# Latest papers in fluid mechanics

### A numerical investigation of dynamics of bubbly flow in a ferrofluid by a self-correcting procedure-based lattice Boltzmann flux solver

In this work, the dynamics of bubbly flow in a dielectric ferrofluid under a uniform magnetic field has been numerically studied by a self-correcting procedure-based lattice Boltzmann flux solver. The investigation cases focus specifically on two bubbles merging and a single bubble rising in ferrofluid with a large density ratio under an applied uniform magnetic field. By accounting for the effects of the magnetic field intensity, susceptibility, Reynolds number, and Eotvos number, the mechanisms of bubble motion and deformation in the ferrofluid under the external magnetic field are analyzed.

### Oscillating grid turbulence in shear-thinning polymer solutions

Oscillating grid apparatuses are well known and convenient tools for the fundamental study of turbulence and its interaction with other phenomena since they allow to generate turbulence supposedly homogeneous, isotropic, and free of mean shear. They could, in particular, be used to study turbulence and mass transfer near the interface between non-Newtonian liquids and a gas, as already done in air-water situations. Although frequently used in water and Newtonian fluids, oscillating grid turbulence (OGT) generation has yet been rarely applied and never characterized in non-Newtonian media. The present work consists of a first experimental characterization of the flow properties of shear-thinning polymer (Xanthan Gum, XG) solutions stirred by an oscillating grid. Various polymer concentrations are tested for a single grid stirring condition. The dilute and semidilute entanglement concentration regimes are considered. Liquid phase velocities are measured by Particle Image Velocimetry. The existing mean flow established in the tank is described and characterized, as well as turbulence properties (intensity, decay rate, length scales, isotropy, etc.). OGT in dilute polymer solutions induces an enhanced mean flow compared to water, a similar decay behavior with yet different decay rates, and enhanced turbulence large scales and anisotropy. In the semidilute regime of XG, turbulence and mean flows are essentially damped by viscosity. The evolution of mean flow and turbulence indicators leads to the definition of several polymer concentration subregimes, within the dilute one. Critical concentrations around 20 ppm and 50 ppm are found, comparable to drag reduction characteristic concentrations.

### Flow structure around and heat transfer from cylinders modified from square to circular

This work aims at numerically investigating the influence of corner modification on the flow structure around and heat transfer from a square cylinder at a Reynolds number Re = 150 based on the cylinder width d and freestream velocity. The sharp corners of the square cylinder are rounded with r/d = 0 (square), 0.125, 0.25, 0.375, and 0.5 (circular), where r is the radius of the corner. The rounded corners have a profound effect on the flow structure from the perspective of flow separation, vortex strength, separation bubble, and wake bubble each playing a role in heat transfer from different surfaces of the cylinder. The boundary layer having a higher friction coefficient on the front and side surfaces leads to a higher local heat transfer. A shorter wake bubble renders a higher heat transfer from the rear surface. The increase in r/d from 0 to 0.5 leads to a 33% enhancement in the heat transfer from the cylinder. The enhancement largely results from a shrink in the wake bubble and an increase in vortex strength. The minimum time-mean drag and fluctuating forces are achieved at r/d = 0.25 and 0.125, respectively. The effect of r/d in various Reynolds averaged quantities is discussed.

### Numerical simulations of a stick-slip spherical particle in Poiseuille flow

The dynamics of a stick-slip “Janus” spherical particle suspended in a Newtonian fluid flowing in a cylindrical microchannel is studied by direct numerical simulations. Partial slip is imposed on half of the particle surface, whereas the no-slip boundary condition is present on the other half. The finite element method is used to solve the balance equations under creeping flow conditions. The translational and rotational velocities of the particle are evaluated at several orientations and distances from the tube centerline. The trajectories are then reconstructed by solving the kinematic equations where the velocities are taken by interpolating the simulation data. The particle dynamics is investigated by varying the initial position and orientation, the slip parameter, and the confinement ratio. The results, presented in terms of particle trajectories and phase portraits, highlight the existence of two relevant regimes: a periodic oscillation or a migration toward the tube axis for particle positions sufficiently far from or near the centerline, respectively. The basin of attraction of the tube axis grows with particle confinement and slip coefficient although the dynamics is qualitatively unaffected.

### Particles dispersion and deposition in inhomogeneous turbulent flows using continuous random walk models

The suitability of the normalized Langevin stochastic equation with appropriate drift correction for simulation of instantaneous fluctuation velocities in inhomogeneous turbulent flows was studied. The Reynolds Stress Transport turbulence model of the ANSYS-Fluent code was used to evaluate the inhomogeneous turbulent flow properties in a two-dimensional duct flow. The simulation results were then used in an in-house Matlab particle tracking code and the trajectories of about 2 × 105 randomly distributed particles in the channel were evaluated by solving the particle equation of motion including the drag and Brownian forces under the one-way coupling assumption. The performance of the Continuous Random Walk (CRW) stochastic model using the conventional nonnormalized, as well as the normalized Langevin equations without and with the drift term for predicting a uniform distribution for the fluid-tracer particles in an inhomogeneous turbulent flow was examined. The accuracy of these models in predicting the deposition velocities and distribution of solid particles with diameters ranging from 10 nm to 30 μm was also carefully examined. In addition, the effects of including the finite-inertia coefficient in the drift term and using the corrected root mean square normal velocity in the near-wall region on the accuracy of the results were emphasized. By exploring the concentration profiles and deposition velocities of particles resulting from different CRW models, it was concluded that the Normalized-CRW model including the appropriate drift term leads to the most accurate results.

### Experimental analysis of one-dimensional Faraday waves on a liquid layer subjected to horizontal vibrations

In this paper, we experimentally show the synchronous (harmonic) nature of the primary surface waves formed on a layer of water (∼1 mm) pinned to a glass substrate and subjected to horizontal (lateral) vibrations. With well-controlled experiments, we attenuated cross-waves and studied the primary standing waves in a one-dimensional wave configuration, with a high precision mechanical vibrator, capable of generating a range of forcing frequencies (100–500 Hz) and amplitudes (1–5 µm). We demonstrate that the emergence of instability (in the form of standing waves) depends upon the forcing amplitude and frequency and the average thickness of the liquid layer. Experiments reveal that the surface remains stable for sufficiently thin and thick layers of the liquid, while instability appears for thicknesses in between the two mentioned lower and upper limits. We show and analyze that, for the average liquid thickness of h = 1.5 mm, asymmetric modes of oscillations appear on the liquid surface; however, with a change in the film thickness and length of the surface profile, symmetric modes may occur as well (h = 2 mm). The problem studied here, i.e., a liquid film with pinned contact lines subjected to horizontal vibrations, shows some of the characteristics of an infinitely extended lateral liquid film, a liquid layer in a container with walls, and a sessile droplet.

### Geostrophic adjustment on the equatorial beta-plane revisited

The process of geostrophic adjustment of localized large-scale pressure anomalies in the standard adiabatic shallow-water model on the equatorial beta-plane is revisited, and it is shown that the standard scenario of generation of westward-moving Rossby and eastward-moving Kelvin waves, which underlies the classical Gill theory of tropical circulation due to a localized heating, is not unique. Depending on the strength and aspect ratio of the initial perturbation, the response to the initial perturbation in the western sector can be dominated by inertia-gravity waves. The adjustment in the diabatic moist-convective shallow water model can be totally different and produces, depending on parameters, either Gill-like response or eastward-moving coherent dipolar structures of the type of equatorial modons, which do not appear in the “dry” adjustment, or vortices traveling, respectively, northwest in the Northern and southwest in the Southern hemispheres.

### Instability of a smooth shear layer through wave interactions

Wave interaction theory can be used as a tool to understand and predict instability in a variety of homogeneous and stratified shear flows. It is, however, most often limited to piecewise-linear profiles of the shear layer background velocity, in which stable vorticity wave modes can be easily identified and their interaction quantified. This approach to understanding shear flow instability is extended herein to smooth shear layer profiles. We describe a method, by which the stable vorticity wave modes can be identified, and show that their interaction results in an excellent description of the stability properties of the smooth shear layer, thus demonstrating the presence of the wave interaction mechanism in smooth shear flows.

### Analytical prediction of electrowetting-induced jumping motion for droplets on hydrophobic substrates

Electric voltage applied in electrowetting can induce spreading of a liquid droplet on solid substrates and yield significant contact angle reduction, which has been widely used for manipulating individual droplets in microfluidics and lab-on-a-chip devices, and even for creating jumping motion of droplets. Here, we present a theoretical closed-form expression of lift-off velocity to predict electrowetting-induced jumping motion of a droplet on hydrophobic substrates. In particular, we consider a liquid droplet wetting on a hydrophobic surface with a voltage applied between the droplet and the substrate. By turning off the applied voltage, the energy stored in the droplet deformation by electrowetting releases and may be sufficient to overcome the energy barrier for detachment. Based on the energy conservation of the droplet-substrate system, we derive a closed-form formula to predict the droplet jumping velocity in terms of the Young contact angle, the Lippmann-Young contact angle, and the Ohnesorge number. The validity of the theoretical prediction is confirmed by comparing the predicted jumping velocities with both experimental observations and numerical simulations. The predictive formula indicates that the jumping motion can be enhanced by increasing the Young contact angle and decreasing the Lippmann-Young contact angle or the Ohnesorge number. Also, a phase diagram of droplet jumping motion is constructed based on this model, which provides insights on accurate control of the electrowetting-induced jumping motion of droplets on hydrophobic surfaces.

### Simulation of microparticle inhalation in rhesus monkey airways

Author(s): Taylor S. Geisler, Madhu V. Majji, Jana S. Kesavan, Valerie J. Alstadt, Eric S. G. Shaqfeh, and Gianluca Iaccarino

Large-eddy simulation is used to study turbulent airflow in anatomically accurate rhesus macaque airways along with the transport of microparticles in the flow. Microparticle deposition predictions are compared with model experiments in the same computed-tomography-based airways.

[Phys. Rev. Fluids 4, 083101] Published Fri Aug 09, 2019

### Dynamics of a helical swimmer crossing an interface between two immiscible fluids

Author(s): Jorge Gonzalez-Gutierrez, Salvador Osorio-Ramirez, Francisco J. Solorio-Ordaz, and Roberto Zenit

Laboratory experiments were conducted with synthetic magnetic helical swimmers to study the dynamics of crossing the interface between two immiscible fluids. This system aims to emulate the process through which bacteria are capable of penetrating mucus layers or membranes to cause infections.

[Phys. Rev. Fluids 4, 083102] Published Fri Aug 09, 2019

### Vortical and thermal interfacial layers in wall-bounded turbulent flows under transcritical conditions

Author(s): Matthew X. Yao, Zeping Sun, Carlo Scalo, and Jean-Pierre Hickey

Evidence of the presence of vortical and thermal interfacial layers in transcritical turbulent channel flow is presented. These interfaces are tied to the uniform momentum zones. In an analogous manner, uniform thermal zones are defined and characterized in these complex flows.

[Phys. Rev. Fluids 4, 084604] Published Fri Aug 09, 2019

### Large-scale characteristics of stratified wake turbulence at varying Reynolds number

Author(s): Qi Zhou and Peter J. Diamessis

Simulations of large-Reynolds-number stratified wakes reveal dynamics of a strongly stratified regime where thin flow layers form under stratification. Shear instabilities develop between the layers and drive turbulence. The ability to predict whether this novel regime is accessible in a wake of given parameters is demonstrated.

[Phys. Rev. Fluids 4, 084802] Published Fri Aug 09, 2019

### Three-dimensional shock interactions and vortices on a V-shaped blunt leading edge

The three-dimensional flow on a plate with a V-shaped blunt leading edge (VsBLEP) is investigated numerically and experimentally at a freestream Mach number 6. A complex saddle-shaped shock front is observed on this VsBLEP under the interactions between the detached shock (DS) induced by the swept blunt leading edge and the bow shock (BS) induced by the crotch. It is demonstrated that a new type of spatial transition exists on this saddle-shaped shock front, which involves the transition of shock interactions (i.e., DS and BS) from the same family upstream of the crotch to opposite families downstream of the crotch. Moreover, this transition is quantitatively identified according to the shock-induced spanwise velocity along the inflection line between DS and BS, which is of great importance because it affects the crossflow significantly. The inward crossflow induced by the swept blunt leading edge is enhanced in the region where the DS and BS are from the same family, and the shear layers generated in this region converge gradually to the spanwise symmetry plane, which results in the formation of a streamwise counter-rotating vortex pair (CVP). In the region where the DS and BS turn to opposite families, the inward crossflow is eliminated, and a five-shock structure is identified downstream of the crotch. The CVP remains close to the spanwise symmetry plane as it trails downstream, showing a far-reaching influence on the flowfield. This study indicates that the V-shaped blunt leading edge affects the downstream flow significantly and therefore should be examined carefully in practical applications, such as in the design of an inlet cowl lip.

### Cell trapping in Y-junction microchannels: A numerical study of the bifurcation angle effect in inertial microfluidics

The majority of microfluidic technologies for cell sorting and isolation involve bifurcating (e.g., Y- or T-shaped junction) microchannels to trap the cells of a specific type. However, the microfluidic trapping efficiency remains low, independently of whether the cells are separated by a passive or an active sorting method. Using a custom computational algorithm, we studied the migration of separated deformable cells in a Y-junction microchannel, with a bifurcation angle ranging from 30° to 180°. Single or two cells of initially spherical shape were considered under flow conditions corresponding to inertial microfluidics. Through the numerical simulation, we identified the effects of cell size, cytoplasmic viscoelasticity, cortical tension, flow rate, and bifurcation angle on the critical separation distance for cell trapping. The results of this study show that the trapping and isolation of blood cells, and circulating tumor cells in a Y-junction microchannel was most efficient and least dependent on the flow rate at the bifurcation angle of 120°. At this angle, the trapping efficiency for white blood cells and circulating tumor cells increased, respectively, by 46% and 43%, in comparison with the trapping efficiency at 60°. The efficiency to isolate invasive tumor cells from noninvasive ones increased by 32%. This numerical study provides important design criteria to optimize microfluidic technology for deformability-based cell sorting and isolation.

### Viscoelastic film flows over an inclined substrate with sinusoidal topography. I. Steady state

Author(s): D. Pettas, G. Karapetsas, Y. Dimakopoulos, and J. Tsamopoulos

Fluid elasticity opposes inertia, creating a static hump and a cusp ahead of it on the film free surface. Nonlinear phenomena, such as resonance of the liquid film with the bottom undulations, are intensified or suppressed by the presence of shear-thinning and elasticity.

[Phys. Rev. Fluids 4, 083303] Published Thu Aug 08, 2019

### Viscoelastic film flows over an inclined substrate with sinusoidal topography. II. Linear stability analysis

Author(s): D. Pettas, G. Karapetsas, Y. Dimakopoulos, and J. Tsamopoulos

Stability to linear disturbances of arbitrary wavelength is studied using Floquet theory. Fluid elasticity stabilizes the flow and creates a small window where all disturbances are damped at supercritical conditions. Shear-thinning is destabilizing and may generate disturbances of wavelength shorter than that of the geometry.

[Phys. Rev. Fluids 4, 083304] Published Thu Aug 08, 2019

### Segmented flows of viscous threads in microchannels

Author(s): Thomas Cubaud

Hydrodynamic interactions between droplets and high-viscosity fluid threads are investigated in microchannels. A complementary approach is adopted where the thread size is varied for diverse droplet concentrations to help reveal a range of basic fluid structures.

[Phys. Rev. Fluids 4, 084201] Published Thu Aug 08, 2019

### Assessing the nonequilibrium of decaying turbulence with reversed initial fields

Author(s): F. Liu (刘锋), L. P. Lu (陆利蓬), Wouter J. T. Bos, and L. Fang (方乐)

Reversed initial fields can generate nonequilibrium decaying turbulence. During the short time interval when the reversed flow reorganizes to restore its energy cascade, a new dissipation scaling is observed, Cε∼Reλ−2, for a nonequilibrium transient with rapidly evolving dissipation.

[Phys. Rev. Fluids 4, 084603] Published Thu Aug 08, 2019

### Conditional dynamic subfilter modeling

A novel “conditional” variation of the dynamic approach for modeling of large eddy simulation subfilter terms is derived and tested. In contrast to the traditional dynamic closure, which stabilizes “raw” dynamic coefficients by averaging across ensembles of expected statistical homogeneity, the novel variation averages conditionally on some set of scalars whose local values are expected to correlate with the local degree of turbulence. Simulations of a nonpremixed jet flame show that the conditional dynamic model is both tractable and stable and produces predictions which are essentially indistinguishable from the traditional dynamic closure, although both models give suboptimal predictions. Future work could potentially improve the predictions of both models—facilitating a fairer comparison—by considering a more uniform or “pancake-like” grid.