# Latest papers in fluid mechanics

### Spiral defect chaos in Rayleigh-Bénard convection: Asymptotic and numerical studies of azimuthal flows induced by rotating spirals

Author(s): Eduardo Vitral, Saikat Mukherjee, Perry H. Leo, Jorge Viñals, Mark R. Paul, and Zhi-Feng Huang

Spiral defect chaos appears near the onset of Rayleigh-Bénard convection for a low Prandtl number fluid. In this state, rotating spirals are continuously nucleated and eliminated, yielding a persistent dynamics. Here we derive an equation for the azimuthal flow induced by an effective body force originating from rotating spirals. This result is verified numerically using a two-dimensional generalized Swift-Hohenberg model and the three-dimensional Boussinesq equations. We identify a correlation between the appearance of spiral defect chaos and the balance between mean-flow advection and diffusive dynamics related to roll unwinding.

[Phys. Rev. Fluids 5, 093501] Published Thu Sep 10, 2020

### Impact and lifecycle of superfluid helium drops on a solid surface

Author(s): Matthew L. Wallace, David Mallin, Michael Milgie, Andres A. Aguirre-Pablo, Kenneth R. Langley, Sigurdur T. Thoroddsen, and Peter Taborek

Superfluid helium droplets impacting on a solid surface behave much differently than any other fluid. After a short period of initial spreading that is similar to classical fluids, superfluid helium drops quickly shrink and disappear as the superfluid drains out through a thin adsorbed layer of helium on the surface. The lifetime and contact angle of these drops is strongly temperature-dependent, and colder drops (with high superfluid fractions) maintain a constant contact angle throughout the contraction. Above Tlambda, helium spreads slowly like other classical fluids.

[Phys. Rev. Fluids 5, 093602] Published Thu Sep 10, 2020

### Pinning-depinning of the contact line during drop evaporation on textured surfaces: A lattice Boltzmann study

Author(s): Kamal Jannati, Mohammad Hassan Rahimian, and Mostafa Moradi

The evaporation of the liquid droplet on a structured surface is numerically investigated using the lattice Boltzmann method. Simulations are carried out for different contact angles and pillar widths. From the simulation for the Cassie state, it is found that the evaporation starts in a pinned cont...

[Phys. Rev. E 102, 033106] Published Wed Sep 09, 2020

### Electro-osmotic instability of concentration enrichment in curved geometries for an aqueous electrolyte

Author(s): Bingrui Xu, Zhibo Gu, Wei Liu, Peng Huo, Yueting Zhou, S. M. Rubinstein, M. Z. Bazant, B. Zaltzman, I. Rubinstein, and Daosheng Deng

The critical Peclet number for an electro-osmotic instability is reduced in inverse proportion to the geometrically increased electric fields due to curvature of the electrode. This electro-osmotic instability, in contrast to the well-known one, appears exclusively at the enriched interface (anode), rather than at the depleted one (cathode).

[Phys. Rev. Fluids 5, 091701(R)] Published Wed Sep 09, 2020

### How does boiling occur in lattice Boltzmann simulations?

The lattice Boltzmann (LB) method has been employed to simulate boiling phenomena in recent years. However, a very important issue still remains open, i.e., how does boiling occur in the LB simulations? For instance, the existing LB studies showed that the boiling on a hydrophobic surface begins at a lower wall superheat than that on a hydrophilic surface, which qualitatively agrees well with experimental studies, but no one has yet explained how this phenomenon appears in the LB simulations and what happened in the simulations after changing the wettability of the heating surface. In this paper, the LB boiling mechanism is revealed by analyzing boiling on a flat surface with mixed wettability and boiling on a structured surface with homogeneous wettability. Through a theoretical analysis, we demonstrate that, when the same wall superheat is applied, in the LB boiling simulations, the fluid density near the heating surface decreases faster on a hydrophobic surface than that on a hydrophilic surface. Accordingly, a lower wall superheat can induce the phase transition from liquid to vapor on a hydrophobic surface than that on a hydrophilic surface. Furthermore, a similar theoretical analysis shows that the fluid density decreases fastest at concave corners in the case of a structured surface with homogeneous wettability, which explains why vapor bubbles are nucleated at concave corners in boiling on structured surfaces.

### Highly dilute gas flows over an ellipse

This paper presents recent investigation results on free molecular flows over a diffusely or specularly reflective ellipse, by using the gaskinetic theory. A virtual density distribution along the diffusely reflective surface is introduced to aid the investigations. Many local surface properties are obtained, including the surface slip velocity and coefficients for pressure, friction, and heat flux. Global coefficients for aerodynamic forces and moments and mass center–force center distances are also obtained by integrating the local surface distributions. In the end, analytical expressions for the flowfields around a diffusely or specularly reflective ellipse are also obtained. Special non-dimensional parameters, such as temperature and speed ratios, are explicitly embedded in these expressions. Particle simulations with the direct simulation Monte Carlo (DSMC) method are performed to validate the above results. Those expressions need computers for evaluations; however, the cost is very minor when compared with DSMC simulations. The approaches are heuristic to investigate other external collisionless flows, and the load coefficients can be considered as baseline references at the high Knudsen number limit. By using these collisionless flow results, it is feasible to further study less rarefied gas flows over an ellipse, for example, with an asymptotic method. Swift parameter studies based on these solutions can be performed to study their effect.

### Role of chemical reactions in the stagnation point heat flux of rarefied hypersonic cylinder flows

This work investigates the variations of the stagnation point heat flux (SPHF) in hypersonic cylinder flows using the direct simulation Monte Carlo method, with the consideration of a constant freestream Knudsen number but different cylinder diameters. Four different freestream Mach numbers and the accompanying chemical reactions are considered. The result reveals a high-density effect in chemical reactions inside the thermal boundary layer, which induces an increasingly rising SPHF with a decreased cylinder diameter for all the cases. The cases at Ma∞ = 30 exhibit a characteristic of peculiarity that the value of SPHF increases the fastest, which is strongly correlated with the different high-density effects at different Ma∞. Further analysis demonstrates that the NO dissociation and recombination reactions always play a vitally important role in the high-density effect. A secondary NO dissociation reaction was observed inside the thermal boundary layer when Ma∞ > 30. This observation is the result of the shift of chemical equilibrium induced by violent recombination reaction and sufficiently high flow temperature. Subsequently, the newly emerging secondary dissociation reaction weakens the influence of recombination reaction; thus, the growth of SPHF at a high Mach number is not so strong as that with Ma∞ ≤ 30. Furthermore, in order to provide more reliable results, additional simulations are discussed by employing the widely accepted total collision energy and catalytic surface reaction models.

### Anchoring mechanisms of a holder-stabilized premixed flame in a preheated mesoscale combustor

A very lean-premixed, laminar methane–air flame is demonstrated, experimentally, to be stable in a mesoscale combustor with a flame holder. Unlike the anchoring location of the flame tip, the anchoring location of the flame root is practically independent of the equivalence ratio, inlet velocity, and thermal conductivity of the solid wall material. When the mixture becomes leaner, both the flame root and tip can adaptively shift toward the locations with higher temperatures, and additionally, the anchoring temperature of the flame root is higher. Subsequently, by means of the three-dimensional computational mechanics, their anchoring mechanisms are thoroughly analyzed in terms of the flow recirculation, stretch effect, preferential diffusion, and conjugate heat exchange. A recirculation zone or a low-velocity zone formed behind/near the flame holder and combustion chamber wall can assist the balance between the flow velocity and the flame speed for the flame anchoring, and the flame root can adaptively shift to a zone of lower local velocity. The stretch effect is not responsible for the flame root anchoring, but this effect stabilizes the flame tip by increasing the local flame speed near the flame tip. Preferential diffusion significantly promotes the local equivalence ratio near the anchoring location of the flame root, thereby facilitating the stability of this flame root, though it stabilizes the flame tip only slightly. Furthermore, the conjugate heat exchange plays an important role in preheating fuel/air and intensifying combustion, which influences the stabilization of both the flame root and tip. The shorter distance between the flame tip and the combustion chamber wall results in a stronger flame–wall coupling. These results indicate that the anchoring mechanisms for the flame root and tip differ.

### Linear stability and energy stability of plane Poiseuille flow with isotropic and anisotropic slip boundary conditions

The linear stability and energy stability of the plane Poiseuille flow with the isotropic and anisotropic slip boundary conditions are theoretically analyzed and numerically calculated in this paper. The asymptotic expansions of the critical parameters for the linear stability and energy stability are derived from the eigenvalue equations characterizing the least stable modes. The critical Reynolds number for the linear stability based on 1.5 times of the bulk mean streamwise velocity is found to be [math] when the non-dimensional isotropic slip length l ≪ 1, where [math] is the critical Reynolds number under the no-slip boundary condition. The critical Reynolds numbers for the linear stability are calculated for a wide range of anisotropic slip lengths and are found to be no larger than their counterparts in the isotropic slip cases with the same streamwise slip lengths. In the energy stability analyses of the two-dimensional and three-dimensional plane Poiseuille flows with the isotropic slip boundary condition, the critical Reynolds numbers are found to be [math] and [math], where [math] and [math] are their counterparts under the no-slip boundary condition. In the three-dimensional plane Poiseuille flow with the anisotropic slip boundary condition, the critical Reynolds number for the energy stability increases with the increase in streamwise slip length lx and with the decrease in spanwise slip length lz, and its first-order approximation is [math].

### Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data

We propose a customized convolutional neural network based autoencoder called a hierarchical autoencoder, which allows us to extract nonlinear autoencoder modes of flow fields while preserving the contribution order of the latent vectors. As preliminary tests, the proposed method is first applied to a cylinder wake at ReD = 100 and its transient process. It is found that the proposed method can extract the features of these laminar flow fields as the latent vectors while keeping the order of their energy content. The present hierarchical autoencoder is further assessed with a two-dimensional y–z cross-sectional velocity field of turbulent channel flow at Reτ = 180 in order to examine its applicability to turbulent flows. It is demonstrated that the turbulent flow field can be efficiently mapped into the latent space by utilizing the hierarchical model with a concept of an ordered autoencoder mode family. The present results suggest that the proposed concept can be extended to meet various demands in fluid dynamics including reduced order modeling and its combination with linear theory-based methods by using its ability to arrange the order of the extracted nonlinear modes.

### Granular flow in rotating drums through simulations adopting a continuum constitutive equation

The need for a detailed description of dense granular flows arises in several practical applications. A continuum approach, where the solid phase is treated as a continuum, is suitable for large-scale flow modeling, as in the case of an industrial drum containing billions of particles. In this work, we present three-dimensional finite volume simulations of dense granular flow inside a rotating cylinder, adopting the viscoplastic Jop–Forterre–Pouliquen constitutive model for the granular medium stress tensor [Jop et al., “A constitutive law for dense granular flows,” Nature 441, 727–730 (2006)], the so-called μ(I)-rheology. The results obtained from our simulations are also compared with several experimental results available in the literature. Qualitative and even quantitative agreement with data is found: we are able to reproduce the experimentally observed flow regime sequence in rotating drums, ranging from rolling to centrifuging, and to predict flow fields of interest within the granular phase in agreement with experimental results, not only on the drum center but also along the axial direction. This approach characterizes a wide variety of regimes by changing both physical and geometrical parameters and gives details on several flow quantities difficult to be accessed through experiments, but of practical interest.

### Reciprocal microswimmers in a viscoelastic fluid

We suggest several reciprocal swimming mechanisms that lead to locomotion only in viscoelastic fluids. In the first situation, we consider a three-sphere microswimmer with a difference in oscillation amplitudes for the two arms. In the second situation, we consider a three-sphere microswimmer in which one of the frequencies of the arm motion is twice as large as the other one. In the third situation, we consider a two-sphere microswimmer with a difference in size for the two spheres. In all these three cases, the average velocity is proportional to the imaginary part of the complex shear viscosity of a surrounding viscoelastic medium. We show that it is essential for a micromachine to break its structural symmetry in order to swim in a viscoelastic fluid by performing reciprocal body motions.

### Dynamic behavior and maximum spreading of droplets impacting concave spheres

Droplet impact is omnipresent in nature and industry, and it is affected by the surface shape. Here, experiments, simulations, and theoretical analyses are conducted to explore the impact behaviors of water droplets on the concave spheres, especially the maximum spreading. The simulation model using the volume of fluid method is validated by comparing the temporal droplet profiles and spreading factors yielded by the simulation and experiment. The effects of the Weber number, contact angle, and sphere-to-droplet diameter ratio on the maximum spreading are exhaustively investigated. The results indicate that both the maximum spreading factor and arc angle increase with the increase in the Weber number and the decrease in the contact angle. The maximum spreading factor and area on the concave sphere generally first increase slightly and then decrease with the reduction in the diameter ratio owing to the combined action of the gravity and the surface shape. As the diameter ratio decreases, the maximum spreading arc angle increases and the maximum diameter of the contact line decreases. For a fixed diameter ratio, the droplet generally spreads less on a concave surface than on a convex one. Based on the energy conservation, a theoretical model is further established to predict the changing trend of the maximum spreading factor with the Weber number, contact angle, and diameter ratio, which yields a ±15% deviation over 93% of all the data points. This work may deepen our understanding of the mechanism of droplet impact on concave spheres and contribute to the associated applications.

### Spreading and retraction kinetics for impact of nanodroplets on hydrophobic surfaces

Impact dynamics of nanodroplets has recently gained extensive attention because of its potential applications in nanoscale inkjet printing, nanodroplet spray cooling, and nanocoating. In this study, a nanodroplet impacting unheated, flat, smooth, and hydrophobic surfaces is investigated via molecular dynamics simulations. The emphasis is placed on spreading and retraction kinetics, i.e., time-dependent wetting radius or r–τ relation, where r and τ are the normalized wetting radius and time. On the basis of an energy conservation approach, an analytical model of r–τ kinetics is developed for impacting nanodroplets. Hypotheses of cylinder droplet and extensional flow are employed to calculate the transient kinetic energy and viscous dissipation rate, which are found to be the most appropriate for impacting nanodroplets. The model is tested in a range of Weber numbers from We = 15 to 60, Reynolds numbers from Re = 11.07 to 22.19, and surface wettability θ0 = 105° and 125°. The tests show that the mean relative deviation ranges from 2.22% to 5.47%, and hence, the developed model captures the spreading and retraction kinetics of a nanodroplet impacting hydrophobic surfaces with satisfactory accuracy. Furthermore, it is found that the model can also be extended to predict the retraction kinetics of nanodroplets on hydrophilic surfaces for high Weber numbers.

### Microscale modeling of nondilute flow and transport in porous medium systems

Author(s): Timothy M. Weigand and Cass T. Miller

Nondilute transport occurs routinely in porous medium systems. Experimental observations have revealed effects that seemingly depend upon density, viscosity, velocity, and chemical activity. Macroscale models based upon averaged behavior over many pores have been relied upon to describe such systems...

[Phys. Rev. E 102, 033104] Published Tue Sep 08, 2020

### Linearly forced isotropic turbulence at low Reynolds numbers

Author(s): Wouter J. T. Bos, Faouzi Laadhari, and Wesley Agoua

We investigate the forcing strength needed to sustain a flow using linear forcing. A critical Reynolds number Rc is determined, based on the longest wavelength allowed by the system, the forcing strength and the viscosity. A simple model is proposed for the dissipation rate, leading to a closed expr...

[Phys. Rev. E 102, 033105] Published Tue Sep 08, 2020

### Regularized representation of bacterial hydrodynamics

Author(s): Kenta Ishimoto, Eamonn A. Gaffney, and Benjamin J. Walker

Fluid flows induced by a flagellated bacterial swimmer are often modeled as a simple force dipole, valid in the far field. A refined swimmer representation is presented that makes use of regularized singularities, retaining simplicity while capturing details of the complex flow field near the swimmer. A simple model system is then considered, demonstrating that these nuanced hydrodynamics are significant for bacterial interactions.

[Phys. Rev. Fluids 5, 093101] Published Tue Sep 08, 2020

### Hydrodynamic model for <i>Spiroplasma</i> motility

Author(s): Christian Esparza López and Eric Lauga

Swimming of *Spiroplasma* is not as kinky as one might suspect. The reversibility of Stokes flow combined with the symmetry of the swimming gait result in straight trajectories.

[Phys. Rev. Fluids 5, 093102] Published Tue Sep 08, 2020

### Dynamics of an idealized respiratory-type flow: Tidal exchange across intermediate Reynolds numbers

Author(s): E. G. Connor, A. C. True, and J. P. Crimaldi

Volume-conserving periodic flows feature inhalant and exhalant phases that interact nonlinearly to create dynamic flow structures. Numerical and experimental approaches provide time-resolved flow fields to map the Lagrangian histories of inhale and exhale phases. For biologically relevant intermediate Reynolds number, it is shown that fluid exchange is especially sensitive to asymmetries between the inhale and exhale flow structures.

[Phys. Rev. Fluids 5, 093103] Published Tue Sep 08, 2020

### Numerical simulation of the crossing of a liquid-liquid interface by a droplet

Author(s): Hassan El Itawi, Benjamin Lalanne, Gladys Massiera, Nathalie Le Sauze, and Olivier Masbernat

Numerical simulations are used to investigate the passage of a droplet through a liquid-liquid interface in the tailing configuration until the breakup of the column, leading to the drop encapsulation. Conditions required for the droplet to cross the interface are discussed. Scaling laws of both the length of the entrained column and the volume of the encapsulating film are proposed, primarily dependent on inertial parameters and exhibiting a strong influence of the drop-to-film viscosity ratio.

[Phys. Rev. Fluids 5, 093601] Published Tue Sep 08, 2020