# Latest papers in fluid mechanics

### Migration behaviors of leaky dielectric droplets with electric and hydrodynamic forces

Author(s): Yanning Wang, Dongliang Sun, Yinshi Li, Shuai Chen, and Bo Yu

The external electric field enables separation and transport of droplets effectively in microfluidic devices. Herein, a volume-of-fluid (VOF) + level-set (LS) + smoothed physical parameters (SPP) method associated with the dynamically adaptive grid technique is extended to simulate three-dimensional...

[Phys. Rev. E 100, 033113] Published Fri Sep 20, 2019

### Self-propelled plate in wakes behind tandem cylinders

Author(s): Wenjiang Wang, Haibo Huang, and Xi-Yun Lu

Fish may take advantage of environmental vortices to save the cost of locomotion. The complex hydrodynamics shed from multiple physical objects may significantly affect fish refuging (holding stationary). Taking a model of a self-propelled flapping plate, we numerically studied the locomotion of the...

[Phys. Rev. E 100, 033114] Published Fri Sep 20, 2019

### Large-amplitude oscillations of foils for efficient propulsion

Author(s): Daniel Floryan, Tyler Van Buren, and Alexander J. Smits

Theory and experiments explain why an inertial swimmer can swim more efficiently by flapping its tail slowly with a large amplitude than by doing so quickly with a small amplitude. The importance of drag is revealed as well as a fundamental tradeoff between thrust and efficiency.

[Phys. Rev. Fluids 4, 093102] Published Fri Sep 20, 2019

### Flow-radiation coupling in ${\mathrm{CO}}_{2}$ hypersonic wakes using reduced-order non-Boltzmann models

Author(s): Amal Sahai, Christopher O. Johnston, Bruno Lopez, and Marco Panesi

This work presents a unified physics-based reduced-order simulation framework for describing non-Boltzmann thermochemistry and radiative heating for hypersonic flows. The new approach is used to analyze afterbody flow dynamics and concomitant carbon dioxide IR radiation for the Mars 2020 mission.

[Phys. Rev. Fluids 4, 093401] Published Fri Sep 20, 2019

### The first and second laws of thermodynamics

This article summarizes an alternative approach to the formulation of the laws of thermodynamics by making use of the conservation equations of transport phenomena. The principal novel element is the inclusion of the law of conservation of momentum in the derivations. This enables one to make the statement of the first and second laws more complete by including terms describing viscous dissipation of energy.

### Symmetric and asymmetric coalescence of droplets on a solid surface in the inertia-dominated regime

We present an investigation of symmetric and asymmetric coalescence of two droplets of equal and unequal size on a solid surface in the inertia-dominated regime. Asymmetric coalescence can result due to the coalescence of two unequal-sized droplets or coalescence of two droplets having different contact angles with the surface due to a step gradient in wettability. Based on the solution of an analytical model and lattice Boltzmann simulations, we analyze symmetric and asymmetric coalescence of two droplets on a solid surface. The analysis of coalescence of identical droplets show that the liquid bridge height grows with time as [math] for θ = 90° and [math] for θ < 90°, where t* is dimensionless time. Our analysis also yields the same scaling law for the coalescence of two unequal-sized droplets on a surface with homogeneous wettability. We also discuss the coalescence of two droplets having different contact angles with the surface due to a step gradient in wettability. We show that the prediction of bridge height with time scales as [math] irrespective of contact angles of droplet with the surface.

### Surface rheological measurements of isolated food foam systems

Liquid foams represent a key component to a vast range of food industry products, from ice creams to the crema on coffee. Longevity of these foams is a highly desirable attribute; however, in order for foam stability to be effectively controlled, a better understanding of the interdependence of the bulk liquid and air-liquid interfacial rheologies is required. This study follows an increasing trend in experimental investigations made of isolated foam structures at the microscale, where the bulk and surface dynamics of a single foam liquid channel can be accurately assessed. Isolated foam channels with adjoining nodes were studied for aqueous solutions of four food grade surfactants. Existing observations of distortions to sodium dodecyl sulphate channel geometries were confirmed for solutions of Tween 20 (T20) and Tween 80 (T80) and were well described by the theory presented here. Moreover, previously unseen distortions to liquid channels were observed for polymeric surfactant systems (hydroxypropyl methylcellulose and hydrolyzed pea protein blend), which were proposed to result from their high surface viscosities. The apparent surface viscosities, μs, of surfactants tested here ranged from high (10 g/s < μs < 10−3 g/s) for polymeric surfactants to very low (10−10 g/s < μs < 10−8 g/s) for Tweens, clearly demarking the regimes of viscous and inertial dominant flows, respectively. It is recommended that further work seeks to investigate the finding of a strong correlation between μs and channel surface tension, γ, for soluble surfactant systems, which could explain the apparent non-Newtonian values of μs that were consistently measured here.

### Homogenized model with memory for two-phase compressible flow in double-porosity media

A completely averaged model of two-phase flow of compressible fluids in a medium with double porosity is developed. The variational asymptotic two-scale averaging method with splitting the nonlocality and nonlinearity is presented. Several mechanisms of delay are detected, as the nonequilibrium capillary redistribution of phases, pressure field relaxation caused by the compressibility, and the cross effects of fluid extrusion from pores due to rock compaction and fluid expansion. A generalized nonequilibrium capillary equation is obtained. All characteristic times of delay are explicitly defined as functions of saturation.

### Bifurcations and pattern evolutions of thermo-solutocapillary flow in rotating cylinder with a top disk

The characteristics of thermosolutocapillary flow bifurcations and pattern evolutions of binary fluid in a rotating cylinder with a top disk on the free surface are investigated through three-dimensional numerical simulations. The mixture of silicon-germanium is employed as the working fluid. For the special case of the capillary ratio equal to minus one, the total thermo and solutocapillary forces are balanced. Once rotation is introduced, the balance among the driving forces is broken, and a wide variety of flow structures are presented as meridional circulations rolling in different directions. When a threshold value of the thermocapillary Reynolds number is exceeded, the stability of capillary flow is destroyed. The two-dimensional steady flow transits to the three-dimensional oscillatory state. The critical conditions for flow bifurcations are explored, and the pattern transitions are mapped. The rotation of the cylinder can suppress the flow instabilities effectively. When the disk counter-rotates with the cylinder, the critical value for the formation of instabilities increases first and then decreases. For the oscillatory flow, various patterns appear with different combinations of the thermocapillary Reynolds number, disk, and/or pool rotation rate. Without rotation, the surface concentration pattern is shown as rosebudlike wave holding still in time but oscillating in space. With the increasing disk rotation rate, the surface pattern transits from hydrosolutal waves to spiral waves, rotating waves, and superimposition of rotating and annular waves propagating in the radial direction. For counter-rotation of the disk and cylinder, a new pattern with coexistence of hydrosolutal and spiral waves traveling in opposite directions is observed.

### Significance of non-Oberbeck-Boussinesq effects augmented by power-law rheology in natural convection studies around fins

The augmentation and diminution of non-Oberbeck-Boussinesq (NOB) effects due to power-law rheology cause significant changes in the results and associated implications of natural convection studies. This study focuses on the combined effect of spatial arrangement with NOB and power-law effects. Non-intuitive changes in heat transfer trends are caused by the additional effect on the shear rate distribution due to spatial arrangement of objects, represented here by an array of fins. An order of magnitude analysis was used to derive Oberbeck-Boussinesq type equations for a class of power-law fluids with all properties considered as linear functions of temperature and pressure. Significant temperature dependent properties were identified, and an explicit criterion to neglect viscous dissipation for power-law fluids in pure natural convection was derived. The identified temperature dependencies were incorporated into NOB equations and solved numerically to investigate their effect on flow field and heat transfer trends. Shear thinning significantly augmented (more than doubled) the accelerating NOB effect, while shear thickening diminished (nearly halved) it. The tendency of power-law rheology to augment or diminish NOB effects was demonstrated to considerably increase the sensitivity of results to temperature dependent properties, over and above that for the Newtonian case. Investigations to note their practical implications revealed that optimization results without NOB effects could be quite misleading for the fin array problem, due to the differing cumulative extents of augmentation. Additionally, correlation studies may be inaccurate as the nature of trends was changed fundamentally due to NOB augmentation.

### Holmboe instability beyond the Boussinesq approximation revisited

With no use of the Boussinesq approximation, the Holmboe instability is studied in sharply stratified shear flows with arbitrary monotonic and bounded velocity profiles without inflection points, including a piecewise-linear one. Particular attention is given to the separation and analysis of contributions to instability made by the wave–wave and wave–particle interactions which are the main physical mechanisms responsible for the loss of stability. It is shown that both mechanisms are equally important for understanding the instability properties and therefore should be taken into consideration simultaneously.

### Three-dimensional flow simulations for polymer extrudate swell out of slit dies from low to high aspect ratios

The impact of the slit die geometry and the polymer melt flow characteristics on the extrudate swell behavior, which is a key extrusion operating parameter, is highlighted. Three-dimensional (3D) numerical simulations based on the finite element method are compared with their conventional two-dimensional (2D) counterparts at the same apparent shear rates using ANSYS Polyflow software. The rheological behavior is described by the differential multimode Phan-Thien-Tanner constitutive model, with polypropylene as a reference. It is shown that increasing the aspect ratio of the die geometry (width/height ratio variation from 1 to 20) contributes to a significant change in the 3D extrudate deformation (relative changes of 10% in several directions; absolute changes up to 30%) and delays the equilibrium axial position (up to a factor 10). High aspect ratios induce a switch to contract flow (swell ratio <1) for the edge height swell. The 3D extrudate swell strongly deviates from the 2D simplified case due to the die effect near the wall, even for higher aspect ratios. Also a different relation with the material parameters is recorded. The initially large swell behavior is followed by a small shrinkage flow in the middle height direction which cannot be captured by the 2D counterpart. The findings are supported by a comprehensive analysis of the velocity and stress fields in and out of the slit dies.

### Numerical investigation of adhesion dynamics of a deformable cell pair on an adhesive substrate in shear flow

Author(s): Ziying Zhang, Jun Du, Zhengying Wei, Zhen Chen, Chang Shu, Zhen Wang, and Minghui Li

Adhesion dynamics of cells is of great value to biological systems and adhesion-based biomedical applications. Although adhesion of a single cell or capsule has been widely studied, physical insights into the adhesion dynamics of aggregates containing two or more cells remain elusive. In this paper,...

[Phys. Rev. E 100, 033111] Published Thu Sep 19, 2019

### Weakly nonlinear analysis of long-wave Marangoni convection in a liquid layer covered by insoluble surfactant

Author(s): Alexander B. Mikishev and Alexander A. Nepomnyashchy

The long-wave oscillatory Marangoni instability in a heated liquid layer covered by insoluble surfactant is considered. It is shown that with the growth of the elasticity number the selected wave pattern is changed from the traveling waves to counterpropagating waves and then again to traveling waves.

[Phys. Rev. Fluids 4, 094002] Published Thu Sep 19, 2019

### Origin of lobe and cleft at the gravity current front

Author(s): C. Y. Xie, J. J. Tao, and L. S. Zhang

In this Rapid Communication, the Rayleigh-Taylor instability (RTI) along the density interfaces of gravity current fronts is analyzed. Both the location and the spanwise wave number of the most unstable mode determined by the local dispersion relation agree with those of the strongest perturbation o...

[Phys. Rev. E 100, 031103(R)] Published Wed Sep 18, 2019

### Spatial analog of the two-frequency torus breakup in a nonlinear system of reactive miscible fluids

Author(s): Dmitry Bratsun

We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction A+B→C in a vertical Hele-Shaw cell under constant gravity. We have recently reported that the concentration-dependent diffusion of species coupled with a frontal neutralization reacti...

[Phys. Rev. E 100, 031104(R)] Published Wed Sep 18, 2019

### Front dynamics in exchange flow of two immiscible iso-viscous fluids in two-dimensional straight and curved plane channels

Exchange flow of two immiscible fluids at a low Atwood number in a straight and curved plane channel is considered in this analytical study. The fluids are considered immiscible, but practically, the results can be applied to miscible fluids for short times and in nearly horizontal channels where mixing is negligible due to strong segregation. The exchange flow and displacement flow in pipes at different inclinations with respect to vertical have been extensively studied and have many applications in industry or environmental settings. For the case of plane two-dimensional channels, however, because of the simpler geometry, it is more convenient to understand the physics of the problem and formulate the physical phenomena mathematically. An equation has been derived that describes the transient front velocity in exchange flow in a straight plane channel. The steady state front velocity in straight channels is estimated. The exchange flow in curved channels demonstrates an unstable front or a separated trail because of the curvature of the path. In the case of curved channels, some of the general behavior of the interface is predicted and validated against some experimental observations in curved pipes but quantitative analysis of the interface and the flow requires more advanced mathematical formulation and more detailed experiments for validation.

### Spectral energy transfer in a viscoelastic homogeneous isotropic turbulence

Energy dynamics in elastoinertial turbulence is investigated by performing different direct numerical simulations of stationary, homogeneous isotropic turbulence for the range of Weissenberg numbers 0 ≤ Wi ≤ 9. Viscoelastic effects are described by the finite extensibility nonlinear elastic-Peterlin model. It is found that the presence of the polymer additives can nontrivially modify the kinetic energy dynamics by suppressing the rate of the kinetic energy transfer and altering the locality nature of this energy transfer. Spectral representation of the elastic field revealed that the elastic energy is also transferred locally through different elastic degrees of freedom via a dominantly forward energy cascade. Moreover, the elastic energy spectrum can display a power-law behavior, k−m, with the possibility of different scaling exponents depending on the Wi number. It is observed that the energy exchange between macro- and microstructures is a two-directional process: there is a dominant energy transfer from the solvent large-scale structures to the polymers alongside a weak energy transfer from polymers to the solvent small-scale structures. This energy exchange consists of three different fluxes. Two of these fluxes equally transfer a small fraction of the kinetic energy into the mean and fluctuating elastic fields. However, the main energy conversion takes place between fluctuating kinetic and elastic fields through a completely nonlocal energy transfer process.

### Three-dimensional simulation of a rising bubble in the presence of spherical obstacles by the immersed boundary–lattice Boltzmann method

The dynamics of a bubble bypassing or passing between spherical obstacles, which is associated with many industrial applications, is investigated numerically. A gas–liquid–solid interaction model is established by combining the lattice Boltzmann method and the immersed boundary method. The deformation and the surface velocity of the bubble, as well as the streamlines of the flow field, are studied as the bubble bypasses a single spherical obstacle or passes between a pair of such obstacles. It is found that for the case of a single sphere, the rise velocity reaches a minimum value at the moment at which an annular bubble forms and the whole sphere is enveloped by the bubble. The initial distance between the bubble and the sphere, as well as the ratio of their sizes, has distinct influences on bubble shape and rise velocity. For a pair of spherical obstacles, the rise velocity of the bubble reaches a minimum value twice as the bubble rises between the obstacles. The distance between the two obstacles has a stronger influence on bubble motion than does their size, although when the two obstacles are of different sizes, the bubble will deviate toward the smaller one.

### Low swirl premixed methane-air flame dynamics under acoustic excitations

In this study, simultaneous particle image velocimetry and planar laser induced fluorescence of hydroxyl radical, chemiluminescence imaging, and hot-wire measurements are utilized to study reacting low swirl flow dynamics under low to high amplitude acoustic excitations. Results show that a temporal weak recirculation zone exists downstream of the flame, which is enlarged in size under acoustic excitations. Investigations show that temporal behaviors of this recirculation zone play a significant role in flame movements and instabilities. As the acoustic wave amplitude increases, the flame lift-off distance changes drastically, resulting in flame instabilities (flashback and blowout) during the excitations. Prior to the flame blowout, although the flame lift-off distance responds periodically to the acoustic perturbations, heat release fluctuations display an aperiodic response. Flame dynamics are further studied by calculated power spectra of acoustic velocity and heat release fluctuations and reconstructed phase portraits of heat release fluctuations. Investigations show that increasing the forcing amplitude results in more deterministic features in the flame dynamics and amplification of the higher harmonic modes in the heat release fluctuations. However, such regular patterns become scattered prior to the flame blowout due to the existence of nonlinearities induced by high amplitude excitations. It is speculated that flame blowout can be a symptom of such nonlinearities. The Rayleigh index is measured to study thermoacoustic couplings. At low amplitude excitations, various coupling patterns occur at the flame. However, such complex patterns are replaced by simple coherent patterns, when the flame is excited by high amplitude acoustic perturbations.