# New Papers in Fluid Mechanics

### Linear stability analysis of a surfactant-laden shear-imposed falling film

A study of the linear stability analysis of a shear-imposed fluid flowing down an inclined plane is performed when the free surface of the fluid is covered by an insoluble surfactant. The purpose is to extend the earlier work [H. H. Wei, “Effect of surfactant on the long-wave instability of a shear-imposed liquid flow down an inclined plane,” Phys. Fluids 17, 012103 (2005)] for disturbances of arbitrary wavenumbers. The Orr-Sommerfeld boundary value problem is formulated and solved numerically based on the Chebyshev spectral collocation method. Two temporal modes, the so-called surface mode and surfactant mode, are detected in the long-wave regime. The surfactant mode becomes unstable when the Péclet number exceeds its critical value. In fact, the instability of the surfactant mode occurs on account for the imposed shear stress. Energy budget analysis predicts that the kinetic energy of the infinitesimal disturbance grows with the imposed shear stress. On the other hand, the numerical results reveal that both surface and surfactant modes can be destabilized by increasing the value of the imposed shear stress. Similarly, it is demonstrated that the shear mode becomes more unstable in the presence of the imposed shear stress. However, it can be stabilized by incorporating the insoluble surfactant at the free surface. Apparently, it seems that inertia does not play any role in the surfactant mode in the moderate Reynolds number regime. Furthermore, the competition between surface and shear modes is discussed.

### The drag reduction performance of low Reynolds number pulsating flow in flexible rectangular channels

This work employed theoretical and experimental methods to study the drag reduction performance of flexible channels for low Reynolds number pulsating flow. A novel theoretical model was proposed to describe flow in a flexible rectangular channel. According to the model, the drag reduction of the flexible channel was speculated. Subsequently, experiments were carried out to verify the theoretical results and to illuminate the drag reduction performance of the flexible channel in detail under the impacts of pulsating frequency, nondimensional velocity amplitude, average Reynolds number, and the thickness of the flexible wall. The results indicated that the flexible channel exhibited superior drag reduction performance for pulsating flow as compared to that for steady flow. Meanwhile, the drag reduction rate increased with the increase of pulsating frequency, nondimensional velocity amplitude, and average Reynolds number, and smaller thickness of the flexible wall was in favor of drag reduction at the same flow parameters. Moreover, the current experimental data were utilized to establish a correlation predicting the drag reduction rate of the flexible channel for pulsating flow, which fits 76.4% of 195 data within ±25%.

### Numerical investigation of piston-modal wave resonance in the narrow gap formed by a box in front of a wall

Piston-modal wave resonance between a ship section and a bottom mounted terminal is studied by employing a numerical wave flume based on OpenFOAM® package. A systematic investigation on the piston-modal behavior is performed to characterize the influence of fluid viscosity and flow rotation. Around the resonant frequency, the fluid viscosity and flow rotation not only dissipate the wave amplitude in the narrow gap, but also increase the wave amplitude in the upstream of the box. The dynamic mechanism behind the phenomenon is found to be the interaction between the energy dissipation induced by the fluid vortical flow and energy transformation associated with free surface motion. The increased incident wave amplitude can cause the normalized wave amplitudes and wave forces to deviate more from the potential flow results, while the variation of reflection coefficient is dependent on box-wall geometries. All of these phenomena imply a more significant effect of fluid viscosity and flow rotation with the increase of incident wave amplitude, but the energy dissipation is not the only factor in piston-modal resonance.

### Experimental verification of anomalous surface tension temperature dependence at the interface between coexisting liquid-gas phases in magnetic and Stockmayer fluids

Our early experimental investigation has demonstrated the anomalous surface tension temperature dependence σ(T) at the interface between coexisting liquid-gas phases in magnetic fluids that undergo field-induced first-order phase transition. The σ(T) dependence is anomalous because the drops of a liquid phase condensed under the action of the applied magnetic field H at high temperature T2 exhibit larger surface tension σ(T2) > σ(T1) than the drops condensed at low temperature T1 < T2. This study verifies and confirms the results of the previous experimental investigation of σ(T) in magnetic fluids by performing the experiment, which is based on the analysis of the Plateau-Rayleigh instability of a gas-liquid interface in a zero magnetic field. A novel explanation of this phenomenon is given in the framework of the Stockmayer model. The anomalous increase in σ(T) is explained by the increase in particle concentration difference in gas and liquid phases, which can be attributed to the high field intensity H needed to generate the phase transition at high temperature.

### Random walks with long-range steps generated by functions of Laplacian matrices

Publication year: 2018

Journal / Book title: Journal of Statistical Mechanics: Theory and Experiment

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### Regime transition in the energy cascade of rotating turbulence

Author(s): T. Pestana and S. Hickel

Transition from a split to a forward kinetic energy cascade system is explored in the context of rotating turbulence using direct numerical simulations with a three-dimensional isotropic random force uncorrelated with the velocity field. Our parametric study covers confinement effects in high-aspect...

[Phys. Rev. E 99, 053103] Published Wed May 08, 2019

### Rayleigh-Taylor-instability experiments with elastic-plastic materials

Author(s): Rinosh Polavarapu, Pamela Roach, and Arindam Banerjee

A rotating wheel experimental facility was developed to investigate incompressible Rayleigh-Taylor instability in elastic-plastic materials. A soft solid (mayonnaise) was chosen as the elastic-plastic material for experiments; material properties that include shear modulus and yield strength were fu...

[Phys. Rev. E 99, 053104] Published Wed May 08, 2019

### Drop impact close to the edge of an inclined substrate: Liquid sheet formation and breakup

Author(s): S. Lejeune and T. Gilet

Experiments on the impact of a drop near the edge of an inclined substrate are reported. A liquid sheet forms beyond the edge, then fragments into droplets. This configuration is a minimal model of the crucial raindrop impacts on plant leaves that are responsible for the dispersal of crop diseases.

[Phys. Rev. Fluids 4, 053601] Published Wed May 08, 2019

### Deformation and stability of a viscous electrolyte drop in a uniform electric field

Author(s): Qiming Wang, Manman Ma, and Michael Siegel

The deformation and breakup of an axisymmetric electrolyte drop in a dielectric medium stretched by an electric field is studied. An accurate and efficient boundary integral method is developed to solve the time-dependent Stokes flow problem in the case of arbitrary Debye layer thickness.

[Phys. Rev. Fluids 4, 053702] Published Wed May 08, 2019

### Influence of Reynolds number on the motion of settling, bidisperse inertial particles in turbulence

Author(s): Mohammadreza Momenifar, Rohit Dhariwal, and Andrew D. Bragg

Using direct numerical simulation it is shown that even when bidisperse particles are settling rapidly, intermittent fluctuations allow turbulence to continue to play a key role in their relative motion, an effect increasing with Re. Low-order statistics relevant to collision rates are found to depend only weakly on Re.

[Phys. Rev. Fluids 4, 054301] Published Wed May 08, 2019

### Destruction-of-dissipation and time-scales in wall turbulence

This paper studies the dynamics and scalings of dissipation processes in wall turbulence, focussing on the destruction-of-dissipation tensor [math] (and its halftrace εε), which acts as destruction-by-molecular-viscosity mechanism in the transport equations for the dissipation tensor εij (or its halftrace ε). Budgets of [math]-transport (and εε-transport) are studied for low-Reynolds turbulent plane channel flow. These transport equations also include a destruction-by-molecular-viscosity mechanism, the destruction-of-destruction tensor [math] (or its halftrace [math]), and indeed, recursively, we identify terms [math] defined by correlations of [n + 1]-derivatives which correspond to the destruction mechanism of [math]. Using halftraces ε[n], we may define time-scales, whose study reveals that [math] is approximately equal to the Kolmogorov time-scale. The dependence of the time-scales on the Reynolds number is discussed.

### Numerical study of the material transport in the viscous vortex dipole flow

This paper presents a numerical study of the material transport of Lamb dipole(s) in the two-dimensional viscous flow. We focus on the properties of the rate of strain tensor, which has received less attention in the literature. It is noted that the eigenpairs of the tensor explicitly indicate the strength and direction of material stretching and compressing. The tensor provides a clear map of the material motion regardless of the complexity of the vortical flow. The strain rate field displays a rich structure as it contains five elliptic points and six hyperbolic points. It is interesting to observe that the left elliptic point of the strain rate field bifurcates into two at t > 0. Two kinds of material curves, circular and vertical, are used to illustrate the flow transport. The transport mechanism discussed here can be employed to explore the transport in more complex vortex flows.

### Second-order sensitivity in the cylinder wake: Optimal spanwise-periodic wall actuation and wall deformation

Author(s): E. Boujo, A. Fani, and F. Gallaire

Two-dimensional flows can be controlled efficiently with spanwise-periodic wall forcing or wall deformation. Optimal “wavy” controls for the linear stability of the laminar flow past a cylinder are obtained with an adjoint method.

[Phys. Rev. Fluids 4, 053901] Published Tue May 07, 2019

### Very large-scale motions in turbulent flows over streamwise traveling wavy boundaries

Author(s): Wu-Yang Zhang, Wei-Xi Huang, and Chun-Xiao Xu

Numerical simulations of turbulent flows over traveling wavy boundaries reveal that very large-scale motions are enhanced by a wavy boundary, but their intensities are decreased as wave phase speed increases. The wave-induced flow provides an extra energy transfer for the very-large-scale motions.

[Phys. Rev. Fluids 4, 054601] Published Tue May 07, 2019

### Shape oscillation of a sessile drop under the effect of high frequency amplitude-modulated magnetic field

The shape oscillation behavior of a sessile mercury drop under the effect of high frequency amplitude-modulated magnetic field (AMMF) is investigated experimentally. It is an effective method to excite the shape oscillation of a liquid metal sessile drop. The high frequency AMMF is generated by a solenoid inductor fed by a specially designed alternating electric current. The surface contour of the sessile drop is observed by a digital camera. At a given modulation frequency and magnetic flux density of the high frequency AMMF, the edge deformations of the drop with azimuthal wave numbers (modes n = 2, 3, 4, 5, 6) were excited. A stability diagram of the shape oscillation of the drop is obtained by analysis of the experimental data. It turns out that when the modulation frequency and magnetic flux density reach a point in the stability diagram which can trigger shape oscillations of the drop of several modes, the shape oscillation of different modes may be seen alternatively.

### Effects of the Atwood number on the Richtmyer-Meshkov instability in elastic-plastic media

Author(s): Qian Chen, Li Li, Yousheng Zhang, and Baolin Tian

The Richtmyer-Meshkov instability of small perturbed single-mode interfaces between an elastic-plastic solid and an inviscid liquid is investigated by theoretical analysis and numerical simulation in this work. A modified model including the Atwood number effect is proposed to describe the long-term...

[Phys. Rev. E 99, 053102] Published Mon May 06, 2019

### Enhanced mixing at inertial microscales using flow-induced flutter

Author(s): Aaron Rips and Rajat Mittal

Flow-induced flutter of flexible flapping membranes can greatly increase scalar mixing in channel flows in the inertial microfluidics regime. We use flow-structure interaction simulations to investigate their flow physics and mixing ability and find rapid mixing with relatively low pressure loss.

[Phys. Rev. Fluids 4, 054501] Published Mon May 06, 2019

### Numerical investigation of planar shock wave impinging on spherical gas bubble with different densities

The interaction between a planar shock wave and a spherical gas bubble containing sulfur hexafluoride, Refrigerant-22, neon, or helium is studied numerically. Influences of the Atwood number (At) on the evolution of the shock wave and gas bubble are clarified by using high-resolution computational simulations. The results show that the difference in the physical properties between the ambient air and the gas bubble has a significant influence on the evolution of wave pattern and bubble deformation. For the fast/slow configuration (At > 0) in the present study (At = 0.67 and 0.51), the incident shock focuses near the interior right interface to form an outward jet. Besides, the mixedness, average vorticity, and the absolute value of circulation all increase as the Atwood number increases. By contrast, for the slow/fast configuration (At < 0) with At = −0.19 and −0.76, the rotational directions of the vorticities formed at the same position are reversed compared with those in the fast/slow configuration, which induces an inward air jet to impact on the gas bubble from the outside. In addition, the mixedness, average vorticity, and the absolute value of circulation all increase as the Atwood number decreases. Nevertheless, regardless of At > 0 or At < 0, the effective volume of the gas bubble basically decreases when the Atwood number decreases. Hence, on the whole, the Atwood number has a nonmonotonic influence on the evolution of effective volume of gas bubble, mixedness, average vorticity, and circulation simultaneously.

### Evaluation of oil production potential in fractured porous media

Based on rock samples of tight oil reservoirs in the buried hills of North China, conventional gas flooding and high-speed centrifugal experiments at different pressures were carried out. Combined with nuclear magnetic resonance experiments, an evaluation method of oil production potential in fractured porous media was established to quantitatively study the gas flooding potential of target reservoirs. Results indicated that the “gas fingering phenomenon” is serious in conventional gas flooding experiments of fractured cores even under low pressures because of fractures. With an increase in flooding pressure, the changes of T2 (T2 relaxation time) spectrum and displacement percentage are relatively small, which means that the displacement efficiency has not been improved significantly (the flooding pressure for these three cores increased from 0.014 MPa to 2.6 MPa, with an average increase in displacement percentage of 6.3%). High-speed centrifugation can realize “homogeneous displacement” of the cores and overcome the influence of gas channeling. With an increase in the displacement pressure, the T2 spectrum and percentage of displaced oil varied obviously, and the displacement efficiency improved greatly (the flooding pressure for these three cores increases from 0.014 MPa to 2.6 MPa, with an average percentage of displaced oil being increased to 16.16%). Using the method of this study, 13 cores of the target reservoir were evaluated for gas flooding potential. The percentage of available pores in the target reservoir ranges from 17.64% to 58.54%, with an average of 33.84%. Movable fluid controlled by microthroats in the reservoirs larger than 0.1 mD is about 20%, while that in the reservoirs smaller than 0.1 mD is about 5%. This study indicates that the development of fractures and microfractures controls the physical properties and fluid productivity of reservoirs.

### A numerical study on bubble dynamics in sinusoidal channels

In the present work, we investigate the dynamics of a bubble, rising inside a vertical sinusoidal wavy channel. We carry out a detailed numerical investigation using a dual grid level set method coupled with a finite volume based discretization of the Navier–Stokes equation. A detailed parametric investigation is carried out to identify the fate of the bubble as a function of Reynolds number, Bond number, and the amplitude of the channel wall and represented as a regime map. At a lower Reynolds number (high viscous force), we find negligible wobbling (path instability) in the dynamics of the bubble rise accompanied only with a change in shape of the bubble. However, at a higher Reynolds number, we observe an increase in the wobbling of the bubble due to the lowered viscous effects. Conversely, at a lower Bond number, we predict a stable rise of the bubble due to higher surface tension force. However, with a gradual increase in the Bond number, we predict a periodic oscillation which further tends to instigate the instability in the dynamics. With a further increase in the Bond number, a significant reduction in instability is found unlike a higher Reynolds number with only change in the shape of the bubble. At lower values of Reynolds numbers, Bond numbers, and channel wall amplitudes, the instability is discernible; however, with an increase in the channel wall amplitude, the bubble retains integrity due to higher surface tension force. At a higher Bond number and channel wall amplitude, a multiple breakup in the form of secondary bubbles is observed. We propose a correlation which manifests the average bubble rise velocity and the fluctuating velocity (due to channel waviness) as a function of Reynolds number, Bond number, and channel wall amplitude. Finally, we conclude that the bubble dynamics pertinent to the offset channels with varying amplitudes does not remain the same as that of the symmetric channel.