# Latest papers in fluid mechanics

### A high-throughput method to characterize membrane viscosity of flowing microcapsules

Microcapsules have many industrial applications and also serve as a widely used mechanical model of living biological cells. Characterizing the viscosity and elasticity of capsules at a high-throughput rate has been a classical challenge, since this is a time-consuming process in which one needs to fit the time-dependent capsule deformation to theoretical predictions. In the present study, we develop a novel efficient method, by integrating a deep convolutional neural network with a high-fidelity mechanistic capsule model, to predict the membrane viscosity and elasticity of a microcapsule from its dynamic deformation when flowing in a branched microchannel. Compared with a conventional inverse method, the present approach can increase the prediction throughput rate by five orders of magnitude while maintaining the same level of prediction accuracy. We also demonstrate that the present approach can deal with capsules with large deformation in inertial flows.

### Force distribution within a barchan dune

Barchan dunes, or simply barchans, are crescent-shaped dunes found in diverse environments such as the bottom of rivers, Earth’s deserts, and the surface of Mars. In our recent paper [“Shape evolution of numerically obtained subaqueous barchan dunes,” Phys. Rev. E 101, 012905 (2020)], we investigated the evolution of subaqueous barchans by using the computational fluid dynamics-discrete element method, and our simulations captured well the evolution of an initial pile toward a barchan dune in both the bedform and grain scales. The numerical method having shown to be adequate, we obtain now the forces acting on each grain, isolate the contact interactions, and investigate how forces are distributed and transmitted in a barchan dune. We present force maps and probability density functions for values in the streamwise and spanwise directions and show that stronger forces are experienced by grains at neither the crest nor the leading edge of the barchan but in positions just upstream the dune centroid on the periphery of the dune. We also show that a large part of grains undergo longitudinal forces of the order of 10−7 N, with negative values around the crest, resulting in decelerations and grain deposition in that region. These data show that the force distribution tends to route a large part of grains toward the crest and horns of subaqueous barchans, being fundamental to comprehend their morphodynamics. However, to the best of the authors’ knowledge, they are not accessible from the current experiments, making our results an important step toward understanding the behavior of barchan dunes.

### On the droplet entrainment from gas-sheared liquid film

We formulate the droplet entrainment detached from a thin liquid film sheared by a turbulent gas in a circular pipe. In a time-averaged sense, the film has a Couette flow with a mean velocity of um. Then, a roll wave of wavelength λ and phase velocity uc is formed destabilized through Kelvin–Helmholtz instability, followed by a ripple wave of wavelength λp due to Rayleigh–Taylor instability, wherein the vorticity thickness of the gas stream is consistently a characteristic length scale. Superposing the two types of waves in axial and transverse directions produces conical cusps as the root of ligaments, from which droplets are torn off. The droplet entrainment rate is derived as [math], validated by recent experimental results.

### Thermodynamics of shear-induced phase transition of polydisperse soft particle glasses

The thermodynamics of the shear-induced phase transition of soft particle glasses is presented. Jammed suspensions of soft particles transform into a layered phase in a strong shear flow from a stable glassy phase at lower shear rates. The thermodynamics of the two phases can be computed based on the elastic energy and excess entropy of the system. At a critical shear rate, the elastic energy, the excess entropy, the free energy, the temperature, and the shear stress undergo discontinuous jumps at the phase transitions from the glassy to the layered phase. An effective temperature is defined from the derivative of the elastic energy and the excess entropy. The Helmholtz free energy is constructed using the elastic energy, excess entropy, and derived temperature. At a fixed shear rate, there is no equilibrium between the states. However, at a fixed temperature, the glassy and layered states may coexist, as indicated by the equality of their Helmholtz free energies. While this first-order phase transition is possible, it cannot be observed in simple shear because the stress is the same in both phases at the same temperature. Thus, shear banding cannot be observed in this system. Finally, an equation of state, which relates the shear stress to the excess entropy, is presented. This equation of state shows that all dynamical properties (e.g., shear-induced diffusivity and first and second normal stresses) of these jammed non-Brownian suspensions can be determined solely by measuring the shear stress.

### Spatiotemporal evolutions of forces and vortices of flow past ellipsoidal bubbles: Direct numerical simulation based on a Cartesian grid scheme

An in-depth investigation of two fixed non-spherical bubbles is an indispensable step toward revealing fundamental mechanisms in complex bubbly flows, where direct numerical simulation (DNS) is one of the most promising approaches to conduct such a task. However, accurately modeling force distribution and efficiently generating satisfactory mesh around a non-spherical bubble pair are challenging to current DNS methods. In this study, an effective non-body-fitted gas–liquid interface tracking scheme based on the Cartesian grid was developed to conduct three-dimensional DNS of two fixed ellipsoidal bubbles with frozen shape in an incompressible Newtonian fluid. The grid-independent analysis and analytical validation prove that our developed non-body-fitted gas–liquid interface tracking scheme is able to accurately retrieve all force components exerted on a bubble with less mesh generation and computational efforts than body-fitted counterparts. Using this non-body-fitted gas–liquid interface tracking scheme, spatiotemporal evolutions of forces and vortices around the two fixed ellipsoidal bubbles were directly simulated under various values of Reynolds numbers, separation distances, and the bubble’s ellipsoidicity. The analysis of drag force shows that the overall drag behaviors of ellipsoidal bubbles are quite similar to those of spherical bubbles though larger ellipsoidicity produces a higher drag coefficient. However, the sign of lift forces, i.e., either the two bubbles attract or repel each other, is highly dependent on ellipsoidicity. For the bubble pair with moderate ellipsoidicity, attractive force dominates at moderate-to-high Reynold numbers, while the two bubbles tend to repel at low Reynolds numbers. For the bubble pair with high ellipsoidicity, the two bubbles repel each other at all values of Reynolds numbers and separation distances. Characteristics of vortex developments, which are the reason behind these ellipsoidicity-dependent force behaviors, are presented and discussed. This study highlights the importance of the bubble’s shape in the interactions and associated vortex between two adjacent fixed ellipsoidal bubbles.

### Cavitation model of the inflationary stage of Big Bang

In this paper, we propose a model for the initial stage of the development of the universe analogous to cavitation in a liquid in a negative pressure field. It is assumed that at the stage of inflation, multiple breaks of the metric occur with the formation of areas of physical vacuum in which the generation of matter occurs. The proposed model explains the large-scale isotropy of the universe without ultrafast inflationary expansion and the emergence of a large-scale cellular (cluster) structure, as a result of the development of cavitation ruptures of a false vacuum. It is shown that the cavitation model can be considered on par with (or as an alternative to) the generally accepted inflationary multiverse model of the Big Bang.

### Dynamic fluid configurations in steady-state two-phase flow in Bentheimer sandstone

Author(s): Ying Gao, Ali Q. Raeini, Martin J. Blunt, and Branko Bijeljic

Fast synchrotron tomography is used to study the impact of capillary number, Ca, on fluid configurations in steady-state two-phase flow in porous media. Brine and n-decane were co-injected at fixed fractional flow, fw=0.5, in a cylindrical Bentheimer sandstone sample for a range of capillary numbers...

[Phys. Rev. E 103, 013110] Published Mon Jan 25, 2021

### Transition from steady to chaotic flow of natural convection on a section-triangular roof

Author(s): Haoyu Zhai, Juan F. Torres, Yongling Zhao, and Feng Xu

Flow phenomena on a roof are investigated by employing direct numerical simulation. A sequence of pitchfork bifurcations of steady plumes on the roof occurs for small Rayleigh numbers, which is analyzed using a topological method. Furthermore, a Hopf bifurcation followed by periodic doubling, quasiperiod bifurcations, and a transition to chaos appear as the Rayleigh number is increased.

[Phys. Rev. Fluids 6, 013502] Published Mon Jan 25, 2021

### Fully coupled model for simulating highly nonlinear dynamic behaviors of a bubble near an elastic-plastic thin-walled plate

Author(s): Wenbin Wu, Moubin Liu, A-Man Zhang, and Yun-Long Liu

On the basis of the boundary element method and explicit finite element method, a three-dimensional fully coupled model is developed to investigate the interaction between a bubble and an elastic-plastic thin-walled plate. The model can accurately calculate the bubble loading acting on the plate surface and describe the structural motion coupling with the flow field on two sides of the plate. As a result of the elastic-plastic effects of the thin-walled plate, the bubble displays attractive motion, repulsive motion, or splitting.

[Phys. Rev. Fluids 6, 013605] Published Mon Jan 25, 2021

### Stability analysis of a resonant triad in a stratified uniform shear flow

Author(s): Lima Biswas and Priyanka Shukla

The existence of a resonant triad interaction among two primary internal waves and a superharmonic wave in a stably stratified uniform shear flow is proved. Under the pump-wave approximation, the resonant triad becomes unstable when the first mode acts as the pump wave. The exact solutions of the amplitude equations reveal that the stability of a triad depends on the mode numbers and initial conditions.

[Phys. Rev. Fluids 6, 014802] Published Mon Jan 25, 2021

### Scalar fluctuation and its dissipation in turbulent reacting flows

The dissipation rate of a scalar variance is related to the mean heat release rate in turbulent combustion. Mixture fraction is the scalar of interest for non-premixed combustion, and a reaction progress variable is relevant for premixed combustion. A great deal of work is conducted in past studies to understand the spectra of passive scalar transport in turbulent flows. A very brief summary of these studies to bring out the salient characteristics of the passive scalar spectrum is given first. Then, the classical analysis of the reactive scalar spectrum is revisited in the lights of recent understanding gained through analyzing the scalar spectrum deduced from direct numerical simulation data of both non-premixed and premixed combustion. The analysis shows that the reactive scalar spectral density in premixed combustion has a dependence on Karlovitz and Damköhler numbers, which comes through the mean scalar dissipation rate appearing in the spectral expression. In premixed combustion, the relevant scale for the scalar dissipation rate is shown to be of the order of the chemical length scale, and the dissipation rate is not influenced by the scales in the inertial-convective range unlike for the passive scalar dissipation rate. The scalar fluctuations produced near the chemical scales cascade exponentially to larger scales. These observations imply that the passive scalar models cannot be extended to premixed combustion.

### Multiplicity of solution for natural convective heat transfer and entropy generation in a semi-elliptical enclosure

The problem of steady natural convection in a bottom-heated semi-elliptical enclosure has been investigated numerically for a wide range of geometric and flow configurations using the finite volume method. The results are presented for varying Rayleigh numbers, Ra, in the range 1 × 102 ≤ Ra ≤ 5 × 104 and different values of aspect ratio, A = 1, 0.75, 0.5, and 0.25, where the aspect ratio, A, is defined as the ratio of lengths of the semi-minor axis to the semi-major axis of the semi-elliptical enclosure. It has been found that the steady-state solution appears in the form of single or multiple pairs of counter-rotating convection cells depending on the values of physical parameters. For A = 1, 0.75, and 0.5, as the value of Rayleigh number exceeds a critical value, natural convective flow inside the semi-elliptical enclosure exhibits multiple steady solutions with varying pairs of counter-rotating convection cells; however, such multiplicity of steady solutions could not be found for the cases of A = 0.25. The parametric variations of heat transfer and entropy generation rates are studied in detail. It is observed that the average Nusselt number associated with the natural convection in the semi-elliptical cavity is governed by several parameters: aspect ratio, Rayleigh number, number of convection cells, and intensity of convective motion inside the convection cells. The entropy generation due to viscous dissipation is found to be negligible as compared to the entropy generation due to conduction.

### Thermocapillary instability in a viscoelastic liquid layer under an imposed oblique temperature gradient

The linear stability analysis of a viscoelastic (Oldroyd-B) liquid layer subjected to an oblique temperature gradient (OTG) is investigated numerically. For the case of low liquid elasticity, the analysis shows a strong stabilizing effect of the horizontal component (HTG) of the OTG on the two elastic modes emerging due to the presence of the vertical component (VTG) of the OTG. However, if the liquid elasticity is sufficiently large, the HTG fails to stabilize the upstream elastic mode. The liquid elasticity stabilizes the Newtonian interaction mode arising out of the interaction between the HTG and the VTG. The thermocapillary flow introduced by the HTG leads to the development of a new elastic mode absent in the case of a Newtonian liquid layer. The present paper thus shows that the elasticity of the liquid plays a major role in the competition between various instability modes to determine the dominant mode of instability.

### Diffusiophoresis of a highly charged soft particle in electrolyte solutions induced by diffusion potential

Diffusiophoresis of a single soft particle in an electrolyte solution with induced diffusion potential is investigated theoretically in this study. A pseudo-spectral method based on Chebyshev polynomials is adopted to solve the resultant governing electrokinetic equations. Parameters of electrokinetic interest are examined extensively to explore their respective effect upon the particle motion, such as the fixed charge density and the permeability of the outer porous layer, the surface potential and size of the inner rigid core, and the electrolyte strength and magnitude of the induced diffusion potential in the solution. The nonlinear effects pertinent to highly charged particles, such as the double layer polarization effect and the counterion condensation effect, are scrutinized, in particular. Here, nonlinear effects refer to the effects that can only be properly revealed by accurately solving the complete nonlinear Poisson–Boltzmann equation governing the electric potential instead of the simplified linear Helmholtz equation under the Debye–Hückel approximation, valid for lowly charged particles only. We found, among other things, that characteristic local extrema in mobility profiles are mainly due to these two effects. Moreover, a soft particle moves fastest in dilute electrolyte solutions, in general. The smaller the soft particle is, the faster it moves under otherwise identical structural and electrokinetic conditions, provided that the particle radius is smaller than the Debye length, the characteristic thickness of the double layer. The shape of the double layer polarization takes an undulating multilayer form at large electrolyte strength. The results provided here are useful in practical applications such as drug delivery as well as microfluidic and nanofluidic operations.

### Sloshing suppression with active controlled baffles through deep reinforcement learning–expert demonstrations–behavior cloning process

This paper presents an effective paradigm to make full use of both Deep Reinforcement Learning (DRL) and expert knowledge to find an optimal control strategy. The paradigm consists of three parts: DRL, expert demonstrations, and behavior cloning. It is the first time that the proposed paradigm is used for suppressing tank sloshing with two active controlled horizontal baffles. Meanwhile, a self-developed computational fluid dynamics (CFD) solver is used to simulate the environment of tank sloshing. For direct DRL, both the proximal policy optimization agent and the twin delayed deep deterministic policy gradient agent are tested for performing learning. The strategies obtained by different algorithms may not be uniform even for the same environment. Then, we derive a simplified parametric control policy informed from direct DRL. Finally, DRL with behavior cloning is used to optimize the simplified parametric control policy. After training, the agent can actively control the baffles and reduce sloshing by ∼81.48%. The Fourier analysis of the surface elevations pinpoints that the aim of the control strategy obtained by DRL with behavior cloning is to disperse the wave energy and change the sloshing frequency of the tank through fast oscillation of baffles. This provides an idea to suppress sloshing, similar to forcing waves to disassemble ahead of time. The experience and insights gained from this study indicate that the future development direction of DRL + CFD is how to couple DRL, expert demonstrations, and behavior cloning.

### Propulsion performance of tandem flapping foils with chordwise prescribed deflection from linear potential theory

Author(s): J. Alaminos-Quesada and R. Fernandez-Feria

Analytical expressions are obtained for the propulsion and the wake structure of tandem flapping foils with chordwise deflection, explaining the propulsive performance improvement in relation to single foils or rigid-foil counterparts for certain combinations of frequency, spacing, and phase shift. The findings are of interest for the design of small aerial or aquatic vehicles using tandem propulsors.

[Phys. Rev. Fluids 6, 013102] Published Fri Jan 22, 2021

### Fluid dynamics and efficiency of colonial swimming via multijet propulsion at intermediate Reynolds numbers

Author(s): Houshuo Jiang, John H. Costello, and Sean P. Colin

Colonial physonect siphonophores swim via laterally distributed multijet propulsion. Here, computational fluid dynamics is employed to investigate the underlying fluid mechanics and adaptive values of this unique way of propulsion. It is found that colonial swimming achieves energetic benefits for jetting individuals within the colony because they require significantly lower per-module power than that required by a lone jet module swimming at the same speed.

[Phys. Rev. Fluids 6, 013103] Published Fri Jan 22, 2021

### Interaction between dual spherical particles during settling in fluid

Settling of solid particles in the fluid is one of the most basic forms of sediment transport. However, due to the complex particle–particle and particle–fluid interactions, the mechanism of settling is not yet fully understood. This study focuses on characterizing the dynamics of dual particles settling side by side. Both settling experiments and simulations are conducted with different initial spacings between particles and Reynolds numbers (Re). The range of Re is from 30 to 300, which corresponds to the transition zone between the Stokes and the Newton regime. Particle tracking velocimetry and particle image velocimetry are used in the experiments to determine particles’ trajectories and velocity fields around particles. A new electromagnetic release device is manufactured, which ensures accurate control of the initial condition. Together with the experiments, settling processes of particles are simulated based on discrete element–lattice Boltzmann method to investigate detailed flow structures. The results show that no attraction exists between particles when released simultaneously side by side. The repulsion between the two particles is a result of the asymmetry between the inside and outside vortices, and this repulsion will vanish when the initial spacing exceeds 5 particle diameters. Depending on the repulsion between particles, the settling process can be divided into three stages. The results also demonstrate that the initial spacing of the particles and Re are the two key parameters in the determination of the final settling velocity and separation distance. Their influence can be separated into two phase regimes depending on a critical Re (≈60), which is consistent with the one for the appearance of the Karman vortex street. In regime I (Re < 60), the settling process is dominated by viscous effects, and the effect of vortex interaction starts to take dominance in regime II (Re > 60). Overall, small initial spacing and large Re lead to strong repulsion between particles.

### Unsteady dynamics of wedge-induced oblique detonations under periodic inflows

Two-dimensional, wedge-induced oblique detonation waves (ODWs) subject to periodic inflow are simulated using the reactive Euler equations with a two-step induction–reaction kinetic model. The focus of this work is how the periodic unsteadiness of a sinusoidal density disturbance with varying frequency and amplitude influences an initially established ODW structure. Three fundamental ODW structures with different transition types and inflow Mach numbers are disturbed, resulting in two types of triple-point formations: the main triple point (MTP) and the train of triple points (TTP). The TTP features multi-triple points arising almost simultaneously and traveling together, which has never been observed before. A parametric study and frequency analysis reveal that the MTP derives from forced destabilization, while the TTP derives from the combined effect of surface instability and inflow disturbance. Furthermore, a new phenomenon of MTP degeneration is observed for a proper inflow Mach number and disturbance amplitude. Finally, the oscillation amplitudes of unsteady ODWs are analyzed with respect to the Mach number and inflow disturbance, demonstrating the effects of transition type on surface unsteadiness.

### Mixed convection between rotating sphere and concentric cubical enclosure

This paper presents numerical investigations of the mix convection between a rotating inner sphere and a concentric cubical enclosure, using the recently developed immersed boundary-simplified lattice Boltzmann method. The validity of the method has been established through benchmark tests, and a grid independence study is also carried out to ensure the accuracy of the conveyed results. Various factors that may influence the mixed convection system, such as the rotational direction, Rayleigh number, and rotational Reynolds number, are considered in the present study. Three representative rotational axes, namely, the vertical, the horizontal, and the diagonal axes, are selected. The Rayleigh number spans from 104 to 106, which covers the transition range from a conduction-dominated system to a convection-dominated one. Moreover, the rotational Reynolds number varies from 0 to 300. Distinct flow patterns, global heat transfer behavior, and the heat transfer rates on cubic walls are studied to reveal the characteristics of this problem. It is found that the rotationality of the inner sphere would increase the global heat transfer rate of the system and the rotating motion would stimulate heat transfer in the radial direction of the rotational axis while suppressing the thermal expansion in the axial direction.