# Latest papers in fluid mechanics

### Transport of flexible fibers in confined microchannels

Author(s): Jean Cappello, Mathias Bechert, Camille Duprat, Olivia du Roure, François Gallaire, and Anke Lindner

The deformation of a flexible fiber transported perpendicularly in a plug flow in a confining microchannel is studied using experiments and numerical simulations. The fiber deflection, resulting from an inhomogeneous force distribution, is a function of an elastoviscous number and fiber confinement.

[Phys. Rev. Fluids 4, 034202] Published Tue Mar 05, 2019

### Orientation dynamics of nonspherical particles under surface gravity waves

Author(s): Michelle H. DiBenedetto, Jeffrey R. Koseff, and Nicholas T. Ouellette

Nonspherical particles in the ocean are relevant to phenomena such as microplastics, plankton and sediment. Experimental results of the orientation dynamics of nonspherical particles in waves find competition between the waves and the inertial effects on particle orientation.

[Phys. Rev. Fluids 4, 034301] Published Tue Mar 05, 2019

### Linear and nonlinear regimes of an inertial wave attractor

Author(s): Maxime Brunet, Thierry Dauxois, and Pierre-Philippe Cortet

We report an experimental study of the nonlinear regime of an inertial wave attractor revealing the emergence of a triadic resonance instability with singular features. The attractor properties are shown to be well described by introducing a turbulent viscosity in the linear attractor model.

[Phys. Rev. Fluids 4, 034801] Published Tue Mar 05, 2019

### Excitation and resonant enhancement of axisymmetric internal wave modes

Author(s): S. Boury, T. Peacock, and P. Odier

Inspired by geophysical phenomena, such as storm generated internal waves in the ocean, an experimental study is performed using an axisymmetric internal wave generator. Radial and vertical confinement lead to Bessel-shaped standing waves and resonance effects caused by multiple cavity reflections.

[Phys. Rev. Fluids 4, 034802] Published Tue Mar 05, 2019

### Effects of subcavity in supersonic cavity flow

An experimental and numerical study is conducted on a rectangular open cavity with a length to depth ratio of 2 at Mach number 1.71 by placing a subcavity at different locations. The subcavity at the front wall has already been established as a passive control device experimentally. In addition, it has been observed that it can act as a passive resonator. However, in the current study, it is found that the location of the subcavity and its dimensions play a crucial role in determining the types of oscillations existing inside the cavity. Cavity models with a subcavity length to main cavity length of 0.2 (l/L = 0.20) were investigated by placing the subcavity at the front wall, aft wall, and simultaneously at both front and aft walls. High speed schlieren visualization revealed the presence of different shock features associated with the cavity flow field. Statistical techniques such as fast Fourier transform, spectrogram, coherence, and correlation are employed to analyze the unsteady pressure data. Numerical computations are carried out to validate the experimental results and also to explore the flow physics. The front wall subcavity acts as a passive control device with a maximum reduction of 34.1 dB in the sound pressure level for the most dominant tone, and there is also a notable reduction in the overall sound pressure level by 11.7 dB. In the case of front wall subcavity, the acoustic wave gets inclined as it interacts with the subcavity, thereby displacing the shear layer to form a dome-shaped structure. The aft wall subcavity acts as a passive resonator with distinct fluid-resonant oscillations and the respective modal frequencies differ widely from those predicted using Rossiter’s expression. The shear layer interacts with a recirculation region formed inside the subcavity at the aft wall, thereby mitigating the effect due to direct impingement of the shear layer on the aft wall. The subcavity at both walls acts as a passive suppression device with a reduction of 34.9 dB in the sound pressure level for the most dominant mode and also with a reduction of 14.5 dB in the overall sound pressure level.

### Epistemic uncertainty quantification for Reynolds-averaged Navier-Stokes modeling of separated flows over streamlined surfaces

It is well known that linear eddy-viscosity turbulence models can introduce uncertainty in predictions for complex flow features such as separation and reattachment. The goal of this paper is to advance our understanding of a physics-based approach to quantify this turbulence model form uncertainty in Reynolds-averaged Navier-Stokes simulations of separated flows over streamlined surfaces. The methodology is based on perturbing the modeled Reynolds stresses in the momentum equations; perturbations are defined in terms of a decomposition of the Reynolds stress tensor, i.e., based on the tensor magnitude and the eigenvalues and eigenvectors of the normalized anisotropy tensor. We demonstrate that the accuracy of the predicted Reynolds stress magnitude is strongly influenced by the turbulence production term and subsequently explore the anisotropy tensor eigenvalue and eigenvector perturbations that maximize or minimize turbulence production; these could be expected to provide bounds on the prediction of separation and reattachment locations. The method uses two user-defined parameters to identify the spatial extent of the perturbed region and the magnitude of the eigenvalue perturbations. Results for the flow over a periodic wavy wall and over a three-dimensional hill indicate that the perturbations that increase turbulence production decrease the extent of the separation region, while perturbations that decrease production increase the region of separated flow. The predicted bounds can successfully encompass the reference data, provided the extent of the perturbed region and the eigenvalue perturbation magnitudes are sufficiently large. Importantly, we observed a monotonic behavior of the magnitude of the predicted bounds as a function of the two user-defined parameters.

### Contraction flow of ionomers and their corresponding copolymers: Ionic and hydrogen bonding effects

The contraction flow of several commercial ionomer melts and their corresponding copolymers was studied numerically using a viscoelastic integral constitutive model developed by Kaye and Bernstein, Kearsley, and Zapas, known as the K-BKZ model. First a detailed rheological characterization was performed to calculate the parameters of the K-BKZ model used in the flow simulations. The effects of ionic and hydrogen bonding associations have been studied on the entry pressure drop, on the corner vortex in the capillary contraction, as well as on the vortex strength. In all cases, the ionomers exhibit much more significant effects compared to their copolymers, the more so as the number of ionic associations present in their backbone increases. This is due to strong ionic associations present in the ionomers that give rise to strong strain hardening effects important in entry flows. Compared to ionic associations, the effects of hydrogen bonds are insignificant particularly at levels less than 5 mol. %.

### Effects of magnetic nanoparticles on mixing in droplet-based microfluidics

High-throughput, rapid and homogeneous mixing of microdroplets in a small length scale such as that in a microchannel is of great importance for lab-on-a-chip applications. Various techniques for mixing enhancement in microfluidics have been extensively reported in the literature. One of these techniques is the mixing enhancement with magnetofluidics using ferrofluid, a liquid with dispersed magnetic nanoparticles. However, a systematic study exploring the mixing process of ferrofluid and its influencing parameters is lacking. This study numerically examines the effect of key parameters including magnetic field, mean velocity, and size of a microdroplet on the mixing process. A microfluidic double T-junction with droplets in merging regime is considered. One of the dispersed phases is a ferrofluid containing paramagnetic nanoparticles, while the other carried neutral species. Under an applied magnetic field, the ferrofluid experiences a magnetic force that in turn induces a secondary bulk flow called magnetoconvection. The combination of the induced magnetoconvection and shear-driven circulating flow within a moving droplet improves the mixing efficiency remarkably. Mixing enhancement is maximized for a specific ratio between the magnetic force and the shear force. The dominance of either force would deteriorate the mixing performance. On the other hand, using a magnetic force and a shear force with comparable order of magnitude leads to an effective manipulation of vortices inside the droplet and subsequently causes an optimized particle distribution over the entire droplet. Furthermore, the smaller the droplets, the better the mixing.

### Order in polymeric liquids under oscillatory shear flow

We examine the second order orientation tensor for the simplest molecular model relevant to a polymeric liquid in large-amplitude oscillatory shear (LAOS) flow, the rigid dumbbell suspension. For this, we use an approximate solution to the diffusion equation for rigid dumbbells, an expansion for the orientation distribution function truncated after the fourth power of the shear rate amplitude. We then calculate the second order orientation tensor, and then use this to calculate the order parameter tensor. We next examine the invariants of both the second order orientation tensor and the order parameter tensor. From the second invariant of the order parameter tensor, we calculate the scalar, the nematic order, and examine its evolution for a polymeric liquid in LAOS. We find this nematic order, our main result, to be even. We use Lissajous figures to illustrate the roles of the Weissenberg and Deborah numbers on the evolving order in LAOS. We use the low frequency limit of our main result to arrive at an expression for the nematic order in steady shear flow. Our work gives a first glimpse into macromolecular order in LAOS. Our work also provides analytical benchmarks for numerical solutions to the diffusion equation for both oscillatory and steady shear flows.

### Power series for normal stress differences of polymeric liquids in large-amplitude oscillatory shear flow

Exact solutions for normal stress differences in polymeric liquids subjected to large-amplitude oscillatory shear flow (LAOS) contain many Bessel functions, each appearing in infinite sums. For the simplest relevant model of a polymeric liquid, the corotational Maxwell fluid, Bessel functions appear 38 times in the exact solution. By relevant, we mean that higher harmonics are predicted in LAOS. By contrast, approximate analytical solutions for normal stress differences in LAOS often take the form of the first few terms of a power series in the shear rate amplitude, and without any Bessel functions at all. Perhaps the best example of this, from continuum theory, is the Goddard integral expansion (GIE) that is arrived at laboriously. There is thus practical interest in extending the GIE to an arbitrary number of terms. However, each term in the GIE requires much more work than its predecessor. For the corotational Maxwell fluid, for instance, the GIE for the normal stress differences has yet to be taken beyond the fifth power of the shear rate amplitude. In this paper, we begin with the exact solution for normal stress difference responses in corotational Maxwell fluids, then perform an expansion by symbolic computation to confirm up to the fifth power, and then to continue the GIE. In this paper, for example, we continue the GIE to the 41st power of the shear rate amplitude. We use Ewoldt grids to show that our main result is highly accurate. We also show that, except in its zero-frequency limit, the radius of convergence of the GIE is infinite. We derive the pattern for the common denominators of the GIE coefficients and also for every numerator for the zeroth harmonic coefficients. We also find that the numerators of the other harmonics appear to be patternless.

### Reduced-order modeling of left ventricular flow subject to aortic valve regurgitation

The present focus of heart flow studies is largely based on flow within the left ventricle and how this flow changes when subject to disease. However, despite recent advancements, a simple tractable model of even healthy left ventricular flow has not been produced and made available. Reduced-order modeling techniques, such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), offer an effective means of expressing the large datasets obtained from experiments or numerical simulations using low-dimensional models. While POD and DMD are often used to identify coherent structures in fluid dynamics, their use as a modeling tool has not found much merit in the cardiovascular flow community. In this work, we use POD and DMD to construct reduced-order models for a healthy left ventricular flow as well as for that under the influence of a particular disease shown to exhibit rich and unique intraventricular fluid dynamics, namely, aortic regurgitation (a leaking aortic valve). The performance of the two methods in reconstructing the intraventricular flows and derived quantities is evaluated, and the selected reduced-order models are made available.

### Is Tollmien-Schlichting wave necessary for transition of zero pressure gradient boundary layer flow?

Comprehensive understanding of the routes of instability and transition for many flows is not complete yet. For a zero pressure gradient (ZPG) boundary layer, linear spatial theory predicted Tollmien-Schlichting (TS) waves, which have been experimentally verified by vortically exciting the flow by a monochromatic source. This is the well-known frequency response of dynamical system theory. Natural transition in real flows occurs due to polychromatic excitation, and to simulate such transition, the ZPG boundary layer has been excited via an impulse response in some of our recent direct numerical simulations. Such impulse responses cause transition even when TS waves are not excited. In the present exercise, we show the theoretical basis of natural transition by spatiotemporal stability analysis, as used in the work of Sengupta et al. [“Spatiotemporal growing wave fronts in spatially stable boundary layers,” Phys. Rev. Lett. 96(22), 224504 (2006)], by invoking finite start-up of the frequency response to wall excitation. There appear to be different instability mechanisms active for the frequency and the impulse responses to localized wall excitation. Here, we show that in both the frequency and impulse responses, the spatiotemporal wave-front (STWF) is the common element. Additionally, we also consider cases, where following different start-ups, the wall excitation remains constant, which also show the presence of the STWF. The presented results for the ZPG boundary layer show that the TS wave is not necessary for transition to turbulence and help us to re-evaluate our understanding of the transition mechanism for this canonical flow.

### Dynamics of supernova bounce in laboratory

Author(s): S. I. Blinnikov, R. I. Ilkaev, M. A. Mochalov, A. L. Mikhailov, I. L. Iosilevskiy, A. V. Yudin, S. I. Glazyrin, A. A. Golubev, V. K. Gryaznov, and S. V. Fortova

We draw attention to recent high-explosive (HE) experiments which provide compression of macroscopic amount of matter to high, even record, values of pressure in comparison with other HE experiments. The observed bounce after the compression corresponds to processes in core-collapse supernova explos...

[Phys. Rev. E 99, 033102] Published Mon Mar 04, 2019

### Convective flow in the presence of a small obstacle: Symmetry breaking, attractors, hysteresis, and information

Author(s): S. J. Bartlett and Y. L. Yung

This work explores the stability and hysteresis effects that occur when a small sink of momentum is introduced into a heat-driven, two-dimensional convective flow. As per standard fluid mechanical intuition, the system minimizes work generation and dissipation when one component of momentum is extra...

[Phys. Rev. E 99, 033103] Published Mon Mar 04, 2019

### Onset of intermittency in stochastic Burgers hydrodynamics

Author(s): G. B. Apolinário, L. Moriconi, and R. M. Pereira

We study the onset of intermittency in stochastic Burgers hydrodynamics, as characterized by the statistical behavior of negative velocity gradient fluctuations. The analysis is based on the response functional formalism, where specific velocity configurations—the *viscous instantons*—are assumed to p...

[Phys. Rev. E 99, 033104] Published Mon Mar 04, 2019

### Wavelength selection of vortex ripples in an oscillating cylinder: The effect of curvature and background rotation

Author(s): M. Duran-Matute, M. D. van Gorp, and G. J. F. van Heijst

We present results of laboratory experiments on the formation, evolution, and wavelength selection of vortex ripples. These ripples formed on a sediment bed at the bottom of a water-filled oscillating cylindrical tank mounted on top of a rotating table. The table is made to oscillate sinusoidally in...

[Phys. Rev. E 99, 033105] Published Mon Mar 04, 2019

### Effects of trailing edge shape on vortex formation by pitching panels of small aspect ratio

Author(s): Arman Hemmati, Tyler Van Buren, and Alexander J. Smits

A study examines wake dynamics for oscillating foils with different trailing edges and relates them to unsteady propulsive performance of the foil. It also connects the main wake features to surface pressure fluctuations on both faces of the foil during an oscillatory period.

[Phys. Rev. Fluids 4, 033101] Published Mon Mar 04, 2019

### Vibration-induced thermal instabilities in supercritical fluids in the absence of gravity

Author(s): Deewakar Sharma, Arnaud Erriguible, Gurunath Gandikota, Daniel Beysens, and Sakir Amiroudine

Supercritical fluids when subjected to vibrations in the direction parallel and normal to the interface lead to Rayleigh-vibrational and parametric instabilities. These instabilities arise in the thermal boundary layer as a result of strong thermomechanical coupling.

[Phys. Rev. Fluids 4, 033401] Published Mon Mar 04, 2019

### Thermocapillary and electrohydrodynamic effects on the stability of dynamic contact lines

Author(s): Devin T. Conroy, Leonardo Espín, Omar K. Matar, and Satish Kumar

Electric fields and temperature fields significantly modify the stability of dynamic contact lines. Electric fields enhance the growth of transverse perturbations, whereas temperature fields can enhance or suppress growth depending on the direction of the temperature gradient.

[Phys. Rev. Fluids 4, 034001] Published Mon Mar 04, 2019

### Steady flow regimes and mixing performance in arrow-shaped micro-mixers

Author(s): A. Mariotti, C. Galletti, E. Brunazzi, and M. V. Salvetti

The steady flow regimes and mixing performances of arrow-like micro-mixers are investigated experimentally and by DNS for varying Re and tilting angles. Arrow-mixers trigger mixing at lower Re than for T-mixers, but for large tilting angles mixing does not increase monotonically with Re.

[Phys. Rev. Fluids 4, 034201] Published Mon Mar 04, 2019