# Latest papers in fluid mechanics

### Multiscale investigation of Kolmogorov flow: From microscopic molecular motions to macroscopic coherent structures

It is extremely expensive to study turbulence using conventional molecular simulation methods such as direct simulation Monte Carlo and molecular dynamics methods, as the molecular scales and the turbulent characteristic scales are significantly separated. To bridge this gap, we employ a particle Fokker-Planck method, namely, the Langevin dynamics simulation method, to study two-dimensional Kolmogorov flow, which is induced by a spatially periodic external force in an unbounded domain. Our simulation results predict that when the Reynolds number (Re) exceeds the critical value, a sequence of bifurcations takes place in the flow as the Reynolds number increases, forming a variety of flow patterns. Correspondingly, the effective diffusion coefficient is enhanced due to convection. Two main regimes of the flow have been observed: the small-scale cellular structure regime (Rec < Re < 8Rec), and the large-scale coherent structure regime (Re > 8Rec). We demonstrate that Langevin dynamics can capture the double kinetic-energy cascade when the large-scale structure is formed in two-dimensional turbulence: the inverse energy cascade has a scaling law of k−4 due to energy condensation in the large-scale structures, while the direct energy cascade has an exponential decay corresponding to the dissipation mechanism. This work provides strong evidence that Langevin dynamics is a promising multiscale tool to study turbulence from molecular motions to large-scale coherent structures.

### Haines jumps: Pore scale mechanisms

Author(s): Zhonghao Sun and J. Carlos Santamarina

Sudden changes in pressure and fluid distribution are often observed in porous systems, and this work proposes and tests a physical model to explain this phenomenon. The analysis enables the authors to predict effects of various factors on the occurrence of such jumps, which are termed Haines instabilities.

[Phys. Rev. E 100, 023115] Published Tue Aug 27, 2019

### Particle tracking velocimetry applied to thermal counterflow in superfluid $^{4}\mathrm{He}$: Motion of the normal fluid at small heat fluxes

Author(s): B. Mastracci, S. Bao, W. Guo, and W. F. Vinen

Thermal counterflow of normal and superfluid components in superfluid helium leads to a form of turbulence confined to the superfluid component. Contrary to usual assumptions, these vortex filaments are shown to induce a strongly nonuniform flow in the normal fluid, even at small flow velocities.

[Phys. Rev. Fluids 4, 083305] Published Tue Aug 27, 2019

### Magnetic eddy viscosity of mean shear flows in two-dimensional magnetohydrodynamics

Author(s): Jeffrey B. Parker and Navid C. Constantinou

At large magnetic Reynolds numbers, magnetic induction leads to enhanced viscosity of mean shear flows. This effect is derived through simple physical arguments and verified in numerical simulations.

[Phys. Rev. Fluids 4, 083701] Published Tue Aug 27, 2019

### Method of regularized stokeslets: Flow analysis and improvement of convergence

Author(s): Boan Zhao, Eric Lauga, and Lyndon Koens

The Stokes flow created by regularized stokeslets (point forces) is analyzed. The authors determine the error made in the approximation compared to the singular solution, show how a source dipole appears generically in the far field, and propose an improved regularized solution.

[Phys. Rev. Fluids 4, 084104] Published Tue Aug 27, 2019

### Anisotropic energy transfers in rapidly rotating turbulence

We perform direct numerical simulations and analyze the ring-to-ring energy transfer in the three-dimensional hydrodynamic turbulence rendered anisotropic by rapid rotation. The rotation rate is taken to be so high that the Zeman scale is well beyond the Kolmogorov dissipation scale. Our main result is that, while the anisotropic transfer of energy is equatorward in the case of the decaying rotating turbulence, in the case of the forced rotating turbulence, the transfer is equatorward only for the scales larger than the forcing scale and poleward for the smaller scales. We also discuss in detail how our results are at odds with the corresponding results for the analogous magnetohydrodynamic turbulence.

### Nearshore natural convection induced by a periodic thermal forcing at the water surface

Field observations reveal that under calm weather conditions, natural convection resulting from spatial variations in the temperature field plays a significant role in promoting exchanges and mixings in lakes and reservoirs. The present investigation is concerned with natural convection generated by a periodically varying surface temperature within a reservoir model consisting of a sloping nearshore section and a flat offshore section. Three approaches, including derivation of analytical solution, numerical simulation, and scaling analysis, are integrated to reveal the variation of flow response with the intensity of the thermal forcing. The analytical solution reveals that for a sinusoidally varying surface temperature, a cosinusoidally varying surface heat flux is imposed if the duration of the period is sufficiently long. Numerical results show dramatic differences in flow response between conduction-dominated and convection-dominated thermal flow. The former is in phase with the cosinusoidal variation of surface heat flux, whereas the latter is in phase with the sinusoidal variation of surface temperature. The thermal forcing for conduction-dominated and convection-dominated flow is prescribed by surface heat flux and surface temperature, respectively. An evident phase lag is observed shortly after the thermal forcing switches sign. For convection-dominated flow with a Rayleigh number of 2 × 107, the maximum velocity during the cooling phase is significantly larger than that during the heating phase owing to the occurrence of flow instability during the cooling phase, which agrees with field observations. The scales for flow velocity and phase lag are derived by scaling analysis and verified by the results of numerical simulations.

### Draining of films on a quasivertical plate using viscous dissipation

This work focused on obtaining an improved and expanded general theoretical analysis of a two-dimensional film draining on a quasivertical plate, solving rigorous mass, momentum, and energy balances. A dimensional analysis and scaling was used to simplify the mathematical description, and a generalized Newtonian fluid was assumed as the film-forming material. A new quantity that governs the draining flow and film characteristics, called viscous dissipation, was proposed as part of the novel analytical expressions obtained in this work. Velocity profile, average velocity, flow rate, and local and average film thickness expressions can be obtained, allowing to simplify the overall calculation complexity and to find new potential analytical expressions using more complex rheological models.

### Self-similar hierarchies and attached eddies

Author(s): Beverley J. McKeon

Time-evolving coherent structure with features consistent with Townsend’s attached eddies and the developments associated with the reconstruction of flow statistics using the attached eddy hypothesis can be obtained from analysis of the (linear) resolvent associated with the Navier-Stokes equations.

[Phys. Rev. Fluids 4, 082601(R)] Published Mon Aug 26, 2019

### Effects of vertical magnetic field on impact dynamics of ferrofluid droplet onto a rigid substrate

Author(s): Jiandong Zhou and Dengwei Jing

The impact dynamics of a ferrofluid droplet on a tempered glass surface in the presence of a vertical magnetic field has been investigated experimentally. The results show how precise control of the impact dynamics of a ferrofluid droplet can be obtained.

[Phys. Rev. Fluids 4, 083602] Published Mon Aug 26, 2019

### Design, modeling, and experimental validation of an acoustofluidic platform for nanoscale molecular synthesis and detection

Microfluidic technologies are increasingly implemented to replace manual methods in biological and biochemical sample processing. We explore the feasibility of an acoustofluidic trap for confinement of microparticle reaction substrates against continuously flowing reagents in chemical synthesis and detection applications. Computational models are used to predict the flow and ultrasonic standing wave fields within two longitudinal standing bulk acoustic wave (LSBAW) microchannels operated in the 0.5–2.0 MHz range. Glass (gLSBAW) and silicon (siLSBAW) pillar arrays comprise trapping structures that augment the local acoustic field, while openings between pillars evenly distribute the flow for uniform exposure of substrates to reagents. Frequency spectra (acoustic energy density Eac vs frequency) and model-predicted pressure fields are used to identify longitudinal resonances with pressure minima in bands oriented perpendicular to the inflow direction. Polymeric and glass particles (10- and 20-µm diameter polystyrene beads, 6 µm hollow glass spheres, and 5 µm porous silica microparticles) are confined within acoustic traps operated at longitudinal first and second half-wavelength resonant frequencies (f1,E = 575 kHz, gLSBAW; f1,E = 666 kHz; and f2,E = 1.278 MHz, siLSBAW) as reagents are introduced at 5–10 µl min−1. Anisotropic silicon etched traps are found to improve augmentation of the acoustic pressure field without reducing the volumetric throughput. Finally, in-channel synthesis of a double-labeled antibody conjugate on ultrasound-confined porous silica microparticles demonstrates the feasibility of the LSBAW platform for synthesis and detection. The results provide a computational and experimental framework for continued advancement of the LSBAW platform for other synthetic processes and molecular detection applications.

### Design, modeling, and experimental validation of an acoustofluidic platform for nanoscale molecular synthesis and detection

Microfluidic technologies are increasingly implemented to replace manual methods in biological and biochemical sample processing. We explore the feasibility of an acoustofluidic trap for confinement of microparticle reaction substrates against continuously flowing reagents in chemical synthesis and detection applications. Computational models are used to predict the flow and ultrasonic standing wave fields within two longitudinal standing bulk acoustic wave (LSBAW) microchannels operated in the 0.5–2.0 MHz range. Glass (gLSBAW) and silicon (siLSBAW) pillar arrays comprise trapping structures that augment the local acoustic field, while openings between pillars evenly distribute the flow for uniform exposure of substrates to reagents. Frequency spectra (acoustic energy density Eac vs frequency) and model-predicted pressure fields are used to identify longitudinal resonances with pressure minima in bands oriented perpendicular to the inflow direction. Polymeric and glass particles (10- and 20-µm diameter polystyrene beads, 6 µm hollow glass spheres, and 5 µm porous silica microparticles) are confined within acoustic traps operated at longitudinal first and second half-wavelength resonant frequencies (f1,E = 575 kHz, gLSBAW; f1,E = 666 kHz; and f2,E = 1.278 MHz, siLSBAW) as reagents are introduced at 5–10 µl min−1. Anisotropic silicon etched traps are found to improve augmentation of the acoustic pressure field without reducing the volumetric throughput. Finally, in-channel synthesis of a double-labeled antibody conjugate on ultrasound-confined porous silica microparticles demonstrates the feasibility of the LSBAW platform for synthesis and detection. The results provide a computational and experimental framework for continued advancement of the LSBAW platform for other synthetic processes and molecular detection applications.

### Diffusion of ellipsoids in laboratory two-dimensional turbulent flow

We report on the transport properties and orientational dynamics of ellipsoidal objects advected by laboratory two-dimensional turbulence. It is found that ellipsoids of different sizes have preferential direction of transport, either along their major axes or minor axes. The two components of the ellipsoid diffusion coefficient depend on the ratio of the length of the ellipsoids along major axes aa to the turbulence forcing scale Lf. Large ellipsoids (aa > Lf) diffuse faster in the direction parallel to their major axes. In contrast, small ellipsoids diffuse faster in the direction transverse to their major axes. We study this transition vs the ratio aa/Lf and relate it to the coupling between translational and rotational motion of anisotropic objects. The features of the turbulent transport of ellipsoids can be understood by considering the interaction of these anisotropic objects with the underlying structure of two dimensional turbulent flows made of meandering coherent bundles.

### Decomposition of the mean friction drag in zero-pressure-gradient turbulent boundary layers

The ability to understand and predict mean friction drag generation in wall-bounded turbulence is highly desirable in many engineering applications. In this paper, we decompose the mean friction drag in incompressible (250 ≤ Reτ ≤ 1270) and compressible (M = 2.0 and 250 ≤ Reτ ≤ 1110) zero-pressure-gradient turbulent boundary layers (TBLs) into three physics-informed contributions, by using the identity of Renard and Deck [“A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer,” J. Fluid Mech. 790, 339–367 (2016)] and its compressible-flow extension [Li et al., “Decomposition of the mean skin-friction drag in compressible turbulent channel flows,” J. Fluid Mech. 875, 101–123 (2019)], respectively. The Reynolds number effects and scaling of each contributing term are investigated. Proportionality of the viscous and logarithmic increase with Reτ of the turbulent one when scaled by [math] are found, with different scaling coefficients in incompressible and compressible TBLs, owing to variation in the thermodynamic properties in the compressible cases. On use of compressibility transformations to account for variation in the thermodynamic properties in the wall-normal direction, the terms contributing to friction in compressible TBLs are found to reduce to those in the incompressible limit, with good accuracy. At M = 2.0, deviations from universality are mainly confined to the near-wall region, say y+ < 30, and account for approximately 16% of the generated friction.

### Self-excited rotation and flow dynamics across a freely rotatable square cylinder confined between two parallel walls

This paper reports on a numerical investigation conducted to study the vortex-induced rotation of a square cylinder confined between two parallel walls. The fluid flow past the cylinder is simulated by solving the Navier–Stokes equations, and the cylinder’s motion is captured using Newton’s law. A dynamic mesh technique is employed to track the movement of the cylinder boundaries. The numerical model is first validated through comparisons with results in the literature. By changing the fluid velocity and wall distance, the influences of the Reynolds number (40 ≤ Re ≤ 800) and blockage ratio (0.10 ≤ br ≤ 0.55) on the rotation characteristics and flow dynamics are then revealed. Six distinct rotating modes are recognized in the present confined geometries, namely, static mode I (with θ = 0), static mode II (with θ = ±π/4), oscillating mode I (with respect to θ = 0), oscillating mode II (with respect to θ = ±π/4), an autorotating mode, and a randomly rotating mode. A phase diagram is made to describe the distribution of these rotating modes with respect to Re and br. To understand the underlying mechanisms, typical fluid–structure interaction details are presented and discussed for each rotating mode. Owing to the confinement of the parallel walls, the shear-induced torque is found to play an important role in the rotation of the cylinder, and its contribution is quantitatively compared with the pressure-induced torque.

### Electric fields enable tunable surfactant transport to microscale fluid interfaces

Author(s): Rajarshi Sengupta, Aditya S. Khair, and Lynn M. Walker

The transport dynamics of oil-soluble surfactants to oil-water interfaces are quantified using a custom-built electrified capillary microtensiometer platform. Dynamic interfacial tension measurements reveal that surfactant transport is enhanced under a dc electric field, due to electro-migration of ...

[Phys. Rev. E 100, 023114] Published Fri Aug 23, 2019

### Criterion for particle rebound during wet collisions on elastic coatings

Author(s): Matthew Ryan Tan, Yumo Wang, and Joelle Frechette

The bouncing of a rigid particle off a soft coating in a viscous fluid is analyzed. The coating thickness moderates the degree to which elasticity affects the rebound criteria (and vice versa) in a fashion distinct from the effect of the elasticity or of the Stokes number.

[Phys. Rev. Fluids 4, 084305] Published Fri Aug 23, 2019

### Particle and rigidized red blood cell concentration distributions in microchannel flows

The motion and concentration distribution of particles and cells in flow are important factors which affect the fluid properties, flow structure, and mass transfer of biological and chemical species in blood vessels and channels. In this study, number density distributions of particles and rigidized red blood cells (RBCs) in a microchannel whose size is comparable to the sizes of the particle and RBCs are measured. Measurements were conducted at several streamwise locations for suspensions of particles and RBCs with hematocrits of the order of 10% and particle sizes of 5 and 8 µm. Analysis of the migration and resulting concentration distribution of the particles and RBCs was conducted using a model that considers the particle–particle collision and fluid dynamic force. As the size of the microchannel is small, the wall effect on the collision and migration of the particles and RBCs was significant. The wall reduced the overlapping area of the particles in collision and their displacement after collision (mobility), which varied the number, location, and magnitude of the maximum peaks observed in the number density distribution. Furthermore, the rotational motion of the rigidized RBCs in the channel flow reduced the effective lengths of the overlapping area and displacement, whereas it produced additional migration at the wall. With these terms added in the model, the number density distributions of the particles and RBCs showed reasonable agreement with those of the measurement. Especially, the number of peaks and their location for the maximum values in the model and measurement matched well.

### Particle and rigidized red blood cell concentration distributions in microchannel flows

The motion and concentration distribution of particles and cells in flow are important factors which affect the fluid properties, flow structure, and mass transfer of biological and chemical species in blood vessels and channels. In this study, number density distributions of particles and rigidized red blood cells (RBCs) in a microchannel whose size is comparable to the sizes of the particle and RBCs are measured. Measurements were conducted at several streamwise locations for suspensions of particles and RBCs with hematocrits of the order of 10% and particle sizes of 5 and 8 µm. Analysis of the migration and resulting concentration distribution of the particles and RBCs was conducted using a model that considers the particle–particle collision and fluid dynamic force. As the size of the microchannel is small, the wall effect on the collision and migration of the particles and RBCs was significant. The wall reduced the overlapping area of the particles in collision and their displacement after collision (mobility), which varied the number, location, and magnitude of the maximum peaks observed in the number density distribution. Furthermore, the rotational motion of the rigidized RBCs in the channel flow reduced the effective lengths of the overlapping area and displacement, whereas it produced additional migration at the wall. With these terms added in the model, the number density distributions of the particles and RBCs showed reasonable agreement with those of the measurement. Especially, the number of peaks and their location for the maximum values in the model and measurement matched well.

### Statics and dynamics of polymeric droplets on chemically homogeneous and heterogeneous substrates

Author(s): Ö. Öztürk and J. Servantie

We present a molecular dynamics study of the motion of cylindrical polymer droplets on striped surfaces. We first consider the equilibrium properties of droplets on different surfaces, we show that for small stripes the Cassie-Baxter equation gives a good approximation of the equilibrium contact ang...

[Phys. Rev. E 100, 023113] Published Thu Aug 22, 2019