# Latest papers in fluid mechanics

### Spreading of rinsing liquids across a horizontal rotating substrate

Author(s): Daniel J. Walls, Andrew S. Ylitalo, David S. L. Mui, John M. Frostad, and Gerald G. Fuller

The time-dependent spreading behaviors of a rinsing liquid across a horizontal, rotating substrate pre-coated with thin liquid films is investigated. Four distinct growth behaviors in time of the azimuthally averaged spreading radius are observed and explained with lubrication theory.

[Phys. Rev. Fluids 4, 084102] Published Wed Aug 07, 2019

### Stability of downslope flows to two-dimensional perturbations

We consider the stability problem for wide, uniform stationary open flows down a slope with constant inclination under gravity. Depth-averaged equations are used with arbitrary bottom friction as a function of the flow depth and depth-averaged velocity. The stability conditions for perturbations propagating along the flow are widely known. In this paper, we focus on the effect of oblique perturbations that propagate at an arbitrary angle to the velocity of the undisturbed flow. We show that under certain conditions, oblique perturbations can grow even when the perturbations propagating along the flow are damped. This means that if oblique perturbations exist, the stability conditions found in the investigation of the one-dimensional problem are insufficient for the stability of the flow. New stability criteria are formulated as explicit relations between the slope and the flow parameters. The ranges of the growing disturbances propagation angles are indicated for unstable flows.

### Nonlinear dispersive Alfvén waves interaction in magnetized plasma

This study is concerned with the nonlinear interactions between pairs of intersecting Alfvén waves in a magnetized plasma and used the modified Korteweg–de Vries equation to study nonlinear interactions. The modulation instability analysis shows the existence of periodic traveling wave solution in the system. Two different types of waves interaction solutions, namely, the periodic wave interaction solutions and the solitary wave interaction ones, are captured analytically. It is found that the wave resonance for the periodic waves interaction could happen as various wave numbers are nearly the same. In this case, the subsidiary waves could not be neglected. It is also found that the interaction for solitary waves, different solitons eventually regain their original states. The solitons with higher energy possess more speed as compared to the low energy solitons. The phenomenon of Alfvén wave interaction can be of importance for understanding the transport mechanism of magnetic waves in various processes of heating and transport of energy in space, solar wind, and astrophysical plasma.

### Evolution of rivulets during spreading of an impinging water jet on a rotating, precoated substrate

The spreading of a liquid film across a rotating surface is inherently unstable due to the centrifugal force, which causes the formation of rivulets along the spreading front. This instability produces a rich diversity of spreading patterns and is important to control for the optimization of spin-coating and spin-rinsing of silicon wafers during the fabrication of microelectronics. The present work is an experimental investigation of the evolution of rivulets arising from this instability during the spreading of an impinging water jet across a rotating substrate that is precoated with a thin, aqueous film. To characterize these rivulets, we developed a high-speed imaging apparatus and image-processing software that traces the spreading front over time. We show how the morphology of the spreading front is qualitatively affected by varying the Reynolds number of the impinging jet, the ratio of centrifugal to Coriolis forces, and the type of liquid used to precoat the substrate. For quantitative analysis of rivulets, we measured the “compactness ratio” of the spreading front, which quantifies deviation from a circular spreading front. We used the compactness ratio to demonstrate that rivulets are suppressed most strongly at low rotation rates, at high flow rates, and on substrates precoated with water, although with notable exceptions.

### Hydrodynamic loading of perforated disks in creeping flows

Author(s): E. F. Strong, M. Pezzulla, F. Gallaire, P. Reis, and L. Siconolfi

The drag of perforated thin disks is studied at low Reynolds numbers via displacement controlled experiments and simulations. It is shown that the drag of the disks is affected by the size of the voids, but not by the disk thickness. Good agreement is observed with existing analytical solutions.

[Phys. Rev. Fluids 4, 084101] Published Tue Aug 06, 2019

### Finite Reynolds number effect and the 4/5 law

Author(s): R. A. Antonia, S. L. Tang, L. Djenidi, and Y. Zhou

A relatively extensive survey of published data shows that the 4/5 law has not yet been observed in either experiments or simulations because the Reynolds number is not sufficiently large.

[Phys. Rev. Fluids 4, 084602] Published Tue Aug 06, 2019

### Multirotor wind turbine wakes

To fulfill the increasing need for large power generation by wind turbines, the concept of multirotor wind turbines has recently received attention as a promising alternative to conventional massive single-rotor wind turbines. To shed light on the viability of this concept, large-eddy simulation is employed in this study to compare wake flow properties of a multirotor wind turbine with those of a single-rotor turbine. The wake of a multirotor turbine is found to recover faster at short downwind distances, where the whole wake is characterized as an array of localized high velocity-deficit regions associated with each rotor. However, as the wake moves downstream, rotor wakes start interacting with each other until they eventually form a single wake. This transition from a wake array to a single wake adversely affects the initial fast recovery of multirotor turbine wakes. A budget analysis of mean kinetic energy is performed to analyze the energy transport into the wake before and after this transition. In addition, the effect of different geometrical configurations on wake characteristics of a multirotor turbine was examined. We found that the recovery rate of multirotor turbine wakes is enhanced by the increase in rotor spacing, whereas the number and rotation direction of rotors do not play a significant role in the wake recovery. A simple analytical relationship is also developed to predict the streamwise distance at which the transition from a wake array to a single wake occurs for multirotor wind turbines.

### Molecular interactions and the viscoelasticity of micellar aggregates

Intermolecular interactions are responsible for the macroscopic properties of materials. Self-assembled micelles of ionic surfactants in the presence of salt are a result of the balance between hydrophobic-hydrophilic and ionic forces. For example, sodium salicylate (NaSal) undoubtedly offers a powerful means of increasing the viscoelasticity of hexadecyl trimethylammonium bromide (CTAB) solutions by orders of magnitude, which results from the formation of wormlike micelles (WLMs). The efficiency of this additive relies on its ability to integrate and alter the repulsive interactions governing CTAB micelles. Consequently, small modifications in the molecular structure of NaSal influences the nature of these interactions. Nevertheless, the full potential of formulation for tailoring the system’s viscoelasticity has yet to be unleashed. Herein, we investigate a series of structurally similar molecules varying in terms of geometry and size. The depth and molecular orientation of their insertion into the micellar core were monitored by proton nuclear magnetic resonance (1H-NMR) and correlated with the corresponding viscoelastic response. After detailed observation of the impact of molecular interactions on zero-shear viscosity η0, we discuss it in terms of the effective packing parameter (PPeff). All the investigated additives increased PPeff, triggering anisotropic micellar growth toward WLMs. The simplicity of our approach is attractive for predicting and controlling the viscoelastic properties of WLM solutions from an intermolecular level.

### Numerical simulation of forced circular jets: Effect of flapping perturbation

The forcing in round jets has large scale effects on the development and characteristics of the flow field such as the entrainment, spreading rate, and mixing of the flow. In the present work, an active control technique called the large scale flapping perturbation is studied for influencing the evolution of the circular jet. Direct numerical simulation of incompressible, spatially developing circular jets at a Reynolds number of 1000 is reported. The flow field has been explored by solving three-dimensional unsteady Navier-Stokes equations using second order spatial and temporal discretization. Among the considered variables (apart from the excitation amplitude), the perturbation frequency is the most important controlling parameter. For a circular jet at an excitation frequency of 0.1, there is evidence of a Y-shaped bifurcation on the bifurcating plane, while no bifurcation is observed on the other orthogonal plane. With an increase in the excitation frequency to 0.3, the circular jet issued from the orifice divides itself into three parts and a ψ-shaped bifurcation is obtained on the bifurcating plane. The development of the ψ-shaped bifurcation may be due to the interaction of the consecutive vortex ring and the formation of elongated vortices. However, with further increase in the excitation frequency, the spreading rate becomes weaker with the evidence of formation of the ψ-shaped bifurcation.

### Hydrodynamics of forward blood spattering caused by a bullet of general shape

A generalized model for the chaotic disintegration of a liquid due to an arbitrarily shaped projectile is proposed. In particular, the model uses percolation theory to predict the fragmentation process of blood, resulting in forward spatter to determine the number of droplets, as well as their sizes and initial velocities resulting from the flow field generated by a 7.62 × 39 mm and a 0.45 auto bullet. Blood viscoelasticity, which slows down the initial velocities of the droplets, is accounted for. The main physical mechanisms responsible for the chaotic disintegration of blood in the case of forward spattering are (i) the Rayleigh-Taylor instability associated with denser blood accelerating toward lighter air and (ii) a cascade of instability phenomena triggered by the original Rayleigh-Taylor instability because the Reynolds number is of the order of 107. Blood is viscoelastic, therefore, its disintegration into individual droplets results in ligament formation with strong uniaxial elongation, which is characterized by the extremely high values of the Deborah number leading to an almost purely elastic behavior and brittlelike fracture. The blood droplet spray then propagates in air, and deposition on the floor is calculated accounting for gravity and air drag forces, with the latter being diminished by the collective effect related to the droplet-droplet interaction. Also, the experimental data acquired in this work are presented and compared with the theoretical predictions. The agreement between the predictions and the data is satisfactory. The present fluid mechanical model holds great promise for forensic applications.

### Large effect of lateral box size in molecular dynamics simulations of liquid-solid friction

Author(s): Koshun Ogawa, Haruki Oga, Hiroki Kusudo, Yasutaka Yamaguchi, Takeshi Omori, Samy Merabia, and Laurent Joly

Molecular dynamics simulations are a powerful tool to characterize liquid-solid friction. A slab configuration with periodic boundary conditions in the lateral dimensions is commonly used, where the measured friction coefficient could be affected by the finite lateral size of the simulation box. Her...

[Phys. Rev. E 100, 023101] Published Mon Aug 05, 2019

### Heavy particles in a persistent random flow with traps

Author(s): J. Meibohm and B. Mehlig

We study a one-dimensional model for heavy particles in a compressible fluid. The fluid-velocity field is modeled by a persistent Gaussian random function, and the particles are assumed to be weakly inertial. Since one-dimensional fluid-velocity fields are always compressible, the model exhibits spa...

[Phys. Rev. E 100, 023102] Published Mon Aug 05, 2019

### Kelvin-Helmholtz and Holmboe instabilities of a diffusive interface between miscible phases

Author(s): T. Zagvozkin, A. Vorobev, and T. Lyubimova

The stability of a shear flow imposed along a diffusive interface that separates two miscible liquids (a heavier liquid lies underneath) is studied using direct numerical simulations. The phase-field approach is employed for description of a thermo- and hydrodynamic evolution of a heterogeneous bina...

[Phys. Rev. E 100, 023103] Published Mon Aug 05, 2019

### Dynamic detonation stabilization in supersonic expanding channels

Author(s): Xiaodong Cai, Ralf Deiterding, Jianhan Liang, Mingbo Sun, and Dezun Dong

Using adaptive numerical solutions of the reactive Navier-Stokes equations we clarify the mechanism of detonation stabilization in supersonic expanding channels, and further demonstrate that by dynamically controlling a moving boundary dynamically stationary detonation propagation is possible.

[Phys. Rev. Fluids 4, 083201] Published Mon Aug 05, 2019

### Instability driven by shear thinning and elasticity in the flow of concentrated polymer solutions through microtubes

Author(s): Bidhan Chandra, Rahul Mangal, Debopam Das, and V. Shankar

Polymers make flow in a tube unstable at low Reynolds numbers. An investigation shows that laminar flows of polymer solutions in a tube become unstable, unlike Newtonian fluids, at a Reynolds number as low as 10. This occurs because of the elastic and shear-thinning nature of polymer solutions.

[Phys. Rev. Fluids 4, 083301] Published Mon Aug 05, 2019

### Stability of plane Poiseuille flow of a Bingham fluid through a deformable neo-Hookean channel

Author(s): Ramkarn Patne and V. Shankar

Flow of Bingham fluids is unstable if channel walls are deformable. Laminar flows of Bingham fluids in rigid-walled channels are stable to tiny disturbances. A study finds that if the walls are made deformable, the flow becomes unstable at very low Reynolds number.

[Phys. Rev. Fluids 4, 083302] Published Mon Aug 05, 2019

### Large-eddy simulation of turbulent natural-bed flow

The turbulent flow in natural rough beds is a complex subject, still poorly understood despite the longstanding effort of several researchers. In the present work, a turbulent open-channel flow experiment, with a pebble bed at Reynolds and Froude numbers, respectively, Re = 4.65 × 104 and Fr = 0.186, has been simulated using the Large-Eddy Simulation (LES) technique, in which the wall-adapting local eddy viscosity subgrid scale closure model is used and in the presence of an air-water interface to take into account the effects of the interface deformation in the flow turbulence statistics under a low relative submergence condition. The simulations have been compared with a companion experiment, where the channel bottom is constituted by four pebble layers. For the simulations, the pebble-bed surface has been captured with a high-resolution three-dimensional laser scanner and used to morphologically characterize the numerical channel bottom. Results are presented in terms of turbulence statistics and turbulent laws, showing a good agreement with those obtained in the experiment. Since a good convergence between simulation and experimental results was obtained, the LES dataset was used to compute the Turbulent Kinetic Energy (TKE) dissipation rate across the water depth. The mesh resolution allows showing a detailed TKE dissipation rate distribution across the water depth. Moreover, the equilibrium between TKE production and dissipation was checked to verify the overlap layer existence under low relative submergence condition. Finally, a new procedure for vortex-visualization is implemented, based on the relationship between the vorticity and the TKE dissipation rate.

### Dynamics of free-surface mutually perpendicular twin liquid sheets and their atomization characteristics

The radially expanding twin (circular and vertical) liquid sheets produced by impingement of a vertical cylindrical liquid jet onto a horizontally placed cone-disk deflector with a single slot were examined experimentally in the present work. Dynamics of these liquid sheets and the events leading to their breakup were studied by carrying out high-speed shadowgraphy simultaneously from side, front, and top views at a 5.4 kHz framing rate and for the jet Weber number (Wejet) range of 993 < Wejet < 3776. In the presence of the slot, the variation of the radial breakup distance of the circular sheet (Rb,CS) with Wejet changed from the monotonically decreasing trend ([math]) to a nonmonotonic increasing and decreasing one. Furthermore, Rb,CS was found to be lowered by about 42% compared to the breakup distance Rb,CS,no-slot of the circular sheet for the no-slot deflector. The vertical sheet breakup distance (Rb,Vs) was found to increase monotonically with the slot Weber number [math]. Three primary sources of droplet production, namely, the lower and front edges of the vertical sheet and the rim of the circular sheet, were identified. The smallest droplets were seen to originate from the front edge (D32,FE) and the largest droplets from the lower edge (D32,LE) of the vertical sheet. The measured droplet diameters followed [math] and [math], whereas the droplets originating at the rim of the circular sheet followed [math]. The droplets at all three edges were found to depend more strongly on the ligament thickness than the ligament length. Following conservation of mass, a linear relation between the droplet diameter, D32, and the ligament thickness, tlig, at each edge has been obtained.

### Quantification of thermally-driven flows in microsystems using Boltzmann equation in deterministic and stochastic contexts

When the flow is sufficiently rarefied, a temperature gradient, for example, between two walls separated by a few mean free paths, induces a gas flow—an observation attributed to the thermostress convection effects at the microscale. The dynamics of the overall thermostress convection process is governed by the Boltzmann equation—an integrodifferential equation describing the evolution of the molecular distribution function in six-dimensional phase space—which models dilute gas behavior at the molecular level to accurately describe a wide range of flow phenomena. Approaches for solving the full Boltzmann equation with general intermolecular interactions rely on two perspectives: one stochastic in nature often delegated to the direct simulation Monte Carlo (DSMC) method and the others deterministic by virtue. Among the deterministic approaches, the discontinuous Galerkin fast spectral (DGFS) method has been recently introduced for solving the full Boltzmann equation with general collision kernels, including the variable hard/soft sphere models—necessary for simulating flows involving diffusive transport. In this work, the deterministic DGFS method, Bhatnagar-Gross-Krook (BGK), Ellipsoidal statistical BGK (ESBGK), and Shakhov kinetic models, and the widely used stochastic DSMC method, are utilized to assess the thermostress convection process in micro in-plane Knudsen radiometric actuator—a microscale compact low-power pressure sensor utilizing the Knudsen forces. The BGK model underpredicts the heat-flux, shear-stress, and flow speed; the S-model overpredicts; whereas, ESBGK comes close to the DSMC results. On the other hand, both the statistical/DSMC and deterministic/DGFS methods, segregated in perspectives, yet, yield inextricable results, bespeaking the ingenuity of Graeme Bird who laid down the foundation of practical rarefied gas dynamics for microsystems.