# Latest papers in fluid mechanics

### Coriolis force-driven instabilities in stratified miscible layers on a rotationally actuated microfluidic platform

Author(s): Saunak Sengupta, Sukhendu Ghosh, Sandeep Saha, and Suman Chakraborty

We find unique perturbations in rotational flows because of flow instabilities.

[Phys. Rev. Fluids 4, 113902] Published Wed Nov 13, 2019

### Resolution-induced anisotropy in large-eddy simulations

Author(s): Sigfried W. Haering, Myoungkyu Lee, and Robert D. Moser

Large eddy simulation (LES) of complex geometries often require discretization with high aspect ratio cells which can cause loss of simulation fidelity. We examine the effects of anisotropic resolution in LES and propose a tensor eddy viscosity to directly address resolution anisotropy.

[Phys. Rev. Fluids 4, 114605] Published Wed Nov 13, 2019

### Rotating magnetic nanorods detect minute fluctuations of magnetic field

Author(s): Vaibhav Palkar, Pavel Aprelev, Arthur Salamatin, Artis Brasovs, Olga Kuksenok, and Konstantin G. Kornev

Magnetic nanorods rotating in a viscous liquid are very sensitive to any ambient magnetic field. We theoretically predicted and experimentally validated the conditions for two-dimensional synchronous and asynchronous rotation as well as three-dimensional precession and tumbling of nanorods in an amb...

[Phys. Rev. E 100, 051101(R)] Published Wed Nov 13, 2019

### Internal flow properties in a capillary bore

In this work, a detailed description of the internal flow field in a collapsing bore generated on a slope in a wave flume is given. It is found that in the case at hand, just prior to breaking, the shape of the free surface and the flow field below are dominated by capillary effects. While numerical approximations are able to predict the development of the free surface as it shoals on the laboratory beach, the internal flow field is poorly predicted by standard numerical models.

### Cross-stream migration and coalescence of droplets in a microchannel co-flow using magnetophoresis

Manipulation of aqueous droplets in microchannels has great significance in various emerging applications such as biological and chemical assays. Magnetic-field based droplet manipulation that offers unique advantages is consequently gaining attention. However, the physics of magnetic field-driven cross-stream migration and the coalescence of aqueous droplets with an aqueous stream are not well understood. Here, we unravel the mechanism of cross-stream migration and the coalescence of aqueous droplets flowing in an oil based ferrofluid with a coflowing aqueous stream in the presence of a magnetic field. Our study reveals that the migration phenomenon is governed by the advection (τa) and magnetophoretic (τm) time scales. Experimental data show that the dimensionless equilibrium cross-stream migration distance δ* and the length [math] required to attain equilibrium cross-stream migration depend on the Strouhal number, St = (τa/τm), as δ* = 1.1 St0.33 and [math], respectively. We find that the droplet-stream coalescence phenomenon is underpinned by the ratio of the sum of magnetophoretic (τm) and film-drainage time scales (τfd) and the advection time scale (τa), expressed in terms of the Strouhal number (St) and the film-drainage Reynolds number (Refd) as ξ = (τm + τfd)/τa = (St−1 + Refd). Irrespective of the flow rates of the coflowing streams, droplet size, and magnetic field, our study shows that droplet-stream coalescence is achieved for ξ ≤ 50 and ferrofluid stream width ratio w* < 0.7. We utilize the phenomenon and demonstrated the extraction of microparticles and HeLa cells from aqueous droplets to an aqueous stream.

### Similarities between the structure functions of thermal convection and hydrodynamic turbulence

In this paper, we analyze the scaling of velocity structure functions of turbulent thermal convection. Using high-resolution numerical simulations, we show that the structure functions scale similar to those of hydrodynamic turbulence, with the scaling exponents in agreement with the predictions of She and Leveque [“Universal scaling laws in fully developed turbulence,” Phys. Rev. Lett. 72, 336–339 (1994)]. The probability distribution functions of velocity increments are non-Gaussian with wide tails in the dissipative scales and become close to Gaussian in the inertial range. The tails of the probability distribution follow a stretched exponential. We also show that in thermal convection, the energy flux in the inertial range is less than the viscous dissipation rate. This is unlike in hydrodynamic turbulence where the energy flux and the dissipation rate are equal.

### Efficient implementation of elastohydrodynamics via integral operators

Author(s): A. L. Hall-McNair, T. D. Montenegro-Johnson, H. Gadêlha, D. J. Smith, and M. T. Gallagher

Many systems in physics and life sciences are characterised by microscopic flexible fibers interacting through viscous flow. We describe an efficient modeling framework taking into account nonlocal interactions, applied to sedimenting and shear flows with multiple fibers, and flagellar propulsion.

[Phys. Rev. Fluids 4, 113101] Published Tue Nov 12, 2019

### Unidirectional large-amplitude oscillatory shear flow of human blood

Blood is a non-Newtonian suspension of red and white cells, platelets, fibrinogen, and cholesterols in Newtonian plasma. To assess its non-Newtonian behaviors, this work considers a newly proposed blood test, unidirectional large-amplitude oscillatory shear flow (udLAOS). In the laboratory, we generate this experiment by superposing LAOS onto steady shear flow in such a way that the shear rate never changes sign. It is thus intended to best represent the unidirectional pulsatile flow in veins and arteries. To model human blood, we consider the simplest model that can predict infinite-shear viscosity, the corotational Jeffreys fluid. We arrive at an exact analytical expression for the shear stress response of this model fluid. We discover fractional harmonics comprising the transient part of the shear stress response and both integer and fractional harmonics, the alternant part. By fractional, we mean that these occur at frequencies other than integer multiples of the superposed oscillation frequency. We generalize the corotational Jeffreys fluid to multimode to best represent three blood samples from three healthy but different donors. To further improve our model predictions, we consider the multimode Oldroyd 8-constant framework, which contains the corotational Jeffreys fluid as a special case. In other words, by advancing from the multimode corotational Jeffreys fluid to the multimode Oldroyd 8-constant framework, five more model parameters are added, yielding better predictions. We find that the multimode corotational Jeffreys fluid adequately describes the steady shear viscosity functions measured for three different healthy donors. We further find that adding two more specific nonlinear constants to the multimode corotational Jeffreys fluid also adequately describes the behaviors of these same bloods in udLAOS. This new Oldroyd 5-constant model may find usefulness in monitoring health through udLAOS.

### Graeme A. Bird

### Graeme A. Bird

### Effect of base-state curvature on self-excited high-frequency oscillations in flow through an elastic-walled channel

Author(s): Thomas J. Ward and Robert J. Whittaker

We derive a new “tube law” for elastic-walled channels, which takes into account the axial stretching that arises because of axial curvature in the base state. We quantify the effect of the new law on oscillatory fluid-structure-interaction modes in the channel and their stability.

[Phys. Rev. Fluids 4, 113901] Published Mon Nov 11, 2019

### Contact line depinning from sharp edges

Author(s): J. Graña-Otero and I. E. Parra Fabián

Precise mathematical criteria for contact line depinning from sharp corners is derived using a variational formulation and turning point arguments. The application of these results to the analysis of the stability of nonwetting equilibria on superhydrophobic surfaces is also briefly addressed.

[Phys. Rev. Fluids 4, 114001] Published Mon Nov 11, 2019

### Logarithmic-layer turbulence: A view from the wall

Author(s): Miguel P. Encinar and Javier Jiménez

The observability of the flow away from the wall in turbulent channels is studied using noiseless, although potentially incomplete, wall measurements. The reconstructions deteriorate with the distance to the wall, but coherent motions are still observable.

[Phys. Rev. Fluids 4, 114603] Published Mon Nov 11, 2019

### Dependence of the drag over superhydrophobic and liquid infused surfaces on the asperities of the substrate

Author(s): Edgardo J. García-Cartagena, Isnardo Arenas, Jaehyeong An, and Stefano Leonardi

We perform direct numerical simulations of turbulent channel flow with superhydrophobic or liquid infused surfaces on the lower wall. The texture reproduces etched sand-blasted aluminum. Dependence of the amount of drag reduction on interface deformation and pinnacle height distribution is discussed.

[Phys. Rev. Fluids 4, 114604] Published Mon Nov 11, 2019

### Lagrangian coherent sets in turbulent Rayleigh-Bénard convection

Author(s): Christiane Schneide, Martin Stahn, Ambrish Pandey, Oliver Junge, Péter Koltai, Kathrin Padberg-Gehle, and Jörg Schumacher

Coherent circulation rolls and their relevance for the turbulent heat transfer in a two-dimensional Rayleigh-Bénard convection model are analyzed. The flow is in a closed cell of aspect ratio four at a Rayleigh number Ra=106 and at a Prandtl number Pr=10. Three different Lagrangian analysis techniqu...

[Phys. Rev. E 100, 053103] Published Mon Nov 11, 2019

### Flow analysis of a shock wave at pulse ionization: Riemann problem implementation

An experimental study of the plasma-gas dynamic fluid formed after pulse ionization of the gas flow with a plane shock wave with Mach number 2.2–4.8 is carried out. Nanosecond volume discharge with UV preionization was switched on when the shock moved in a tube channel test section. Energy input occurs in the low-pressure gas volume separated by the shock surface within a time less than 200–300 ns; a single shock wave breaks into three discontinuities in accordance with the 1D Riemann problem solution. The initial (plasma-dynamic) stage of the flow in the nanosecond time range is visualized by glow recording; the supersonic gas processes in the microsecond time range are recorded using high-speed shadow imaging. Quantitative information about the dynamics of the shocks and contact surface (plots of horizontal distance) was obtained within time up to 25 µs. A region with an increased gas-discharge plasma glow intensity, after the discharge electric current termination, was recorded in the time interval from 0.3 to 1.5 µs; it was explained by a jump in gas temperature and density between the new shock wave and the contact discontinuity.

### In-depth description of electrohydrodynamic conduction pumping of dielectric liquids: Physical model and regime analysis

In this work, we discuss the fundamental aspects of Electrohydrodynamic (EHD) conduction pumping of dielectric liquids. We build a mathematical model of conduction pumping that can be applied to all sizes, down to microsized pumps. In order to do this, we discuss the relevance of the Electrical Double Layer (EDL) that appears naturally on nonmetallic substrates. In the process, we identify a new dimensionless parameter related to the value of the zeta potential of the substrate-liquid pair, which quantifies the influence of these EDLs on the performance of the pump. This parameter also describes the transition from EHD conduction pumping to electro-osmosis. We also discuss in detail the two limiting working regimes in EHD conduction pumping: ohmic and saturation. We introduce a new dimensionless parameter, accounting for the electric field enhanced dissociation that, along with the conduction number, allows us to identify in which regime the pump operates.

### Eulerian conditional statistics of turbulent flow in a macroscale multi-inlet vortex chemical reactor

The conditional velocity time averages (⟨Ui|ξ⟩) and conditional mixture fraction time averages (⟨Φ|ωi⟩) were computed based on the Eulerian approach from the experimental data measured in a macroscale multi-inlet vortex chemical reactor. The conditioning events were determined by equally sized intervals of the sample space variable for the mixture fraction (ξ) and the velocity vector (ωi). The experimental data, which consisted of instantaneous velocities and concentration fields for two Reynolds numbers (Re = 3250 and 8125), were acquired using the simultaneous stereoscopic particle image velocimetry (stereo-PIV) and planar laser induced fluorescence techniques. Two mathematical models, the linear approximation and probability density function (PDF) gradient diffusion, were validated by experimental results. The results of the velocity conditioned on the mixture fraction demonstrated that the linear model works well in a low turbulence region away from the reactor center. Near the reactor center, high velocity gradients coupled with low concentration gradients reduce the accuracy of the linear model predictions. Nevertheless, an excellent agreement was found for the conditional events within ±2Φrms (mixture fraction root mean square). Due to lower concentration gradient in the tangential direction, the linear model better predicted the tangential velocity component for all locations investigated. The PDF model with an isotropic turbulent diffusivity performed inadequately for the tangential and axial velocity components. A modified version of the PDF model that considers the three components of the turbulent diffusivity produced a better agreement with the experimental data especially in the spiral arms regions of significant concentration gradients. Furthermore, the mixture fraction conditioned on the velocity vector components showed a more linear behavior near the reactor center, where the PDF of the mixture fraction is a Gaussian distribution. As the concentration gradients became prominent away from the reactor, ⟨Φ|ωi⟩ also deviated from the linear pattern. This was especially remarkable for the mixture fraction conditioned on the tangential velocity. The overall prediction of ⟨Φ|ωi⟩ improves at higher Reynolds number as the fluid mixing is enhanced.

### Intermittent locomotion of a self-propelled plate

Many fish and marine animals swim in a combination of active burst and passive coast phases, which is known as burst-and-coast swimming. The immersed boundary method was used to explore the intermittent locomotion of a three-dimensional self-propelled plate. The degree of intermittent locomotion can be defined in terms of the duty cycle (DC = Tb/Tf), which is the ratio of the interval of the burst phase (Tb) to the total flapping period (Tf = Tb + Tc), where Tc is the interval of the coast phase. The average cruising speed ([math]), the input power ([math]), and the swimming efficiency (η) were determined as a function of the duty cycle (DC). The maximum [math] arises for DC = 0.9, whereas the maximum η arises for DC = 0.3. The hydrodynamics of the intermittent locomotion was analyzed by examining the superimposed configurations of the plate and the phase map. The characteristics of the flapping motions in the burst and coast phases are discussed. A modal analysis was performed to examine the role of the flapping motion in the propulsion mechanism. The velocity map and the vortical structures are visualized to characterize qualitatively and quantitatively the influence of intermittent locomotion on propulsion.

### Exact moment analysis of transient dispersion properties in periodic media

This paper develops a homogenization approach, based on the introduction of exact local and integral moments, to investigate the temporal evolution of effective dispersion properties of point-sized and finite-sized particles in periodic media. The proposed method represents a robust and computationally efficient continuous approach, alternative to stochastic dynamic simulations. As a case study, the exact moment method is applied to analyze transient dispersion properties of point-sized and finite-sized particles in sinusoidal tubes under the action of a pressure-driven Stokes flow. The sinusoidal structure of the tube wall induces a significant variation of the axial velocity component along the axial coordinate. This strongly influences the transient behavior of the effective axial velocity [math] and of the dispersivity [math], both exhibiting wide and persistent temporal oscillations, even for a steady (not-pulsating) Stokes flow. For a pointwise injection of solute particles on the symmetry axis, many interesting features appear: negative values of the dispersion coefficient [math], values of [math] larger than the asymptotic value [math], and anomalous temporal scaling of the axial variance of the particle distribution. All these peculiar features found a physical and theoretical explanation by adopting simple transport models accounting for the axial and radial variation of the axial velocity field and its interaction with molecular diffusion.