# Latest papers in fluid mechanics

### Entropic characterization of the coil-stretch transition of polymers in random flows

Author(s): F. Sultanov, M. Sultanova, G. Falkovich, V. Lebedev, Y. Liu, and V. Steinberg

Polymer molecules in a flow undergo a coil-stretch phase transition on an increase of the velocity gradients. Model-independent identification and characterization of the transition in a random flow has been lacking so far. Here we suggest to use the entropy of the extension statistics as a proper m...

[Phys. Rev. E 103, 033107] Published Wed Mar 17, 2021

### Oil-coated bubble formation from submerged coaxial orifices

Author(s): Bingqiang Ji, Zhengyu Yang, and Jie Feng

Dispersions of bubbles with a compound interface in liquids are ubiquitous in nature and various industrial processes. Here, we experimentally investigate the formation of oil-coated bubbles at submerged coaxial orifices in quiescent liquids. A force balance model is developed to accurately predict the bubble size, which is determined by the revised Bond number, size ratio of the coaxial orifices, and the interfacial tension ratio of oil-water and oil-air interfaces. The results may be useful in estimating the size distribution of oil-coated bubbles as an input to characterize the transport and dynamics of bubbly flows where compound interfaces are present.

[Phys. Rev. Fluids 6, 033602] Published Wed Mar 17, 2021

### Gamma instability in an inhomogeneous environment and salt-fingering staircase trapping: Determining the step size

Author(s): Yuchen Ma and W. R. Peltier

For mid-latitude salt-fingering staircases in the oceans, the staircase step-sizes are always observed to be smaller at vertical positions of relatively higher background gradients than at vertical positions characterized by relatively lower gradients. We extend the gamma instability theory of Radko (2003) to a system with inhomogeneous background gradients for temperature and salinity to explain this observed trend. On the basis of our three-dimensional turbulence analyses and mean-field model simulation, we successfully explain the origins of such step-size differences and test our proposed mechanism against the historical staircase data recorded in the Tyrrhenian Basin.

[Phys. Rev. Fluids 6, 033903] Published Wed Mar 17, 2021

### Phase-locking of laminar wake to periodic vibrations of a circular cylinder

Author(s): M. A. Khodkar, Joseph T. Klamo, and Kunihiko Taira

The periodic wake flow past a bluff body immersed in a moving fluid can be synchronized to the harmonic vibrations of the body. A low-dimensional, phase-based analysis has been adopted to uncover the theoretical conditions necessary for synchronization between the wake and body oscillations. The present phase-based methodology allows for modifying the transient features of unsteady flows, thereby enabling the online control and analysis of aerodynamic forces on flyers/swimmers, vortex-induced vibrations, and fluid-structure interactions.

[Phys. Rev. Fluids 6, 034401] Published Wed Mar 17, 2021

### Internal layers in turbulent free-shear flows

Author(s): D. Fiscaletti, O. R. H. Buxton, and A. Attili

In turbulent free-shear flows, layers of intense shear bound regions of nearly uniform momentum. The thickness of these layers scales as the Kolmogorov length scale and the velocity across these layers presents a jump of approximately 10% of the characteristic large-scale velocity of the flow. In layers of intense shear, rotation dominates, whereas in layers of intense scalar gradient, strain is prevalent.

[Phys. Rev. Fluids 6, 034612] Published Wed Mar 17, 2021

### Self-consistent hydrodynamic two-fluid model of vortex plasma

We propose the system of self-consistent equations for vortex plasma in the framework of hydrodynamic two-fluid model. These equations describe both longitudinal flows and the rotation and twisting of vortex tubes taking into account internal electric and magnetic fields generated by fluctuations of plasma parameters. The main peculiarities of the proposed equations are illustrated with the analysis of electron and ion sound waves.

### Scaling of the mean transverse flow and Reynolds shear stress in turbulent plane jet

Proper scaling for the mean transverse flow and Reynolds shear stress in a turbulent plane jet is determined using a scaling patch approach. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity equation, a proper scale for the mean transverse flow in a turbulent plane jet is found as [math], where δ is the jet half width and [math] is the decay rate of the mean axial velocity at the jet centerline. By seeking an admissible scaling for the mean axial momentum equation, a proper scale for the kinematic Reynolds shear stress is found as [math], which is a mix of the velocity scales in the axial and transverse directions. Approximation functions for the scaled mean transverse flow and Reynolds shear stress are developed and found to agree well with experimental and numerical data. Similarities and differences between the scales of the mean transverse flow and Reynolds shear stress in turbulent plane jets and zero-pressure-gradient turbulent boundary layer flows are clarified.

### A high-fidelity body-force modeling approach for plasma-based flow control simulations

The well-known “ion wind” induced by a dielectric barrier discharge plasma actuator (DBD-PA) has been extensively used as an active flow control device in the boundary layer. Developing an accurate and efficient model for plasma-induced body force becomes the linchpin of the computational studies of DBD-PA-based flow control; both phenomenological and first-principle approaches have been largely investigated in the literature. In this research, a charged-particle model named Drift-Diffusion (D-D) model is employed to compute the body-force fields with ultra-high temporal resolution in a range of alternating voltage (peak-to-peak) from 7 kV to 20 kV. The analytical Suzen–Huang (S–H) model as an economical approach is also applied for comparison. Large-eddy simulations are employed to investigate the relationship between the DBD-PA-induced flow in quiescent air and the DBD-PA-controlled flow field over a stalled airfoil. The significance of body-force unsteadiness is well understood in the two flow fields by the model comparison. The results based on D-D model show good agreement with the corresponding experiments in both quiescent and separated flow fields, where the induced flow structure and separation control effect are carefully checked, respectively. As to the S–H model, the almost same magnitude but different location of the maximum wall-parallel induced velocity results in the stronger induced flow in quiescent field; however, the similar control effects in the separated flow. The present research provides a new approach to study the effect of DBD-PA-induced flow on separation control using the high-fidelity body-force field directly without any parametric calibration.

### Bell–Plesset effects on Rayleigh–Taylor instability at cylindrically divergent interfaces between viscous fluids

We report the first experiments on divergent Rayleigh–Taylor instability (RTI) at well-controlled single-mode cylindrical interfaces between air and viscous liquid. At early stages, only the amplitude of the dominant single mode grows with time while the higher harmonics starts to grow in the late stage. The transition point from the linear stage to the nonlinear stage is defined as the moment when the higher harmonics starts to grow and the linear stage before the Poiseuille flow fully developed is concerned in this paper. We find that the growth rate is lower than that in convergent or planar geometry due to geometric divergence. Both divergent Bell–Plesset (BP) effects and viscosity effect inhibit the growth rate of RTI. The attenuation strength of viscosity effect is reduced by divergent BP effects compared with the planar case. It is observed that the value ka ∼ (0.188–0.314), at the transition point, is much lower than that in planar geometry (ka ∼ 1), where [math] is the amplitude of the dominant single mode and k is the initial wavenumber. To take viscosity into account, a new approximate model based on the Bell theory is proposed, which well predicts the perturbation growth in a divergent geometry in the linear stage before the Poiseuille flow fully developed.

### Flow and heat transfer for a two-phase slug flow in horizontal pipes: A mechanistic model

In view of the practical importance of gas–liquid two-phase flow in many applications, such as chemical engineering, petroleum engineering, nuclear engineering, etc., a reliable model of flow and heat transfer for two-phase flow is of practical importance in the two-phase flow analysis. Among various two-phase flow regimes, slug flow is most complicated due to the intrinsic randomness and intermittency. This paper aims at developing a novel mechanistic model of flow and heat transfer for two-phase slug flow in horizontal pipes. First, a hydrodynamic model of two-phase slug flow is developed using the concept of slug unit cell. Then, a heat transfer model is deduced based on the hydrodynamic model. The overall heat transfer coefficient is integrated by the local heat transfer coefficients of liquid slug, liquid film, and elongated bubble. The newly developed mechanistic model is well validated by the experimental results. Finally, the dependence of the heat transfer performance on the overall flow parameters, such as superficial liquid velocity and superficial gas velocity, and the local flow parameters, such as slug frequency, pressure drop, void fraction, and ratio of slug length to unit cell length, is comprehensively investigated. The heat transfer enhancement of two-phase slug flow compared with single-phase flow is mainly attributed to the turbulence increase in liquid by the injection of air and the decrease in thermal boundary layer by the frequent alternation between the liquid slug and the elongated bubble.

### On the peristaltic pumping

Peristaltic pumping in a two-dimensional conduit using vibrations in the form of traveling waves has been investigated. Two qualitatively different responses producing vastly different flow rates have been identified, with a transition occurring at wavelengths of the order of the conduit opening. The flow rate is always proportional to the wave phase speed and the second power of the amplitude. Long waves produce sloshing which extends across the whole conduit producing a small, nearly wave-number-independent flow rate. The use of such in-phase waves on both walls nearly eliminates this flow while the use of out-of-phase waves maximizes it. Short waves affect the near-wall regions, which appear to the bulk of the fluid as moving walls. Such waves produce an order of magnitude larger flow rate, with its magnitude increasing proportionally to the second power of the wavenumber. Each vibrating wall produces its own wall boundary layer with an unmodulated core flow in the central zone of the conduit. The core flow looks like a Couette flow and reduces to a plug flow when both waves have identical amplitudes. The phase difference between such waves does not affect the flow rate. Wave tilting increases the flow rate similarly to the increase in distance between these waves. The use of waves characterized by a combination of wavenumbers increases the flow rate but only when the commensurability index is greater than one. The best performance is achieved by concentrating all wave energy in a single and largest achievable wavenumber.

### Numerical analysis of charged droplets size distribution in the electrostatic coating process: Effect of different operational conditions

This paper presents a numerical performance evaluation of the electrostatic rotary bell sprayer (ERBS) with a particular focus on droplet charge, electric field, and ambient conditions through the implementation of a high-voltage control-ring field pattern effect into the fully turbulent airflow and by including the atomized droplets discrete phase. The simulation shows that the inclusion of droplet charging and electric field coupling, with different parametric values, significantly impacts the atomized droplet distribution over the spray plume and the deposition rate. This analysis was conducted using a three-dimensional (3D) Eulerian–Lagrangian model to describe the two-phase spraying flow by extending the base OpenFOAM package. The procedure includes an unsteady compressible Navier–Stokes solver combined with a large Eddy simulation approach to model turbulence effects on the air flowfield. This is coupled to the spray dynamics by including droplet trajectory tracking, wall film dynamics, and electric field charge. The approach is further extended to include the evaporation phenomenon and the transport of its products. Compared to a conventional ERBS, herein, we provide an in-depth analysis of the fluid dynamic characteristics around the ERBS with a control-ring field pattern for vorticity, velocity, and electrical fields. The results indicate that the control-ring operation improves the performance and transfer efficiency of the ERBS, and it also helps to harmonize the direction of the charged paint droplets. For the first time, finding a balance between the effect of the inside bell cup surface and control-ring voltage and charged droplet has been conducted.

### Heat transfer characteristics of successive oil droplet impingement under minimum quantity lubrication

During oil–gas minimum lubrication, lubricating oil droplets are easily formed into hollow oil droplets containing bubbles when disturbed by a high-speed airflow. Microbubbles have an important influence on the heat transfer characteristics and movement of multiple oil droplets successively impinging on an oil film. In this work, the behavior of multiple oil droplets successively impacting an oil film is numerically simulated on the basis of the coupled level set-volume fraction method, and the influences of different bubble distributions on the heat transfer characteristics of double oil droplets successively impinging on the oil film are investigated. The formation mechanism of some unique heat transfer phenomena in the impingement process is discussed, and the influences of different bubble distribution forms on the geometric size of the thermal wake and cooling effect of the impingement area are analyzed. Results showed that a “cicada wing-like” thermal wake appears during the falling process of high-temperature oil droplets. The combined effects of heat transfer, flow field, and air flow separation behavior are the main reasons behind this wake. During the falling and spreading process of solid and hollow oil droplets, the velocity gradient difference at the tail of the oil droplet affects the geometric size of the wake. In the later stages of the impingement process, a vortex is formed in the impingement pit under the combined action of the space flow field and the pressure field. This vortex strongly improves the heat flux density in the impingement area. Different bubble distribution forms have different effects on the cooling and heat dissipation effect during impingement, and hollow oil droplets are unfavorable for cooling and heat dissipation.

### Microstructure and rheology of shear-thickening colloidal suspensions with varying interparticle friction: Comparison of experiment with theory and simulation models

Two colloidal suspensions of paucidisperse, spherical silica particles with different surface chemistries leading to extreme limits of surface contact friction are studied to identify experimental differences in shear rheology and microstructure and quantitatively test theory and simulation models. The nonequilibrium microstructure in the plane of shear is measured by flow-small angle neutron scattering for steady shear states spanning the shear thinning and shear thickening regimes. The shear rheology and microstructure are compared against predictions from theory for Brownian hard sphere suspensions and state-of-the-art simulation methods that incorporate either contact friction or enhanced lubrication hydrodynamics. The first normal stress differences are confirmed to distinguish between these micromechanical mechanisms for stress enhancement in the shear thickened regime. The nonequilibrium microstructure in the plane of shear shows more anisotropy for the suspension with higher interparticle friction. A significant fourfold symmetry is confirmed and found to be amplified with increasing surface contact friction in the shear thickened state. The differences in shear-induced microstructures between suspensions with varying contact friction demonstrate that the nonequilibrium microstructure can distinguish between nanotribological interactions in the shear thickened state. Statistical comparison of experiments with simulations indicates that better resolution of microstructures in simulation models is required to be validated by the experimental data presented. Implications for the development of theories for colloidal suspension rheology are discussed.

### Theoretical elucidation of effect of drag force and translation of bubble on weakly nonlinear pressure waves in bubbly flows

Theoretical investigation of the effects of a translation of bubbles and a drag force acting on bubbles on the wave propagation in bubbly flows has long been lacking. In this study, we theoretically and numerically investigate the weakly nonlinear (i.e., finite but small amplitude) propagation of plane progressive pressure waves in compressible water flows that contain uniformly distributed spherical gas bubbles with translation and drag forces. First, we assume that the gas and liquid phases flow at independent velocities. Then, the drag force and virtual mass force are introduced in an interfacial transport across the bubble–liquid interface in the momentum conservation equations. Furthermore, we consider the translation and spherically symmetric oscillations as bubble dynamics and deploy a two-fluid model to introduce the translation and drag forces. Bubbles do not coalesce, break up, extinct, or appear. For simplicity, the gas viscosity, thermal conductivities of the gas and liquid, and phase change and mass transport across the bubble–liquid interface are ignored. The following results are then obtained: (i) Using the method of multiple scales, two types of Korteweg–de Vries–Burgers equations with a correction term due to the drag force are derived. (ii) The translation of bubbles enhances the nonlinear effect of waves, and the drag force acting on bubbles contributes the nonlinear and dissipation effects of waves. (iii) The results of long-period numerical analysis verify that the temporal evolution of the wave (not flow) dissipation due to the drag force differs from that caused by the acoustic radiation.

### A lattice Boltzmann modeling of the bubble velocity discontinuity (BVD) in shear-thinning viscoelastic fluids

The bubble velocity discontinuity (BVD), when single bubble rising in shear-thinning viscoelastic fluids, is studied numerically. Our three-dimensional numerical scheme employs a phase-field lattice Boltzmann method together with a lattice Boltzmann advection-diffusion scheme, the former to model the macroscopic hydrodynamic equations for multiphase fluids, and the latter to describe the polymer dynamics modeled by the exponential Phan–Thien–Tanner (ePTT) constitutive model. An adaptive mesh refinement technique is implemented to reduce computational cost. The multiphase solver is validated by simulating the buoyant rise of single bubble in a Newtonian fluid. The critical bubble size for the existence of the BVD and the velocity-increasing factor of the BVD are accurately predicted, and the results are consistent with the available experiments. Bubbles of different sizes are characterized as subcritical (smaller than critical size) and supercritical (larger than critical size) according to their transient rising velocity behaviors, and the polymeric stress evolution affecting the local flow pattern and bubble deformation is discussed. Pseudo-supercritical bubbles are observed with transition behaviors in bubble velocity, and their sizes are smaller than the critical value. The formation of bubble cusp and the existence of negative wake are observed for both the pseudo-supercritical and the supercritical bubbles. For the supercritical bubble, the trailing edge cusp and the negative wake arise much earlier. The link between the BVD, the bubble cusp, and the negative wake is discussed, and the mechanism of the BVD is explained.

### Falling clouds of particles with finite inertia in viscous flows

When sedimenting in a viscous fluid under gravity, a cloud of particles undergoes a complex shape evolution due to the hydrodynamic interactions. In this work, Lagrange particle dynamic simulation, which combines the Oseen solution for flow around a particle and a Gauss–Seidel iterative procedure, is adopted to investigate the effects of the particle inertia and the hydrodynamic interactions on the cloud's sedimentation behavior. It is found that, with a small Stokes number ([math]), the cloud evolves into a torus and then breaks up into secondary clouds. In contrast, the cloud with a finite Stokes number becomes compact in the horizontal direction and is elongated along the vertical direction. The critical St value that separates the breakup mode and the vertical elongation mode is around 0.2. The cloud response time ([math]) and the maximum settling velocity ([math]) are measured at different Stokes numbers, particle Reynolds numbers, and particle volume fractions. A linear relationship, [math], is found between [math] and the Stokes number and the correlation between [math] and [math] can be well described by an exponential function [math]. At last, the chaotic dynamics of the sedimentation system are discussed. A small difference between the initial configurations diverges exponentially. The sedimentation system containing particles with larger inertia has a lower divergence rate.

### Characterization of vortical structures in T-shaped branches depending on shear-thinning

The characteristics of vortical structures in T-shaped branches with respect to the shear-thinning effect are numerically investigated using a power-law fluid model. By varying the power-law index n, we observe three different flow structures, namely, steady-, harmonic-, and turbulent-like regimes. The time-averaged and instantaneous vortical structures are examined for different values of the local Reynolds number. In the steady regime, stationary vortical structures form near the corners of the T-shaped branch. As n decreases, the vortical structures oscillate back and forth, giving rise to the harmonic regime. Decreasing n further, we observe the turbulent-like regime. In this regime, the vortical structures are torn off near the tips of the vortices and small-scale structures are vigorously generated, constituting more violent behavior than in the harmonic regime. If the local Reynolds number near the wall and near the cores of the vortical structures reaches a critical value, the flow structure becomes turbulent-like after the bifurcation of the T-shaped branch. In addition, the modal characteristics of the vortical structures are analyzed using dynamic mode decomposition with respect to the degree of shear-thinning. As shear-thinning appears in the flow, various high-frequency modes with small-scale vortical structures are observed, and their energies are evenly distributed. This supports the present observation of the vortical structures depending on shear-thinning and -thickening.

### A model of micro lubrication between two walls with unequal temperature distribution based on kinetic theory

Micro lubrication of a gas between two walls with arbitrary and independent temperature distributions is studied on the basis of the Bhatnagar–Gross–Krook–Welander (BGKW) model of the Boltzmann equation. The BGKW equation is studied analytically using the slowly varying approximation. Following the author's previous study [T. Doi, “A model of micro lubrication between two walls with an arbitrary temperature difference based on kinetic theory,” Phys. Fluids 32, 052005 (2020)], the leading-order approximation, which ought to be the solution of the nonlinear heat transfer problem, is replaced by its free molecular solution. A lubrication model of the Reynolds-type equation is derived in closed form. A direct numerical analysis of the lubrication flow subject to localized heating or cooling of the walls is conducted for an assessment of the lubrication model. The lubrication lift calculated using the model agrees with that of the direct numerical solution within an error of 5% when the Knudsen number based on the gap size lies between 0.1 and 10. The result of the lubrication model agrees also with that of the Boltzmann equation for a variable hard sphere gas. A sharp peak arises in the pressure distribution for large Knudsen numbers owing to the effect of thermal creep flows induced by localized heating.

### A dynamical overview of droplets in the transmission of respiratory infectious diseases

The outbreak of the coronavirus disease has drawn public attention to the transmission of infectious pathogens, and as major carriers of those pathogens, respiratory droplets play an important role in the process of transmission. This Review describes respiratory droplets from a physical and mechanical perspective, especially their correlation with the transmission of infectious pathogens. It covers the important aspects of (i) the generation and expulsion of droplets during respiratory activities, (ii) the transport and evolution of respiratory droplets in the ambient environment, and (iii) the inhalation and deposition of droplets in the human respiratory tract. State-of-the-art experimental, computational, and theoretical models and results are presented, and the corresponding knowledge gaps are identified. This Review stresses the multidisciplinary nature of its subject and appeals for collaboration among different fields to fight the present pandemic.