration of the orifice.

### Capillary rise in superhydrophilic rough channels

Surface tension forces enable a liquid to rise against gravity when wettable tubes or porous media are in contact with the pool of liquid. While the rise dynamics in the media of homogeneous porosity are well known, those in heterogeneous porous media still remain poorly understood. Here, we employ a vertical channel formed by two parallel plates decorated with micropillars, as a simple model of bidisperse porous media, and observe the rise dynamics of various viscous liquids. We find the bulk rise speed to be higher than that in dry smooth channels but equal to that between prewetted smooth channels. As the bulk approaches its equilibrium height, a film emerges ahead of the bulk meniscus, which is driven by the high surface energy of the microdecorated surface. The film extension grows initially like t but later like t1/2, with t being time. We construct theoretical models to predict the critical height where the film emerges and to rationalize the power laws of the film extension. In particular, we show that the dominant viscous resistance to the film extension is provided by the flow from the reservoir through the bulk in the early stages and by the film itself in the late stages. Our study opens a pathway to scrutinize the complicated flow dynamics arising within and across voids of heterogeneous porous media with an easily observable experimental setup of a well-defined geometry.

### Van Gurp–Palmen relations for long-chain branching from general rigid bead-rod theory

Empirically, we find that parametric plots of mechanical loss angle vs complex shear modulus may depend neither on temperature [M. van Gurp and J. Palmen, “Time-temperature superposition for polymeric blends,” Rheol. Bull. 67, 5–8 (1998)] nor on average molecular weight [S. Hatzikiriakos, “Long chain branching and polydispersity effects on the rheological properties of polyethylenes,” Polym. Eng. Sci. 40, 2279 (2000)]. Moreover, Hatzikiriakos (2000) discovered that, for fixed polydispersity, these van Gurp–Palmen curves descend with long-chain branching content. In this paper, we find that general rigid bead-rod theory [O. Hassager, “Kinetic theory and rheology of bead-rod models for macromolecular solutions. II. Linear unsteady flow properties,” J. Chem. Phys. 60(10), 4001–4008 (1974)] can explain these descents. We explore the effects of branching along a straight chain in small-amplitude oscillatory shear flow. Specifically, we explore the number of branches, branch length, branch position, and branch distribution.

### Numerical investigation on formation and motion of bubble or droplet in quiescent flow

This paper describes the dynamic mechanisms of bubbles and droplets moving in quiescent flows. An improved diffuse interface method is adopted to capture the interfacial evolution of a two-phase flow, which can effectively suppress the phenomenon of interface dispersion. Preliminary simulations of a circular bubble/droplet moving from rest are first performed, and then, the interface shapes and vorticity distributions are compared to study the differences in the deformation mechanisms of bubbles and droplets. The processes of bubbles and droplets formed from a submerged orifice are, then, explored. The bubble formation process can be divided into nucleation, expansion, and detachment stages; for droplets, the characteristics of chaotic drip flow are considered. The interface shape and vorticity distribution of bubbles/droplets are analyzed, and the effects of the Weber number and Bond number on the detached bubble size and droplet flow regime are investigated. The effect of the contact angle on bubble formation is also examined. To reduce the detached bubble size, an improved method using an inserted orifice is proposed and confirmed. The inserted orifice is shown to have almost no effect on the formation of droplets, and the bubble/droplet formation and motion are independent of the inserted orifice length.

### Numerical investigation on formation and motion of bubble or droplet in quiescent flow

This paper describes the dynamic mechanisms of bubbles and droplets moving in quiescent flows. An improved diffuse interface method is adopted to capture the interfacial evolution of a two-phase flow, which can effectively suppress the phenomenon of interface dispersion. Preliminary simulations of a circular bubble/droplet moving from rest are first performed, and then, the interface shapes and vorticity distributions are compared to study the differences in the deformation mechanisms of bubbles and droplets. The processes of bubbles and droplets formed from a submerged orifice are, then, explored. The bubble formation process can be divided into nucleation, expansion, and detachment stages; for droplets, the characteristics of chaotic drip flow are considered. The interface shape and vorticity distribution of bubbles/droplets are analyzed, and the effects of the Weber number and Bond number on the detached bubble size and droplet flow regime are investigated. The effect of the contact angle on bubble formation is also examined. To reduce the detached bubble size, an improved method using an inserted orifice is proposed and confirmed. The inserted orifice is shown to have almost no effect on the formation of droplets, and the bubble/droplet formation and motion are independent of the inserted orifice length.

### Initial regime of drop coalescence

Author(s): Christopher R. Anthony, Michael T. Harris, and Osman A. Basaran

What is the initial regime of coalescence when two drops just touch at a point? This long-standing problem has proven formidable because of the smallness of the bridge that is required to connect the drops at the initial instant in any continuum simulation. Here, initial bridge radii, heights, and radii of curvature as small as 10−6, 10−12, and 10−18 are achieved, showing that coalescence always begins in a Stokes regime. The inertially limited viscous regime is shown to be a Taylor-Culick-like regime seen only when drops are initially separated by a finite distance.

[Phys. Rev. Fluids 5, 033608] Published Fri Mar 13, 2020

### Length of standing jumps along granular flows down smooth inclines

Author(s): Ségolène Méjean, François Guillard, Thierry Faug, and Itai Einav

Predicting the flows of dense granular media is still a challenging issue. Here, numerical discrete element method simulations are used to investigate the diversity of patterns within granular jumps that accompany height, velocity, and density discontinuities in gravity-driven free-surface flows. It is demonstrated that standing granular jumps can serve as a useful gauge for evaluating the dissipation mechanisms that govern the flowability of granular media.

[Phys. Rev. Fluids 5, 034303] Published Fri Mar 13, 2020

### Wave damping of a sloshing wave by an interacting turbulent vortex flow

Author(s): Francisco Reyes, Vicente Torrejón, and Claudio Falcón

We report on the enhancement of the hydrodynamic damping of gravity waves at the surface of a fluid layer as they interact with a turbulent vortex flow in a sloshing experiment. Gravity surface waves are excited by oscillating horizontally a square container holding our working fluid (water). At the...

[Phys. Rev. E 101, 033106] Published Thu Mar 12, 2020

### Deformable microswimmer in an external force field

Author(s): Mohd Suhail Rizvi, Philippe Peyla, Alexander Farutin, and Chaouqi Misbah

External forces, such as gravity, influence swimming microorganisms. For flagellar microorganisms, such as Chlamydomonas, gravitactic swimming has been attributed to back-heaviness. Using a simple bead-spring microswimmer model, we show that back-heaviness is not necessary for the gravitactic swimming of flagellar microorganisms. The hydrodynamic interaction among beads results in the alignment of swimming direction with external force. By modulating flagellar beating patterns a microorganism can also change its swimming direction. This understanding can aid in the design of robotic swimmers.

[Phys. Rev. Fluids 5, 033101] Published Thu Mar 12, 2020

### Erratum: “Non-Newtonian perspectives of pulsatile blood-analog flows in a 180° curved artery model” [Phys. Fluids 27, 071901 (2015)]

### Vortex-dynamical implications of nonmonotonic viscous dissipation of off-center droplet bouncing

In this paper, vortex-dynamical perspectives were adopted to interpret the recently reported observation that the total viscous dissipation of off-center droplet bouncing varies nonmonotonically with the impact parameter [C. He, X. Xia, and P. Zhang, “Non-monotonic viscous dissipation of bouncing droplets undergoing off-center collision,” Phys. Fluids 31, 052004 (2019)]. The particular interest of this study is on analyzing the velocity and vorticity vector fields and their correlations, such as helicity and enstrophy. The helicity analysis identifies a strong interaction between the “ring-shaped” vortices and the “line-shaped” shear layers in the non-axisymmetric droplet internal flow. A general relation between the total enstrophy and the total viscous dissipation rate for an unsteady free-surface flow was theoretically derived and numerically verified. It shows that the equality between the total enstrophy and the total viscous dissipation rate holds for a single-phase flow confined by stationary boundaries but is not satisfied for a gas–liquid two-phase flow due to the interfacial movement. Both the total enstrophy and a defined “half-domain” helicity show the nonmonotonic variation with the impact parameter, implying their interrelation with the nonmonotonic viscous dissipation.

### Analysis of elastohydrodynamics and nutrient transport through deformable porous scaffold inside a hollow fiber membrane bioreactor

Hydrodynamics and nutrient transport in a hollow fiber membrane bioreactor is studied by developing a two-dimensional mathematical model in Cartesian coordinates. In a more realistic scenario, the scaffold is considered to be elastic and deformable, which undergoes deformation with the applied pore pressure. A mixture model is used to deal with the scaffold matrix, cells, and the fluid present in the scaffold region. The method of lubrication theory is incorporated when the aspect ratio of the lumen is small. The nutrient transport in the scaffold region is assumed to be governed by advection–diffusion–reaction mass balance due to the presence of cells and by advection–diffusion in the lumen and porous membrane. Analytical solution of the coupled system is presented for a short time scale where the cell growth, death, or differentiation is neglected. The results obtained focus on the effect of various parameters on the fluid flow, solid deformation, and consumption of nutrients due to different kinds of cells. It is observed that the deformation of the scaffold matrix increases monotonically with the flow rate supplied to the bioreactor. This behavior ensures that one can adjust the fluid flux to achieve optimum deformation in favor of cell growth and avoid damage of the scaffold. Moreover, a general criterion for the distribution of adequate nutrient concentration inside the bioreactor is developed to prevent the formation of the necrosis region inside the scaffold. Accordingly, the current investigation helps to arrive at suitable parameter combinations to monitor and control an ongoing experiment for optimum cell growth.

### Splashing of fuel drops impacting on heated solid surfaces

Liquid drop impact on dry, solid surfaces has been studied to elucidate the role of control parameters, such as drop size, impact velocity, liquid properties, surface roughness, and wettability, on the mechanism of splashing phenomenon. It has been shown more recently that ambient gas plays a pivotal role in initiating the disintegration mechanisms leading to the ejection of secondary droplets from an impacting drop. Through systematic experiments, the role of target surface temperature in altering the morphology of a splash outcome of impacting fuel drops is investigated in the present work. It is observed that at elevated surface temperatures, the heated air film present very close to the hot surface suppresses splashing and consequently raises the splash threshold Weber number of the impacting fuel drop. For a given Weber number, the morphology of the impacting drop shifts from splashing to spreading with a rise in the surface temperature through an intermediate transition regime, characterized by the tendency of the liquid sheet to recontact the drop lamella without ejecting any secondary droplets. The experimental observations are compared with theoretical model predictions reported in the literature, and fair agreement is found in terms of both the observed splash suppression and the underlying mechanisms that govern the identified morphological regimes.

### Space experimental study on wave modes under instability of thermocapillary convection in liquid bridges on Tiangong-2

We carried out space experiments on thermocapillary convection in liquid bridges with large Prandtl number in the Tiangong-2 space laboratory, studying the influence of geometrical parameters, including aspect ratio (Ar, height to diameter) and volume ratio (Vr). It is found that there are two modes of temperature oscillation in thermocapillary convection in liquid bridges: low- and high-frequency oscillation, corresponding to different critical temperature difference and geometrical parameters, respectively. In this paper, the geometrical effect on the wave pattern and its transformation in the oscillating thermocapillary flow is studied in detail. Temperature signals from thermocouples on five measuring spots are analyzed to distinguish different oscillation modes corresponding to characteristics of azimuthal waves, such as wave number, traveling wave, and standing wave. Under a small volume ratio, the low-frequency traveling wave mode transits to the high-frequency standing wave mode; under a large volume ratio, the high-frequency standing wave has abundant mode transformations, such as standing wave → traveling wave, standing wave → traveling wave → standing wave, and so on, and the transformation process of the wave mode is sensitive to the aspect ratio.

### Scaling laws for external fluid flow induced by controlled periodic heating of a solid boundary

Author(s): Debashis Pal and Suman Chakraborty

We demonstrate that considerable variation of mean Prandtl number (Pr0) from unity brings in an additional length scale (called the viscous penetration depth, δv) into the dynamics of instantaneous as well as time-averaged (mean) flow induced by thermoviscous expansion along a periodically heated so...

[Phys. Rev. E 101, 033105] Published Wed Mar 11, 2020

### Inhomogeneous distribution of particles in coflow and counterflow quantum turbulence

Author(s): Juan Ignacio Polanco and Giorgio Krstulovic

Particles are a useful tool for studying superfluid turbulence and visualizing quantum vortices. We study the dynamics of inertial particles in finite-temperature quantum turbulence with the two-fluid Hall-Vinen-Bekarevich-Khalatnikov model. We find that, at low temperatures, when the superfluid mass fraction is dominant, particles cluster on superfluid vortex filaments regardless of their physical properties, as in the figure. Furthermore, under strong counterflow, the flow is dominated by quasi-two-dimensional large-scale structures that govern the spatial distribution of particles.

[Phys. Rev. Fluids 5, 032601(R)] Published Wed Mar 11, 2020

### Small scale structures of turbulence in terms of entropy and fluctuation theorems

Author(s): André Fuchs, Sílvio M. Duarte Queirós, Pedro G. Lind, Alain Girard, Freddy Bouchet, Matthias Wächter, and Joachim Peinke

Fundamental results in nonequilibrium thermodynamics are shown to be associated with small-scale features of turbulent flows. The estimation of entropies allows the selection of distinct realizations of turbulent cascade trajectories through a hierarchy of spatial scales. Entropy-consuming cascade trajectories lead to small-scale intermittent structures with piling up of velocity increments and finite “jumps.” This finding is of interest for fundamental questions on singularities or rare extreme velocity gradients.

[Phys. Rev. Fluids 5, 034602] Published Wed Mar 11, 2020

### Geometric constraints on energy transfer in the turbulent cascade

Author(s): Joseph G. Ballouz and Nicholas T. Ouellette

Turbulent flows famously display a net cascade of energy from the injection scales to the dissipation scales. This cascade can be interpreted as the interplay of an emergent turbulent stress and a scale-dependent strain rate, which reveals the key role of geometric alignment in the energy transfer process. It is argued that the constraints placed on the cascade process by geometry are surprisingly significant and may provide important but under-appreciated ingredients for understanding turbulence phenomenology.

[Phys. Rev. Fluids 5, 034603] Published Wed Mar 11, 2020

### Numerical investigation of central breakup of large bubble induced by liquid jet

A large spherical bubble rising in quiescent liquid generally leads to the formation of a toroidal bubble (central breakup). In this paper, we investigate the bubble dynamics during the central breakup process using the three dimensional Volume of Fluid method implemented in OpenFOAM. The potential energy of the large bubble is converted into the kinetic energy of the liquid jet, resulting in the formation of the toroidal bubble. Before the central breakup of the bubble, a high pressure zone is formed on the top of the bubble due to the collision of the liquid jet with the top of the bubble. We report for the first time that a protrusion is formed on the top of the toroidal bubble for a large spherical bubble rising in quiescent liquid. The velocity of the gas inside the toroidal bubble around the liquid jet is much faster than that in other places after the central breakup, which leads to the formation of the protrusion against the restriction of the surface tension force. We find that the bubble size, liquid viscosity, and density can influence the formation of the toroidal bubble, while the influence of surface tension is negligible. We summarize the above influencing factors into two dimensionless numbers: Galilei (Ga) number and Eötvös number (Eo). In the end, we discover a simple linear relation between the jet Reynolds number and the Ga number by analyzing all numerical experiments.

### Effect of array submergence on flow and coherent structures through and around a circular array of rigid vertical cylinders

Flow past a submerged array of rigid cylinders is more complex compared to the limiting case of an emerged array because part of the flow approaching the array is advected over it and the mean-flow three-dimensionality is increased inside and around the array. For sufficiently high submergence, the flow moving over the top of the array generates a vertical separated shear layer (SSL) and modifies the structure of the wake flow. The case of a circular array of diameter D containing solid cylinders of diameter d (=0.03D) and height hp placed in a flat-bed open channel of depth h = 0.56D is investigated. Detached eddy simulations that resolve the flow past the individual cylinders are conducted at a Reynolds number ReD = 37 500 for two solid volume fractions (SVF) of the array region (SVF = Nd2/D2 = 0.09 and SVF = 0.23 corresponding to aD = 3.9 and 9.6, where N is the number of cylinders in the array and aD is the nondimensional frontal area per unit volume for the array) and several values of the relative height of the cylinders (hp/h = 0.25, 0.5, 0.75, and 1). Results are also compared with the limiting case of a solid cylinder (SVF = 1). The strong weakening of the antisymmetric vortex-shedding mode observed for submerged cases with hp/h ≤ 0.75 is related to the flow component advected over the array and the formation of a U-shaped vortex behind the array, which impedes the interactions of the two lateral (horizontal) SSLs forming on the sides of the array. For sufficiently high SVFs and high array submergence, the U-shaped vortex penetrates inside the array, which means that fluid and particles from the near wake can enter the array region. The decrease in hp/h reduces the coherence of the horseshoe vortex forming in front of the array, the length of the steady wake region, and the Strouhal number associated with the antisymmetric shedding mode. Simulation results show that billow vortices have a much reduced capacity to entrain and carry sediments in the wake of the array even for relatively low array submergences (e.g., for hp/h = 0.75) compared to hp/h = 1. The decrease in the mean streamwise drag coefficient for the cylinders in the array, [math], with the decrease in hp/h, is nearly linear for hp/h > 0.25. The rate of decay of [math] with the decrease in hp/h increases with the SVF. Using the simulation results, the paper also discusses how changes in the flow structure triggered by increased array submergence affect nutrient and sediment transport inside and around vegetated patches in natural erodible channels.