# Latest papers in fluid mechanics

### Pressure drop reduction of power-law fluids in hydrophobic microgrooved channels

Using hydrophobic surfaces is one of the efficient methods to preserve energy in fluid transfer systems. However, the studies have been concentrated on Newtonian fluids despite the wide applications of non-Newtonian fluids in daily life and many industries such as the biological, foodstuff, chemical, petroleum, cosmetic, and lab on a chip fields. In this study, we consider power-law fluids as a typical example of non-Newtonian fluids and investigate the effect of hydrophobic microgrooves on the pressure drop in channels by utilizing the phase field method. We demonstrate that the optimum size of the rectangular microgrooves in which the maximum pressure drop reduction (PDR) happens for both the considered Newtonian and non-Newtonian fluids is identical, but the PDR is different for the Newtonian and non-Newtonian fluids. For shear-thickening fluids, the PDR is more than shear-thinning fluids, which means that using the hydrophobic surfaces in dilatant fluids provides the best performance. It is seen that pressure drop reduces more at lower Reynolds numbers. We also investigate the efficiency of the microgrooved surfaces in convergent and divergent channels for both the Newtonian and non-Newtonian fluids and find the critical slope angles for a specific length of the channels in which the hydrophobic microgrooves have a sufficient performance in the PDR and stability.

### Controlling dispersive hydrodynamic wavebreaking in a viscous fluid conduit

Author(s): Dalton V. Anderson, Michelle D. Maiden, and Mark A. Hoefer

Quantitative boundary control of buoyant, interfacial dynamics between two high-viscosity-contrast Stokes fluids is achieved by the technique of characteristic tracking. This enables the experimental generation of desired wave breaking profiles that produce dispersive shock waves and solitons.

[Phys. Rev. Fluids 4, 074804] Published Wed Jul 17, 2019

### Aging continuous time random walks in fluids

The subject of aging continuous time random walks (CTRWs) has attracted increasing attention in recent years. To describe the aging behaviors of random particles whose jumps are biased by a nonhomogeneous velocity field, we propose herein a generalized scheme of aging CTRWs in flows and obtain the corresponding generalized master equation in Fourier–Laplace space for probability density functions. Moreover, we derive the generalized aging advection diffusion equation for particles with a power law waiting time and Gaussian jump length densities, investigate the corresponding ensemble and time mean square displacements, and show how anomalous diffusion depends on the age of the process and on the moving fluids.

### Surface-averaged quantities in turbulent reacting flows and relevant evolution equations

Author(s): Rixin Yu and Andrei N. Lipatnikov

While quantities conditioned to an isosurface of reaction progress variable c, which characterizes fluid state in a turbulent reacting flow, have been attracting rapidly growing interest in the recent literature, a mathematical and physical framework required for research into such quantities has no...

[Phys. Rev. E 100, 013107] Published Tue Jul 16, 2019

### Violent expansion of a rising Taylor bubble

Author(s): Guangzhao Zhou and Andrea Prosperetti

The gradual expansion of large bubbles rising in a liquid-filled tube can become violent in the last few seconds before reaching the tube top. This process is responsible for Strombolian volcanic eruptions and for accidents in deep-water oil drilling such as the 2010 Deepwater Horizon explosion.

[Phys. Rev. Fluids 4, 073903] Published Tue Jul 16, 2019

### Instabilities in the flow around an impulsively rotated sphere

Author(s): Sophie A. W. Calabretto and James P. Denier

A computational study shows that the flow induced by a sphere rotating in an otherwise quiescent fluid is convectively unstable to spiral vortices, which once induced are swept down through the sphere’s boundary layer and then out into the radial jet that emanates from sphere’s equator.

[Phys. Rev. Fluids 4, 073904] Published Tue Jul 16, 2019

### Flow-driven compaction of a fibrous porous medium

Author(s): Daniel T. Paterson, Tom S. Eaves, Duncan R. Hewitt, Neil J. Balmforth, and D. Mark Martinez

A combined theoretical and experimental study is presented for rapid flow-induced compaction of a fibrous porous medium. The model is used to understand the dynamics of a standard test for pulp suspensions: the Canadian Standard Freeness test, which depends sensitively on the solid bulk viscosity.

[Phys. Rev. Fluids 4, 074306] Published Tue Jul 16, 2019

### Viscoelastic properties of suspensions of noncolloidal hard spheres in a molten polymer

We report an experimental study on suspensions of solid particles in a viscoelastic polymer matrix. A commercial entangled poly([math]-caprolactone) was used as the suspending fluid. Noncolloidal solid spheres (diameter = 15 μm) made of polymethylmethacrylate were dispersed in the polymer via a solvent casting method. The volume fraction of the spheres was varied from 5% to 30%, thus allowing to explore both dilute and concentrated regimes. Electron scanning microscopy demonstrated homogeneous dispersion of the spheres in the matrix. We measured the rheological properties of the suspensions both in linear and nonlinear regimes with both dynamic and transient tests. The experimental results demonstrate the reinforcement effect of the particles. Both viscous and elastic moduli increase as the concentration of the particles is increased. The results show good agreement with available theories, simulations, and previous experimental data. In particular, the second order parameter of the quadratic equation that describes the dependence of the shear viscosity of the suspension upon the volume fraction of particles is in agreement with the predicted value found by Batchelor [G. K. Batchelor and J. T. Green, “The hydrodynamic interaction of two small freely-moving spheres in a linear flow field,” J. Fluid Mech. 56, 375–400 (1972); G. K. Batchelor and J. T. Green, “The determination of the bulk stress in a suspension of spherical particles to order c2,” J. Fluid Mech. 56, 401–427 (1972); and G. K. Batchelor, “The effect of Brownian motion on the bulk stress in a suspension of spherical particles,” J. Fluid Mech. 83, 97–117 (1977)]. We probe experimentally that the linear rheological behavior of suspensions of particles in viscoelastic fluids is the same as for Newtonian fluids.

### Scaling and spatial intermittency of thermal dissipation in turbulent convection

We derive scaling relations for the thermal dissipation rate in the bulk and in the boundary layers for moderate and large Prandtl number (Pr) convection. Using direct numerical simulations of Rayleigh-Bénard convection, we show that the thermal dissipation in the bulk is suppressed compared to passive scalar dissipation. The suppression is stronger for large Pr. We further show that the dissipation in the boundary layers dominates that in the bulk for both moderate and large Pr. The probability distribution functions of thermal dissipation rate, both in the bulk and in the boundary layers, are stretched exponential, similar to passive scalar dissipation.

### The spontaneous breaking of axisymmetry in shallow rotating flows

We show that the axial symmetry of a shallow rotating flow is spontaneously broken in the absence of an externally forced velocity gradient. It is caused by an instability excited by the gradients that arise from the axisymmetric counter-rotating vortices. The experimental setup consists of an electrolyte poured into a cylindrical container with radius R and height h and subject to electromagnetic forcing caused by an axial magnetic field and a radial current (J) leading to an azimuthal rotation Vθ. The flow motion is considered to be two-dimensional at large aspect ratio (R/h) and low Reynolds number, Re = Vθh/ν, where ν is the kinematic viscosity. At a moderate aspect ratio, we record the existence of an axisymmetric vortex at the edge caused by the no-slip boundary condition at the walls. When Re is increased by changing h or J, the flow becomes unstable at the radial position where gradients exist due to the edge vortices at a critical Reynolds number of about 220. The most unstable mode of this nonaxisymmetric instability is found to be m = 1 followed by m = 2 and other higher mode numbers. Using perturbation theory, we found that two counter-rotating vortices that are in azimuthal motion are unstable when subject to nonaxisymmetric perturbations with the onset of low azimuthal mode numbers in agreement with the experiment. We conclude that the axial symmetry breaking in shallow rotating flows occurs at relatively low Reynolds numbers caused by the gradients generated by the vortices in the height-radial plane.

### Mechanism of pressure oscillation in Taylor-Couette-Poiseuille flow with abruptly contracting and expanding annular gap

This study numerically investigates the effects of an abruptly contracting and expanding annular gap on the propagation of Taylor vortices in Taylor-Couette-Poiseuille flow. The results show that the pressure drop between the inlet and the outlet exhibits oscillations with low frequency and large amplitude. The nondimensional amplitude of oscillating pressure increases linearly with an increase in the rotating Reynolds number, whereas the nondimensional oscillating frequency remains nearly invariant with varying rotating and axial Reynolds numbers. Owing to the alternate action of counter-rotating Taylor vortex pairs in front of the block, local flow resistance periodically increases and decreases, resulting in the pressure drop oscillation. By analyzing the drift velocity and wavelength of the propagating Taylor vortex pair, a prediction model for the oscillating frequency is developed. Its results show that the nondimensional frequency is proportional to the blockage ratio. With an increase in the latter, the oscillating amplitude nonmonotonically changes as a result of the tunneling phenomenon, whereby the anticlockwise rotating Taylor roller is punctured by axial flow. Based on the above mechanism of pressure oscillation, the structure of a vortex breaker is proposed that can effectively reduce the oscillation in pressure.

### Collision of a steepened wave with a blast wave in dusty real reacting gases

In this paper, we study the collision of a one-dimensional steepened wave with a blast wave for the system of partial equations describing the unsteady flow of dusty real reacting gases with the same γ-law. The real gas is characterized by a van der Waals type equation of state. Special attention is devoted to analyzing the effects of real, reaction, and dusty gas parameters on the steepened wave. The amplitudes of the reflected and/or transmitted waves along with the jump in shock acceleration after the interaction are also obtained.

### Effective mean free path and viscosity of confined gases

The molecular mean free path (MFP) of gases in confined geometries is numerically evaluated by means of the direct simulation Monte Carlo method and molecular dynamics simulations. Our results show that if calculations take into account not only intermolecular interactions between gas molecules but also collisions between gas molecules and wall atoms, then a space-dependent MFP is obtained. The latter, in turn, permits one to define an effective viscosity of confined gases that also varies spatially. Both the gas MFP and viscosity variation in surface-confined systems have been questioned in the past. In this work, we demonstrate that this effective viscosity derived from our MFP calculations is consistent with those deduced from the linear-response relationship between the shear stress and strain rate using independent nonequilibrium Couette-style simulations as well as the equilibrium Green-Kubo predictions.

### Development of specific structures occurring from hyper-breakable vorticity

The spatial development of hyperbreakable vorticity in a supersonic coaxial flow with an annular swirl is investigated using direct numerical simulation at Mach number 1.5. The results show that the unstable modes originate from inside and outside the vortex depending on the ratio of vorticity thicknesses and then specific structures develop with small scales as distinct from conventional shear flows; furthermore, the evolutions lead to generate a number of fine scales due to the secondary instability. The mechanism is caused by the instability due to the helicity profile in addition to the barotropic instability based on the inflection point of the inner vorticity. This study strongly indicates that rapid evolutions on a plane perpendicular to the streamwise direction are insensitive to compressibility effects in supersonic flows. Therefore, the novel vorticity is found to undergo a breakdown at a short distance.

### Phenomenology of droplet collision hydrodynamics on wetting and non-wetting spheres

In this study, the spreading characteristics of water droplets impacted on a solid spherical target have been investigated experimentally and theoretically. Droplet impact and postimpact feature studies have been conducted on hydrophilic and superhydrophobic spherical surfaces. Effects of the impact Weber number and target-to-drop diameter ratio on the spreading hydrodynamics have been discussed. Postcollision dynamics are explored with side and top views of impaction phenomenon using a high speed imaging technique. The morphological outcome of this impingement process has been quantitatively discussed with three geometric parameters, namely, liquid film thickness at the north-pole of the target surface, spread factor, and the maximum spread angle. Observations revel that spread factor and the maximum spread angle increases with the decrease in the size of the spherical target, whereas opposite of this is true for liquid film thickness at the north-pole of the target surface. Temporal variations of liquid film thickness at the north pole of the target have been plotted and found in agreement with the theoretical predictions made in the earlier studies. Finally, a mathematical model based on the energy balance principle has been proposed to predict the maximum spread angle on spherical targets. The theoretical values are found in good agreement with the experimental results for a wide range of spherical diameters studied. The findings may have implications toward a better understanding of fluid wetting, spraying, and coating behavior of complex shapes and geometries.

### Momentum of vortex tangles by weighted area information

Author(s): Simone Zuccher and Renzo L. Ricca

Here we show how to apply a recently introduced method based on the geometric interpretation of linear momentum of vortex lines to determine dynamical properties of a network of knots and links. To show how the method works and to prove its feasibility, we consider the evolution of quantum vortices ...

[Phys. Rev. E 100, 011101(R)] Published Mon Jul 15, 2019

### Experimental characterization of the growth dynamics during capillarity-driven droplet generation

Author(s): Bhaskarjyoti Sarma, Vijay Shahapure, Amaresh Dalal, and Dipankar N. Basu

The transient dynamics of a growing droplet in a yarn is explored following the spatiotemporal evolution of the three-phase contact line as well as the liquid-air interface with the help of videographic techniques and subsequent image analyses. The spontaneous capillary flow of liquids in a porous n...

[Phys. Rev. E 100, 013106] Published Mon Jul 15, 2019

### Statistics of rigid fibers in strongly sheared turbulence

Author(s): Dennis Bakhuis, Varghese Mathai, Ruben A. Verschoof, Rodrigo Ezeta, Detlef Lohse, Sander G. Huisman, and Chao Sun

Despite tremendous turbulent fluctuation in a high-Reynolds number Taylor-Couette flow, dispersed millimetric fibers show a preferred alignment with respect to the inner cylinder of the apparatus. Using a simplified model based on Jeffery’s equations, the orientation can be reasonably predicted.

[Phys. Rev. Fluids 4, 072301(R)] Published Mon Jul 15, 2019

### Consolidation of freshly deposited cohesive and noncohesive sediment: Particle-resolved simulations

Author(s): Bernhard Vowinckel, Edward Biegert, Paolo Luzzatto-Fegiz, and Eckart Meiburg

Mud is widely present in the environment and it can bind contaminants or nutrients. Since particles that make up mud are small and sticky, it is difficult to perform precise measurements. To this end, we present a numerical framework, which yields results that have so far been impossible to obtain.

[Phys. Rev. Fluids 4, 074305] Published Mon Jul 15, 2019

### A study on dual role of viscosity on the stability of a viscous planar liquid sheet surrounded by inviscid gas streams of equal velocities, and prediction of resulting droplet distribution using maximum entropy formulation

Low sensitivity to rheological properties of fluid and ability to produce fine sprays at low liquid pressure make airblast atomizers a preferred choice to process viscous liquids. Airblast atomizers essentially employ kinetic energy of coflowing gases to disintegrate a liquid sheet into fine spray. The present study employs the perturbation technique to carry out nonlinear investigation of the sinuous mode of instability in a thin planar viscous liquid sheet sandwiched between two inviscid gas streams moving at equal velocities. This paper analyzes temporal instability as well as droplet characteristics for a range of Reynolds numbers, Weber numbers, gas to liquid density ratios, and velocity ratios and reports the dual behavior of liquid viscosity at different operating conditions. For higher gas to liquid velocity ratios, this study identifies three regimes at all Weber numbers and gas to liquid density ratios: the first regime represents the stabilizing effect of viscosity at low Reynolds numbers, the second regime indicates the destabilizing effect of viscosity at intermediate Reynolds numbers, and the third regime further depicts the stabilizing effect of viscosity at high Reynolds numbers. However, for low gas to liquid velocity ratios, the third zone disappears at lower Weber numbers and gas to liquid density ratios, and the effect of viscosity is characterized by two regimes representing the weak stabilizing and destabilizing effect at low and relatively higher Reynolds numbers, respectively. Investigation of spray characteristics reveals that an increase in liquid viscosity produces relatively larger droplets at all flow conditions.