# Latest papers in fluid mechanics

### Influence of initial phase on subharmonic resonance in an incompressible boundary layer

The influence of the initial phase of fundamental and subharmonic waves on subharmonic resonance is investigated for an incompressible boundary layer with zero and adverse pressure gradients. Parabolized stability equation analyses are carried out for various combinations of the initial phases of fundamental and subharmonic waves. The amplification of subharmonic and higher modes is found to depend strongly on the initial phases, and this dependence is consistent with observations from previous experimental studies. There exists a certain combination of initial phases that leads to resonance or anti-resonance condition (i.e., maximum or minimum growth, respectively). For all combinations of the initial phases, the phase dependence appears to be a function of a single parameter that represents the initial phase difference between the fundamental and subharmonic waves. The amplification in the subharmonic resonant interaction depends on the initial phase difference rather than the individual initial phase of the fundamental or subharmonic wave. In the downstream direction, the phase difference changes from the initial value and eventually converges to a specific value approximately ranging from 80° to 90°, regardless of the initial phase difference. This transient behavior does not start until the subharmonic wave enters the parametric resonant stage, which yields double-exponential growth. The qualitative characteristic of the phase dependence remains unchanged for the fundamental frequencies and spanwise wavenumbers as well as for the pressure gradients studied. The method of analysis and results contribute to the physical foundations of controlling boundary-layer transition dominated by the subharmonic resonance.

### Regulating droplet impact on a solid hydrophobic surface through alternating current electrowetting-on-dielectric

The phenomenon of droplet impact is commonly found in industrial and agricultural processes. The basic characteristics and theories of a droplet impacting solid walls have been extensively studied, but the regulation of the droplet impact phenomenon has not been adequately examined. This study investigates the regulation of droplet impact on a hydrophobic surface based on alternating current electrowetting-on-dielectric (AC EWOD). When a water droplet impacts a virgin Teflon surface at 1.06 m/s, the phenomenon of partial rebound occurs. When an AC voltage is applied to an electrode pair underneath the Teflon layer, the droplet is stabilized on the hydrophobic surface after impact. To investigate the mechanism of influence of the AC signal on the regulation of droplet impact, the variation in the spread diameter and height of the droplet were characterized at different frequencies and amplitudes of the AC signal. An oscillation in the diameter of the droplet was observed in the retraction stage with the application of AC EWOD, which was the dominant effect in neutralizing the retraction kinetic energy and yielded the rebound inhibition effect. A transition diagram between partial droplet rebound and rebound inhibition was plotted in terms of voltage, frequency, and the Weber number, and theoretical analysis was carried out to determine the retraction kinetic energy dissipated by the viscous force when the AC EWOD signal was applied.

### Numerical study of interactions between shock waves and a circular or elliptic bubble in air medium

The interaction of shock waves with bubbles is of interest in a variety of areas, such as shock wave lithotripsy, cavitation erosion, and sonoluminescence. For these, the spatial technology, which is based on the five-equation model and the finite volume method, is employed to numerically study this issue in this paper. Research on the interaction between shock waves and circular bubbles indicates that the generation and distribution of vorticity have an important influence on the deformation of the bubble interface, and the vorticity will accelerate the turbulent mixing of the two-phase gas. In addition, the interaction processes between shock waves and elliptic bubbles aligned horizontally and elliptic bubbles aligned vertically in air medium with different aspect ratios are investigated. Results show that the time required to generate the transverse jet and vortex structure decreases, and the deformation degree and the collapse speed increase when increasing the aspect ratio of elliptic bubbles aligned horizontally. For elliptic bubbles aligned vertically, the position of the transverse jet is related to the aspect ratio; the greater the aspect ratio, the farther the jet position is from the centerline.

### A many-body dissipative particle dynamics study of eccentric droplets impacting inclined fiber

The phenomenon of droplets impacting fiber has important applications in the recovery of waste liquid, separation of solid and liquid phases, gas and liquid phases, and glass wool manufacturing. This study explored the impact of droplets on fiber based on the many-body dissipative particle dynamics (MDPD) method. First, the impact of droplets on fiber at different angles was simulated, and the results were found to be in good agreement with the experimental results. We then investigated the influence of droplet eccentricity, fiber tilt angle, and wettability on the collision results and found that droplet critical velocity [math], wetting length L, contact time t, and droplet capture rate all increased with tilt angle and decreased with the increase in eccentricity. In addition, fiber wettability had little effect on contact time t but had a greater effect on critical velocity [math]. Except for hydrophobicity, wettability also had little effect on droplet capture rate. The theoretical derivation obtained the analytical formulas of critical velocity [math], dimensionless wetting length [math], and dimensionless contact time [math] when the eccentric droplet hits the inclined fiber. The simulation results are highly consistent with the theoretical values. This research possesses important guiding significance for actual production and life.

### Asymmetric instability in thin-film flow down a fiber

Author(s): Chase T. Gabbard and Joshua B. Bostwick

Experiments show that thin film flow down a fiber exhibits beading patterns whose symmetry about the fiber depends upon the fiber diameter and liquid surface tension. Both symmetric and asymmetric morphologies exhibit absolute (isolated, Plateau-Rayleigh) and convective instabilities, with the asymmetric beading dynamics resembling that of the free viscous jet indicating a minimal interaction between the liquid and fiber.

[Phys. Rev. Fluids 6, 034005] Published Mon Mar 29, 2021

### Unified wall-resolved and wall-modeled method for large-eddy simulations of compressible wall-bounded flows

Author(s): Francesco De Vanna, Michele Cogo, Matteo Bernardini, Francesco Picano, and Ernesto Benini

Wall-resolved large eddy simulations and wall-modeled large eddy simulations are still separate strategies in the field of wall-turbulence applications, and no significant attempts have been documented to blend them in order to exploit the full potential of the two methods. This work enables a smooth transition between these two techniques, designing a robust algorithm that dynamically adapts the wall treatment. In particular, we propose a unified method that employs augmented turbulent viscosity and diffusivity at the wall location and allows for preservation of both the no-slip and isothermal/adiabatic conditions.

[Phys. Rev. Fluids 6, 034614] Published Mon Mar 29, 2021

### Viscous vortex layers subject to more general strain and comparison to isotropic turbulence

Viscous vortex layers subject to a more general uniform strain are considered. They include Townsend's steady solution for plane strain (corresponding to a parameter a = 1), in which all the strain in the plane of the layer goes toward vorticity stretching, as well as Migdal's recent steady asymmetric solution for axisymmetric strain (a = 1/2), in which half of the strain goes into vorticity stretching. In addition to considering asymmetric, symmetric, and antisymmetric steady solutions [math], it is shown that for a < 1, i.e., anything less than the Townsend case, the vorticity inherently decays in time: only boundary conditions that maintain a supply of vorticity at one or both ends lead to a non-zero steady state. For the super-Townsend case a > 1, steady states have a sheath of opposite sign vorticity. Comparison is made with homogeneous-isotropic turbulence, in which case the average vorticity in the strain eigenframe is layer-like, has wings of opposite vorticity, and the strain configuration is found to be super-Townsend. Only zero-integral perturbations of the a > 1 steady solutions are stable; otherwise, the solution grows. Finally, the appendix shows that the average flow in the strain eigenframe is (apart from an extra term) the Reynolds-averaged Navier–Stokes equation.

### Lagrangian models of particle-laden flows with stochastic forcing: Monte Carlo, moment equations, and method of distributions analyses

Deterministic Eulerian–Lagrangian models represent the interaction between particles and carrier flow through the drag force. Its analytical descriptions are only feasible in special physical situations, such as the Stokes drag for low Reynolds number. For high particle Reynolds and Mach numbers, where the Stokes solution is not valid, the drag must be corrected by empirical, computational, or hybrid (data-driven) methods. This procedure introduces uncertainty in the resulting model predictions, which can be quantified by treating the drag as a random variable and by using data to verify the validity of the correction. For a given probability density function of the drag coefficient, we carry out systematic uncertainty quantification for an isothermal one-way coupled Eulerian–Lagrangian system with stochastic forcing. The first three moment equations are analyzed with a priori closure using Monte Carlo computations, showing that the stochastic solution is highly non-Gaussian. For a more complete description, the method of distributions is used to derive a deterministic partial differential equation for the evolution of the joint PDF of the particle phase and drag coefficient. This equation is solved via Chebyshev spectral collocation method, and the resulting numerical solution is compared with Monte Carlo computations. Our analysis highlights the importance of a proper approximation of the Dirac delta function, which represents deterministic (known with certainty) initial conditions. The robustness and accuracy of our PDF equation were tested on one-dimensional problems in which the Eulerian phase represents either a uniform flow or a stagnation flow.

### The dynamics of flow-induced flutter of a thin flexible sheet

The dynamics of the flow-induced flutter of a thin flexible sheet attached to a streamlined support was experimentally studied in a low-speed wind tunnel. In this study, both the structural dynamics and the fluid dynamics aspects of flutter were considered. The kinematics of the oscillating sheet was investigated using high-speed imaging and the flowfield was examined using hotwire anemometry and particle image velocimetry (PIV). The small-scale perturbation in the flow over the sheet was found to induce a low-amplitude vibration, which changed to a large-amplitude flutter as the wind speed was increased to a critical value. The initiation of flutter occurs with the second mode limit cycle oscillation (LCO), bypassing the first mode, and changes to third mode LCO at a higher wind speed. Based on the behavior of the sheet, five different regimes are identified and discussed in this paper. The natural frequencies of the sheet were found to have a significant role in the initiation of the LCO and its transition to the higher modes. The PIV results show a highly accelerated flow over the curved surface of the oscillating sheet, which induces a lift force that acts as a driving force. The accelerated flow over the sheet separates at its tail and forms a large-scale undulating wake. In the LCO regimes, any large-scale flow separation over the sheet could not be observed and the flow appears to be attached even at high deflection of the sheet.

### Overstable rotating convection in the presence of a vertical magnetic field

Recently, Banerjee et al. [Phys. Rev. E 102, 013107 (2020)] investigated overstable rotating convection in the presence of an external horizontal magnetic field and reported a rich bifurcation structure near the onset. However, the bifurcation structure near the onset of overstable rotating convection in the presence of a vertical magnetic field has not been explored yet. We address the issue here by performing three dimensional direct numerical simulations and low-dimensional modeling of the system using a Rayleigh–Bénard convection model. The control parameters, namely, the Taylor number (Ta), the Chandrasekhar number (Q), and the Prandtl number (Pr) are varied in the ranges [math], and [math]. Our investigation reveals two qualitatively different onset scenarios including bistability (coexistence of subcritical and supercritical convections). Analysis of the low-dimensional model shows that a supercritical Hopf bifurcation is responsible for the supercritical onset and a subcritical pitchfork bifurcation is responsible for the subcritical onset. It is also observed that the appearance of a subcritical convection at the onset has strong dependence on all three control parameters: Ta, Q, and Pr. The scenario of a subcritical convection is found to disappear as Pr is increased for fixed Ta and Q. However, most striking findings of the investigation are that the increment in Ta for fixed Q and Pr opposes the subcritical convection, whereas the increment in Q for fixed Ta and Pr favors it. This is in sharp contrast with the earlier results reported in rotating magnetoconvection.

### Effect of face shield design on the prevention of sneeze droplet inhalation

A flow simulation was performed for face shields to investigate whether varying a shield's edge shape could prevent droplets from entering the shield. Face shields with two types of edge shapes were used. The “Type I” shield had small plates mounted on the top and bottom edges of the shield to physically inhibit the sneeze inflow. The “Type II” shield had small brims sticking forward from the shield surface and small plates sticking upward and downward at the top and bottom edges to inhibit the entrainment flow produced by the vortex ring using sneeze flow. We confirmed that the flow characteristics around a face shield can be controlled using the shield's edge shape. In Type I, the entraining flow inside the shield was inhibited by the mounted small plate at the bottom edge, ensuring the inhibiting effect, but not at the top edge. In Type II, the entrained flow inside the shield was inhibited by the mounted brim and small plate at the top edge, ensuring the inhibiting effect, but not at the bottom edge. The effects of the Type II design parameters on the flow characteristics around the face shield were examined. The results indicate that at the top edge, increasing the length of the brim and not mounting the small plate at an incline from the shield surface improves the inhibition effect. At the bottom edge, shortening the length of the brim and mounting the small plate at an incline from the shield surface improves the inhibition effect.

### Resonance behaviors in periodic viscoelastic electrokinetic flows: A universal Deborah number

The electrokinetic transports of viscoelastic fluids are investigated in different channel geometries. The fluid elasticity is responsible for the generation of resonance behaviors under periodic pressure gradient driving. We introduce a universal Deborah number defined by the surface-to-volume ratio of the channel, and thereby a critical value Dec = 1/4 can be applied to different channel geometries. Above this threshold, the resonances occur at particular frequencies and result in a dramatic increase in the amplitudes of the flow rate, streaming potential, and energy conversion efficiency. The locations of resonant peaks are determined by the ratio of the effective characteristic size of the channel to the wavelength of viscoelastic shear waves. Interestingly, in the annular geometry with small effective size, even order resonances are suppressed significantly relative to odd order resonances. For the maximum energy conversion efficiency in steady flows in different geometries, we find that the annular geometry is optimal, which has a 20% increase in the maximum efficiency compared to the cylindrical geometry.

### Deep-learning of parametric partial differential equations from sparse and noisy data

Data-driven methods have recently made great progress in the discovery of partial differential equations (PDEs) from spatial-temporal data. However, several challenges remain to be solved, including sparse noisy data, incomplete library, and spatially or temporally varying coefficients. In this work, a new framework, which combines neural network, genetic algorithm, and stepwise methods, is put forward to address all of these challenges simultaneously. In the framework, a trained neural network is utilized to calculate derivatives and generate a large amount of meta-data, which solves the problem of sparse noisy data. Next, the genetic algorithm is used to discover the form of PDEs and corresponding coefficients, which solves the problem of the incomplete initial library. Finally, a stepwise adjustment method is introduced to discover parametric PDEs with spatially or temporally varying coefficients. In this method, the structure of a parametric PDE is first discovered, and then the general form of varying coefficients is identified. The proposed algorithm is tested on the Burgers equation, the convection-diffusion equation, the wave equation, and the KdV equation. Results demonstrate that this method is robust to sparse and noisy data, and is able to discover parametric PDEs with an incomplete initial library.

### Local velocity of thermoresponsive colloidal gels in rate-driven flow

The interplay between flow and attractive interactions in colloidal gels results in complex particle trajectories and velocity profiles that are not evident from bulk rheological measurements. We use high-speed confocal microscopy to investigate the local velocity of a low volume fraction (ϕ = 0.20) thermogelling nanoemulsion system as it flows through a cylindrical capillary at temperatures below and above the gel point. The nanoemulsions are composed of poly(dimethyl siloxane) droplets in a continuous phase of sodium dodecyl sulfate, de-ionized water, and a gelator molecule, poly(ethylene glycol diacrylate). The trajectories of fluorescent polystyrene tracer beads in the oil-rich domains are tracked using two-dimensional image processing. While the velocity profiles agree with those computed from rheometry measurements for nanoemulsion suspensions below the gel point temperature, increasing attractive interactions above the gel point results in statistically significant deviations. Specifically, the velocity measurements indicate a higher yield stress and a larger degree of shear thinning than expected from bulk rheology measurements, resulting in a more plug-shaped velocity profile as temperature and associated interdroplet attraction increase. These deviations from theoretical predictions are likely due to structural heterogeneity. Confocal microscopy images show that small, fluidized clusters are found in high shear rate regions near the capillary walls, while large dense clusters form in low shear rate regions closer to the center of the capillary.

### Nonuniformities in miscible two-layer two-component thin liquid films

Author(s): Christopher Larsson and Satish Kumar

Depositing and obtaining liquid films of uniform thickness is a problem integral to numerous applications that require multilayer films where each layer has distinct properties. Through a lubrication-theory-based model, this work studies the mechanisms that may initiate dewetting in miscible two-layer two-component films. Numerical solutions reveal that disparities in initial solute concentration between the film layers couple with circulatory flows to produce significant film-height nonuniformities. Several scaling relationships are developed to shed light on the underlying physical mechanisms.

[Phys. Rev. Fluids 6, 034004] Published Fri Mar 26, 2021

### Simulating particle settling in inclined narrow channels with the unresolved CFD-DEM method

Author(s): Junsheng Zeng, Pengfei Tang, Heng Li, and Dongxiao Zhang

Sediment settling in inclined fractures (channels with high aspect ratio) is studied numerically. Unlike the conventional Boycott effect, heterogeneous particle-clustering plumes are observed from the simulation results. Granular-induced Kelvin-Helmholtz and Rayleigh-Taylor instabilities are found to be the dominating mechanisms in this process. This work deepens the understanding of the Boycott effect in fractures, and provides various quantitative relationships of acceleration ratio versus inclination angle.

[Phys. Rev. Fluids 6, 034302] Published Fri Mar 26, 2021

### Violations of Jeffery's theory in the dynamics of nanographene in shear flow

Author(s): Simon Gravelle, Catherine Kamal, and Lorenzo Botto

By using molecular dynamics simulations we demonstrate that at high Péclet numbers a nanographene suspended in a shear flow aligns at a constant orientation angle, in contrast with the rotary motion predicted by Jeffery’s theory. This instantaneous alignment with the flow of the nanographene is due to hydrodynamic slip at the fluid-particle interface, and produces a marked reduction in suspension viscosity compared to the no-slip case.

[Phys. Rev. Fluids 6, 034303] Published Fri Mar 26, 2021

### Effects of approach flow conditions on the unsteady three-dimensional wake structure of a square-back Ahmed body

Author(s): Nam Kang, Ebenezer E. Essel, Vesselina Roussinova, and Ram Balachandar

We investigate the effects of approach flow conditions (uniform flow (UF): Case A and thick turbulent boundary layer (TBL): Case B) on the unsteady three-dimensional wake characteristics and bimodality of a square back Ahmed body. Using improved delayed detached eddy simulations we show that TBL induces a much higher ground clearance momentum deficit than UF, which significantly alters wake asymmetry orientation in the wall-normal plane and completely suppresses bimodal wake behavior in the spanwise plane. Both time-averaged and time-resolved turbulence statistics are used to explore the differences between the wake structure of the Ahmed body subject to the two approach flow conditions.

[Phys. Rev. Fluids 6, 034613] Published Fri Mar 26, 2021

### The role of elasticity in thixotropy: Transient elastic stress during stepwise reduction in shear rate

Despite the wide-spread use and importance of thixotropic materials, accurate theoretical descriptions are still limited to a handful of model transient flow conditions. We employ an iterative series of tests to experimentally probe the complex dynamics exhibited by thixotropic materials. We use flow cessation tests to identify transient elastic stresses during stress jump tests. It is shown that the evolution of the elastic stress closely follows that of total stress in the series of stress jump tests, indicating that elasticity is a significant contributor to thixotropy.

### Eccentric disks falling in water

The freely falling of solid bodies in viscous liquids is an interesting issue concerned with many hydrodynamics and engineering problems. The eccentricity of the solid bodies may lead to new dynamic behaviors and complex paths of falling. Eccentric annular disks with holes covered by transparent tapes are used to study the effect of eccentricity on the descent flight. This paper experimentally investigates the falling regimes of the eccentric disks in water with Reynolds number between 4000 and 21 000 and classifies the descent modes into three types, i.e., the fluttering, chaotic, and tumbling motions, the transition motion, and the new stable descending motion. Finally, we map out the three descent modes of eccentric disks in a two-dimensional phase space of eccentricity e and dimensionless moment of inertia I*. It is found that eccentricity is a significant parameter when describing the descent modes of eccentric disks. Enough large eccentricity stabilizes freely falling disks, while small eccentricity (e < 0.06) leads to the rotation of disk in an arc in the x-y plane accompanied by chaotic and tumbling motions or asymmetric zigzag motion. The descent modes are mainly dependent on e for I* higher than 0.02, and dependent on both e and I* for I* lower than 0.02.