# Latest papers in fluid mechanics

### Enhanced performance of tandem plunging airfoils with an asymmetric pitching motion

The flapping wings or fins in an in-line arrangement are a common scene in flocks and schools, as well as flying creatures with multiple pairs of wings, e.g., dragonflies. Conventional studies on these topics are underpinned by tandem plunging airfoils in either a vertical or a declined stroke plane. The former model mostly considers a symmetrical pitching motion, and the latter model fails to separate the effect of the asymmetric pitching from that of the declined incoming flow. However, our study focuses on the tandem airfoils with vertical plunging and asymmetric pitching in a horizontal freestream and, therefore, explains the effects of asymmetric pitching on tandem plunging airfoils. Using numerical methods, the aerodynamic performance and vortical structures of the tandem airfoils are examined, and the effects of the non-zero geometric angle of attack (α0), phase angles in the plunging and pitching motion (φ and θ), and inter-foil spacing (G/c) are discussed. Our results show that the tandem arrangement is beneficial to enhance the propulsion thrust while retaining the lifting capacity of the airfoil at a non-zero α0. The effects of φ and G/c are coupled since they both determine the interaction between the hind airfoil and the leading-edge vortex in the wake and the out-of-phase mode is suggested for the tandem airfoils at G/c = 1 to enhance both lift and thrust. For a tandem airfoil with in-phase mode, the optimal G/c is around 1.5 to 2. Moreover, the asymmetric pitching of the in-phase plunging airfoils should be synchronized to retain the enhanced performance.

### Water drop impacts on regular micropillar arrays: The impact region

A liquid drop impact on to a rough solid typically produces an “impact region,” which is an area of fully wetted surface smaller than or equal to the projected area of the drop. Here, high-speed photography is used to study the size and symmetry of this impact region and microbubbles within it for water drop impacts on regular square arrays of hydrophobic micropillars. Outcomes are most strongly influenced by pillar pitch and impact Weber number (We), and there is an apparent transition from vertical to more horizontal wetting near the edge of the projected area of the falling drop. The impact region size is well described by energetic and pinning transition analyses, but profound asymmetries are observed, indicating the influence and superposition of cross-flows for gas and liquid escape. Zipping of the liquid–air interface between pillars during later stages of drop spreading is also studied. The surfaces have 20 μm wide polydimethylsiloxane pillars of circular or square cross section. Variations in array pitch (40–80 μm) and height (15–30 μm) are systematically investigated using droplets of diameter 2.51 ± 0.04 mm over the range [math] We [math]. The geometric regularity of these surfaces could give rise to technological applications, but the results are also relevant to the many natural and industrial processes in which liquid drops impact upon dry surfaces with micrometer scale roughness.

### Flexible cylinder flow-induced vibration

In this paper, we conducted a selective review on the recent progress in physics insight and modeling of flexible cylinder flow-induced vibrations (FIVs). FIVs of circular cylinders include vortex-induced vibrations (VIVs) and wake-induced vibrations (WIVs), and they have been the center of the fluid-structure interaction (FSI) research in the past several decades due to the rich physics and the engineering significance. First, we summarized the new understanding of the structural response, hydrodynamics, and the impact of key structural properties for both the isolated and multiple circular cylinders. The complex FSI phenomena observed in experiments and numerical simulations are explained carefully via the analysis of the vortical wake topology. Following up with several critical future questions to address, we discussed the advancement of the artificial intelligent and machine learning (AI/ML) techniques in improving both the understanding and modeling of flexible cylinder FIVs. Though in the early stages, several AL/ML techniques have shown success, including auto-identification of key VIV features, physics-informed neural network in solving inverse problems, Gaussian process regression for automatic and adaptive VIV experiments, and multi-fidelity modeling in improving the prediction accuracy and quantifying the prediction uncertainties. These preliminary yet promising results have demonstrated both the opportunities and challenges for understanding and modeling of flexible cylinder FIVs in today's big data era.

### Reconstructing Rayleigh–Bénard flows out of temperature-only measurements using nudging

Nudging is a data assimilation technique that has proved to be capable of reconstructing several highly turbulent flows from a set of partial spatiotemporal measurements. In this study, we apply the nudging protocol on the temperature field in a Rayleigh–Bénard convection system at varying levels of turbulence. We assess the global, as well as scale by scale, success in reconstructing the flow and the transition to full synchronization while varying both the quantity and quality of the information provided by sparse measurements either on the Eulerian or Lagrangian domain. We assess the statistical reproduction of the dynamic behavior of the system by studying the spectra of the nudged fields as well as the correct prediction of heat transfer properties as measured by the Nusselt number. Furthermore, we analyze the results in terms of the complexity of solutions at various Rayleigh numbers and discuss the more general problem of predicting all state variables of a system given partial or full measurements of only one subset of the fields, in particular, temperature. This study sheds new light on the correlation between the velocity and temperature in thermally driven flows and on the possibility to control them by acting on the temperature only.

### Energy density balance during shock wave implosion in water

Analytical modeling of the evolution of cylindrical and spherical shock waves (shocks) during an implosion in water is presented for an intermediate range of convergence radii. This range of radii was observed in experiments when the exploding wire expansion dynamics does not influence on shock propagation, but not yet described by well-known self-similar solutions. The model is based on an analysis of the change in pressure and kinetic energy density as well as on the corresponding fluxes of internal and kinetic energy densities behind the shock front. It shows that the spatial evolution of the shock velocity strongly depends on the initial compression, the adiabatic index of water, and the geometry of convergence. The model also explains the transition to a rapid like a self-similar increase in the shock velocity at only a certain radius of the shock that is observed in experiments. The dependence of the threshold radius, where the shock implosion follows the power law (quasi self-similarity), on the initial compression is determined. It is stated that in the entire range of the shock radii, the internal and kinetic energy density fluxes are equal, which agrees with known experimental data.

### Experimental investigation of chaotic induced-charge electro-osmosis

Near-surface chaotic induced-charge electro-osmosis (ICEO) was numerically predicted on a metallic cylinder some years ago [Davidson et al., “Chaotic induced-charge electro-osmosis,” Phys. Rev. Lett. 112, 128302 (2014)]. However, no systematic experimental investigation has yet been conducted on this problem. In this paper, we experimentally observed that ICEO is stable in weak electric fields and becomes chaotic in strong electric fields. Unlike the numerical prediction, the observed chaotic ICEO is irregular and unstable across the whole velocity field. The chaotic ICEO flow pattern varies significantly with time. The chaos degree grows upon increasing the electric field. Moreover, the critical electric field at which the ICEO transits from the stable to chaotic state shows a dependence on the sodium chloride concentration and electric field frequency. The new findings can contribute to the understanding of ICEO and facilitate the development of ICEO-based micro- and nano-fluidic applications.

### Consistent hydrodynamics of ferrofluids

We develop a consistent hydrodynamic theory for ferrofluids that can be concentrated, strongly interacting, and polydisperse. We analyze the dynamics of ferrocolloids under imposed flow and magnetic field, from micro-, meso-, and macroscopic points of view. We settle the long-standing debate on the correct reactive contribution to magnetization dynamics near or far from equilibrium. We obtain a fundamental mesoscopic rotational fluctuation-dissipation relation, linking vortex viscosity and rotational self-diffusivity and with far-reaching consequences on ferrofluid hydrodynamics. It distinguishes from the traditional Stokes–Einstein–Debye relation that only applies to dilute and noninteracting systems. Furthermore, it is used to infer the size of structure units whose rotational diffusion is responsible for the primary Debye peak of water. The characteristic hydrodynamic radius is estimated to be [math] nm, considerably larger than the geometrical radius of water molecules. This is in contrast to the result obtained by naively employing the Stokes–Einstein–Debye relation. We revisit the magnetoviscous effect in ferrofluids and obtain novel expressions for the rotational viscosity, shedding new light on the effects of inter-particle correlations and particle packing. In particular, previous models usually confuse solvent vorticity with suspension vorticity and do not yield the actual rotational viscosity measured in experiments. We compare our theoretical predictions with recent simulations and find quantitatively good agreements. Our work is to be a cornerstone for understanding ferrofluid dynamics and of considerable importance to various applications. It can be also valuable for studying the hydrodynamics of other structured fluids.

### Main modes of microfilament particles deformation in rough channels

The fate and transport of microfilaments in complex structured porous systems are largely affected by the geometry of the irregular pore space in these media. Local features of fluid flow, including local flow instabilities, vorticities, stagnant zones, and reverse flows, which result from the spatially varying pore throat size and altering shear stresses along the channel due to the presence of rough walls, can cause various modes of deformation of filaments and them being carried in reverse direction of the general fluid flow. Furthermore, the buildup of microfilaments along the channel can clog the pore space and rearrange the flow in the channel. In this study, we focus on investigating the role of channel wall roughness on the motion and deformation of five deformable filaments flowing in a channel filled with fluid. A bead-spring model is used for the filament model. At low Reynolds numbers, roughness simply increases the length of the path line along which the filament is being transported. Moreover, at higher Reynolds numbers, the filament closer to the walls can get stuck in the dead flow zones within the rough geometry peaks. The filaments closer to the centerline of the channel undergo less deformation compared to those located closer to the walls. A larger Reynolds number or a more rough geometry of the walls can result in a more wiggly form of the filament. Intermediate roughness and a medium Reynolds number result in more of a hairpin-like filament shape.

### Dense velocity reconstruction from particle image velocimetry/particle tracking velocimetry using a physics-informed neural network

The velocities measured by particle image velocimetry (PIV) and particle tracking velocimetry (PTV) commonly provide sparse information on flow motions. A dense velocity field with high resolution is indispensable for data visualization and analysis. In the present work, a physics-informed neural network (PINN) is proposed to reconstruct the dense velocity field from sparse experimental data. A PINN is a network-based data assimilation method. Within the PINN, both the velocity and pressure are approximated by minimizing a loss function consisting of the residuals of the data and the Navier–Stokes equations. Therefore, the PINN can not only improve the velocity resolution but also predict the pressure field. The performance of the PINN is investigated using two-dimensional (2D) Taylor's decaying vortices and turbulent channel flow with and without measurement noise. For the case of 2D Taylor's decaying vortices, the activation functions, optimization algorithms, and some parameters of the proposed method are assessed. For the case of turbulent channel flow, the ability of the PINN to reconstruct wall-bounded turbulence is explored. Finally, the PINN is applied to reconstruct dense velocity fields from the experimental tomographic PIV (Tomo-PIV) velocity in the three-dimensional wake flow of a hemisphere. The results indicate that the proposed PINN has great potential for extending the capabilities of PIV/PTV.

### Wall shear stress and wall heat flux in a supersonic turbulent boundary layer

We report the characteristics of wall shear stress (WSS) and wall heat flux (WHF) from direct numerical simulation (DNS) of a spatially developing zero-pressure-gradient supersonic turbulent boundary layer at a free-stream Mach number M∞ = 2.25 and a Reynolds number Reτ = 769 with a cold-wall thermal condition (a ratio of wall temperature to recovery temperature Tw/Tr = 0.75). A comparative analysis is performed on statistical data, including fluctuation intensity, probability density function, frequency spectra, and space–time correlation. The root mean square fluctuations of the WHF exhibit a logarithmic dependence on Reτ similar to that for the WSS, the main difference being a larger constant. Unlike the WSS, the probability density function of the WHF does not follow a lognormal distribution. The results suggest that the WHF contains more energy in the higher frequencies and propagates downstream faster than the WSS. A detailed conditional analysis comparing the flow structures responsible for extreme positive and negative fluctuation events of the WSS and WHF is performed for the first time, to the best of our knowledge. The conditioned results for the WSS exhibit closer structural similarities with the incompressible DNS analysis documented by Pan and Kwon [“Extremely high wall-shear stress events in a turbulent boundary layer,” J. Phys.: Conf. Ser. 1001, 012004 (2018)] and Guerrero et al. [“Extreme wall shear stress events in turbulent pipe flows: Spatial characteristics of coherent motions,” J. Fluid Mech. 904, A18 (2020)]. Importantly, the conditionally averaged flow fields of the WHF exhibit a different mechanism, where the extreme positive and negative events are generated by a characteristic two-layer structure of temperature fluctuations under the action of a strong Q4 event or a pair of strong oblique vortices. Nevertheless, we use the bi-dimensional empirical decomposition method to split the fluctuating velocity and temperature structures into four different modes with specific spanwise length scales, and we quantify their influence on the mean WSS and WHF generation. It is shown that the mean WSS is mainly related to small-scale structures in the near-wall region, whereas the mean WHF is associated with the combined action of near-wall small-scale structures and large-scale structures in the logarithmic and outer regions.

### Analysis of preconcentration patterns in microfluidic ion concentration polarization devices

The analysis of governing parameters on the preconcentration of charged analytes is of utmost importance for ion concentration polarization-based devices. The interaction between applied voltage and microchannel length, i.e., the electric field, can be used to obtain optimum operation of ion concentration polarization (ICP) in terms of enrichment factor. In this paper, the affecting parameters of ICP were studied numerically and experimentally to investigate the preconcentrating behavior of analytes upon applying voltage. We showed that applying different electric fields changes the accumulation patterns of the preconcentrated analytes. We classified the patterns for the first time based on the range of electric fields as no preconcentration, dispersed, protruded, and focused preconcentration. In addition, the analysis of the effect of buffer concentration on enrichment factor revealed that unlike the electric field, the buffer concentration only affects the enrichment factor without influencing the preconcentrated analyte pattern. The results demonstrated that by decreasing the buffer concentration, the enrichment factor is increased. The comparison of the experimental findings with the numerical results, obtained from COMSOL Multiphysics®, manifested acceptable correspondence. The findings of this study can be used for further optimization, to develop high-performance ICP devices in biomedical and analytical applications.

### Kaolinite colloidal suspensions under the influence of sodium dodecyl sulfate

Rheological properties of kaolinite particle suspensions in water were studied in the presence of sodium dodecyl sulfate (SDS). The characterization of slightly and strongly sonicated samples revealed the impact of particle initial clustering and agglomeration on their flow behavior; findings revealed that sonicated samples exhibit a stronger network. The influence of kaolinite concentration, sonication, and SDS loading on the apparent slip of kaolinite suspensions was also studied. The presence of SDS molecules prevents particle aggregation and network formation, which leads to a gradual reduction in yield stress. Through a suggested spatial hindrance mechanism, adding SDS above the minimum amount for micelle formation also stops network formation. Finally, it was found that increasing the concentration of kaolinite and sonication reduces the apparent slip, whereas increasing the surfactant concentration increases slip significantly. As a result of shear-induced migration, adding surfactant causes the interface to deplete and thus exhibit apparent slip.

### Phase separation and spreading dynamics of French vinaigrette

Phase separation can be observed when vinaigrette is poured on a kitchen plate under certain conditions. The phase separation in vinaigrette, which comprises olive oil, vinegar, and mustard for stabilization and taste, is characterized by the outward spreading of olive oil from the main film. This phase separation and the phenomena that trigger it were investigated in this study. Moreover, the spreading dynamics of the vinaigrette were examined by analyzing the spreading factor and its rate. The spreading of different formulations of the vinaigrette was probed in this regard by varying the mass concentration of vinegar from 10% to 40% and the amount of mustard from 0.1 to 0.5 g. The emulsion films were placed on a white tile substrate with similar characteristics to those of a kitchen plate at 21 °C and a relative humidity of 50%. The spreading dynamics followed two distinct regimes; increasing the vinegar concentration of mustard-free formulations led to decreases in the spreading factor of the first regime and the spreading rate. The addition of mustard had a similar effect on the spreading factor of the first regime. The variations in these two parameters were related to changes in the system viscosity. The latter was found to be a function of the mustard and vinegar concentrations. Phase separation occurred at vinegar concentrations below 30% because of a competition between the spreading and the existing instabilities in the vinaigrette. This phenomenon did not affect spreading dynamics.

### Small-scale fluctuation and scaling law of mixing in three-dimensional rotating turbulent Rayleigh-Taylor instability

Author(s): Yikun Wei, Yumeng Li, Zhengdao Wang, Hui Yang, Zuchao Zhu, Yuehong Qian, and Kai H. Luo

The effect of rotation on small-scale characteristics and scaling law in the mixing zone of the three-dimensional turbulent Rayleigh-Taylor instability (RTI) is investigated by the lattice Boltzmann method at small Atwood number. The mixing zone width h(t), the root mean square of small scale fluctu...

[Phys. Rev. E 105, 015103] Published Tue Jan 25, 2022

### Ternary modeling of the interaction between immiscible droplets in a confined shear flow

Author(s): Wankun Liu and Jang Min Park

The interaction between two immiscible droplets in a confined shear flow is studied numerically by using a ternary diffuse-interface model. Three different types of interaction are observed: (1) reverse motion, (2) pass-over motion, and (3) rotary Janus motion after wetting. We investigate the effects of initial droplet position, capillary number, and confinement on the droplet trajectory and the deformation.

[Phys. Rev. Fluids 7, 013604] Published Tue Jan 25, 2022

### Effects of surface-charge regulation, convection, and slip lengths on the electrical conductance of charged nanopores

Author(s): Yoav Green

The nanofluidic paradigm that low-concentration conductance is concentration-independent has recently come under scrutiny. Recent works have shown that the conductance depends on the concentration and that the slope, α, ranges between 0 and 1/2. However, experiments have also measured slopes of 2/3 and 1. In this work an analytical solution for the conductance is derived that accounts for surface charge regulation (SCR), advection (ADV), and slip-lengths (SL). This parameter free model demonstrates that α is determined by SCR, ADV, SL, and ranges between 0 and 1. Consequently our results imply that all three phenomena are essential in the design of nanofluidic systems.

[Phys. Rev. Fluids 7, 013702] Published Tue Jan 25, 2022

### Reaching for the surface: Spheroidal microswimmers in surface gravity waves

Author(s): Kunlin Ma, Nimish Pujara, and Jean-Luc Thiffeault

The trajectories of microswimmers, such as plankton or artificial active particles, are altered by their interactions with the ambient flow. We show here that microswimmers swimming beneath surface gravity waves can resurface or swim to deep depths depending on their coupling to the flow. We obtain a system of equations describing wave-averaged microswimmer trajectories, from which we calculate the probability of reaching the surface as a function of swimming speed and body shape.

[Phys. Rev. Fluids 7, 014310] Published Tue Jan 25, 2022

### Multifractality in a nested velocity gradient model for intermittent turbulence

Author(s): Yuan Luo, Yipeng Shi, and Charles Meneveau

Small scale intermittency is ubiquitous in turbulent flows. Many features of small-scale motions can be described by the velocity gradient tensor (VGT) for which the nonlinear term in the Navier-Stokes equations (NSE) is a source of strong fluctuations. The figure shows intermittent time signals of longitudinal VGT elements along Lagrangian trajectories from five levels of a recently proposed nested multiple time-scale model (MTSM), partly derived from NSE. We show that a single level of MTSM valid at moderate Reynolds numbers (Re) can generate valid statistics and scaling exponents for arbitrarily high Re. Excellent agreement with direct numerical simulation and experimental data is found.

[Phys. Rev. Fluids 7, 014609] Published Tue Jan 25, 2022

### Dynamics of Brownian Janus rods at a liquid–liquid interface

Amphiphilic Janus nanoparticles exhibit higher interfacial activity and adsorb more strongly to fluid interfaces than homogeneous nanoparticles of similar sizes. Taking advantage of both shape and chemical anisotropy on the same particle, Janus particles offer rich self-assembly possibilities for nanotechnology. By using dissipative particle dynamics simulation, the translational diffusion of Janus nanoparticles at the interface between two immiscible fluids is investigated. The particle aspect ratio affects both particle's translational thermal motion and the average orientation of the particle with respect to the interface at equilibrium. This behavior is also linked to the interfacial tension of the system. Our findings provide fundamental insights into the dynamics and self-assembly of anisotropic Brownian particles at interfaces.

### Effects of exercise on flow characteristics in human carotids

Carotid is one of the focal regions prone to atherosclerosis. Previous studies have shown that hemodynamics plays an important role in the initiation and formation of atherosclerosis plaques. In this work, we numerically investigate the flow patterns in two carotids with different flares and proximal curvatures under inflows from three age groups with/without exercise. The simulation results show that the effects of exercising on the carotid flow and wall shear stress are different at different time instants and for different age groups. As for the oscillatory shear index, exercise does not have significant effects. The effects of inflow waveforms on the reversed flow volume are also examined. For the carotid C1 with low flare and high proximal curvature, it is found that exercising increases and decreases the reversed flow volume for young and senior people, respectively. For middle-aged people, on the other hand, the reversed flow volume is increased and decreased in the middle of the sinus and near the bifurcation, respectively, for the carotid C1. For the carotid C2 with high flare and low curvature, on the other hand, it is found that exercising increases the reversed flow volume for all age groups. This work suggests that the effects of exercise on atherosclerosis should be evaluated by fully considering patient-specific geometries and ages.