# Latest papers in fluid mechanics

### Effect of thermal convection on thermocapillary migration of a surfactant-laden droplet in a microchannel

Despite its significance in droplet-based microfluidic technologies with the use of thermal stimuli and surfactants, coupling effects of thermal- and surfactant-induced Marangoni stresses on the transport of droplets in microchannels are not fully uncovered yet. To facilitate studies in this area, we present a three-dimensional numerical study on the thermocapillary migration of an insoluble-surfactant-laden droplet under Poiseuille flow in a microchannel. This work is realized via our own front-tracking finite-difference method with further integration of the energy conservation equation and the surface surfactant transport equation. Our numerical results agree well with the previously reported analytical results for ambient conditions with negligible thermal convection. In this study, we mainly focus on the effects of the thermal convection at high thermal Peclet numbers and find that it induces a significant change in the thermal Marangoni stress. As a consequence, the migration of surfactant-laden droplets in the microchannel is significantly retarded by the thermal convection, which is observed for two different ambient conditions, i.e., the imposed temperature increasing or decreasing along the main flow direction. To understand the mechanism underlying the effects of the thermal convection, we analyze the distributions of the temperature, surfactant concentration, and the thermal- and surfactant-induced surface tension variations over the droplet surface. Notably, the surfactant-induced Marangoni stress always opposes the thermal-induced Marangoni stress for the entire range of thermal Peclet numbers considered in this study, but the competition between them is significantly alternated by the thermal convection in a quantitative manner.

### Small-Peclet-number approximation for stellar turbulent mixing zones

Author(s): Jean-Cédric Chkair, Olivier Soulard, Jérôme Griffond, and Xavier Blanc

The purpose of this work is to derive a small turbulent Péclet–small turbulent Mach number approximation for hydroradiative turbulent mixing zones encountered in stellar interiors where the radiative conductivity can overwhelms the turbulent transport. To this end, we proceed to an asymptotic analys...

[Phys. Rev. E 102, 033111] Published Fri Sep 18, 2020

### Spontaneous dynamics of two-dimensional Leidenfrost wheels

Author(s): Rodolfo Brandão and Ory Schnitzer

In a two-dimensional model of a Leidenfrost drop levitating above a flat hot substrate, it is found that the lubrication layer of vapor can develop an asymmetry which has the effect of propelling the drop sideways.

[Phys. Rev. Fluids 5, 091601(R)] Published Fri Sep 18, 2020

### Deflection of phototactic microswimmers through obstacle arrays

Author(s): Marvin Brun-Cosme-Bruny, Andre Förtsch, Walter Zimmermann, Eric Bertin, Philippe Peyla, and Salima Rafaï

A study of the effect of inhomogeneous environments on the swimming direction of the microalgae *Chlamydomonas reinhardtii* in the presence of a light stimulus is presented. A mean deflection of microswimmers is measured that shows an interesting nonlinear dependence on the direction of the guiding light beam with respect to the symmetry axes of the pillar lattice. This is shown both in experiments and numerical simulations. On the basis of these results, an analytical model for microswimmers is suggested, where the pillar lattice is replaced by an anisotropic scattering medium.

[Phys. Rev. Fluids 5, 093302] Published Fri Sep 18, 2020

### Revisiting the Taylor-Culick approximation. II. Retraction of a viscous sheet

Author(s): Hiranya Deka and Jean-Lou Pierson

The retraction of a viscous liquid sheet is studied using direct numerical simulations and long-wave asymptotic models. In the viscous regime, there exists a self-similar solution for the interface and the velocity profiles of a retracting sheet. This similarity solution reveals that the tip speed decreases as a function of time for a finite liquid sheet in contrast to the steady speed reached in the inertia dominated regime. Direct numerical simulations corroborate these theoretical predictions.

[Phys. Rev. Fluids 5, 093603] Published Fri Sep 18, 2020

### Low Mach number fluctuating hydrodynamics model for ionic liquids

Author(s): Katherine Klymko, Andrew Nonaka, John B. Bell, Sean P. Carney, and Alejandro L. Garcia

Room temperature ionic liquids (RTILs) are mixtures of large ionic molecules of importance to energy technology applications, such as supercapacitors and high-performance batteries. A new computational model that uses fluctuating hydrodynamics to allow for efficient and accurate investigation of complex nanometer scale structures is presented. This hydrodynamic model is derived to be consistent with the thermodynamic and electrical properties ultimately responsible for the rich phenomena observed in RTILs. Simulation results demonstrate that the model reproduces important physical effects observed in RTIL experiments.

[Phys. Rev. Fluids 5, 093701] Published Fri Sep 18, 2020

### Gravity-driven thermoviscous liquid film down a heated or cooled vertical cylinder

Author(s): Sana Khanum and Naveen Tiwari

Gravity-driven flow of a liquid over an isothermal cylinder is unconditionally unstable. The flow of a thermoviscous fluid over a heated or cooled substrate shows interesting stability behavior. The relevant parameters in the model affect the spatiotemporal nature of the instability.

[Phys. Rev. Fluids 5, 094005] Published Fri Sep 18, 2020

### Symmetry-breaking waves and space-time modulation mechanisms in two-dimensional plane Poiseuille flow

Author(s): Roger Ayats, Alvaro Meseguer, and Fernando Mellibovsky

Two distinct scenarios of spatial modulation in two-dimensional plane Poiseuille flow have been studied. The first one is based on the identification of a new family of asymmetric Tollmien-Schlichting waves (TSW) breaking the reflectional symmetry about the channel midplane. The second follows the fate of a branch of time-periodic space-modulated waves that exclusively bridge upper-branch TSW-trains of different number of replicas by means of a codimension-2 bifurcation point. These modulated waves may therefore play a relevant role in the strange saddle governing domain-filling turbulent dynamics at high Reynolds numbers.

[Phys. Rev. Fluids 5, 094401] Published Fri Sep 18, 2020

### Local energy flux of turbulent flows

Author(s): Alexandros Alexakis and Sergio Chibbaro

The local energy flux rate toward small scales in isotropic turbulent flows is investigated. The joint probability density function is calculated, with the local filtered strain rate, for a scale in the inertial range. The flux shows good correlation with the strain, in support of the Smagorinsky eddy viscosity model. The implications of the results for subgrid scale models are discussed and new modeling directions are proposed.

[Phys. Rev. Fluids 5, 094604] Published Fri Sep 18, 2020

### Electric field induced dynamics of viscoplastic droplets in shear flow

We investigate the dynamics of viscoplastic droplets under the combined action of electric field and shear flow by performing direct numerical simulations. The electro-hydrodynamic equations are solved in a two-dimensional finite volume framework, and the interface is captured using a volume-of-fluid approach. The rheology of the viscoplastic droplet is modeled as a Bingham plastic fluid. Both the drop and the surrounding medium are considered to be perfect dielectric fluids. The simulations reveal that in the sole presence of the shear flow, the plasticity of the fluid plays a pivotal role in deciding the magnitude of droplet deformation and orientation. The local viscosity inside the drop is significantly augmented for higher plasticity of the fluid. Under the action of the electric field, the droplet deformation and orientation can be suitably tuned by varying the magnitude of the permittivity contrast between the fluids. The droplets experience enhanced deformation and preferred orientation against the flow direction when the permittivity ratio is greater than unity. Increasing the droplet plasticity leads to reduction in the droplet deformation. Conversely, by increasing the electric field strength, the deformation of the droplets can be notably enhanced, with a stronger response observed for a permittivity ratio beyond unity. Finally, it is observed that by suitably manipulating the strength of the shear flow and the electric field, droplet breakup can be engendered. The mode of droplet disintegration differs due to variation of the parameters, which can be attributed to the competing influence of shear and electric forces on the droplet.

### Pore-scale modeling of wettability effects on infiltration behavior in liquid composite molding

The effect of wettability on the infiltration behavior in the liquid composite molding process has not been fully studied, and the available evidence appears to be conflicting. Based on the three-dimensional microcomputed tomography images of porous media, a series of immiscible displacement simulations under a wide range of wettability conditions was established by the phase field method. Interestingly, we found that increasing the affinity of the porous matrix for the invading fluid can increase the displacement efficiency and reduce the void content until the critical wetting transition is reached, beyond which the displacement efficiency decreases sharply. The nonmonotonic behavior of the wettability effect can be explained by the competition among complex and intriguing pore-scale displacement events, mainly involving the Haines jump, cooperative pore filling, and corner flow. These novel findings provide a theoretical basis for extracting the optimal wettability range, thus minimizing the void content formed during the liquid infiltration process.

### Bifractal nature of turbulent reaction waves at high Damköhler and Karlovitz numbers

Governing physical mechanisms of the influence of Kolmogorov turbulence on a reaction wave (e.g., a premixed flame) are often discussed by adopting (combustion) regime diagrams. While two limiting regimes associated with (i) a high Damköhler number Da, but a low Karlovitz number Ka, or (ii) a low Da, but a high Ka drew significant amount of attention, the third limiting regime associated with (iii) Da ≫ 1 and Ka ≫ 1 has yet been beyond the mainstream discussions in the literature. The present work aims at filling this knowledge gap by adapting the contemporary understanding of the fundamentals of the regimes (i) and (ii) in order to describe the basic features of the influence of intense turbulence on a reaction wave in the regime (iii). More specifically, in that regime, the entire turbulence spectrum is divided in two subranges: small-scale and large-scale eddies whose influence on the reaction wave is modeled similarly to the regimes (ii) and (i), respectively. Accordingly, the surface of the reaction wave is hypothesized to be a bifractal with two different fractal dimensions of Df = 8/3 and 7/3 at small and large scales, respectively. The boundary between the two ranges is found by equating the local eddy turn-over time to the laminar-wave time scale. Finally, a simple scaling of UT ∝ u′ is obtained for the turbulent consumption velocity at Da ≫ 1 and Ka ≫ 1. Here, u′ is the rms turbulent velocity.

### Correction of second-order slip condition for higher Knudsen numbers by approximation of free-molecular diffusion

The computational predictions of channel and pipe flows with classical models and no-slip condition at the wall reach excellent results for lower Knudsen numbers (Kn) only. Linear slip models reach a very good approximation of measurement results over the region of 10−3 < Kn < 10−1. The numerical results of higher-order slip models match experimental data up to Kn ≈ 1. The present work derives an analytical model for the transition from the slip regime to the free-molecular flows by the superposition of diffuse molecular boundary reflection and the molecular diffusion inside the bulk flow. The methodology of the present publication models the mass flow resulting from the molecular diffusion for the approximation of the mass flow in microchannels and micropipes for the regime of molecular mass flows (1 < Kn < 100) in an excellent way. The present model shows good agreement with the former models, measurement data, and direct simulation Monte Carlo results for the complete region from the transitional regime up to free-molecular flow (10−2 < Kn < 102).

### The effects of double-diffusion and viscous dissipation on the oscillatory convection in a viscoelastic fluid saturated porous layer

The effects of the double-diffusion and viscous dissipation on the convective instability in a horizontal porous layer are investigated. The porous medium is saturated with a binary viscoelastic fluid. The Oldroyd-B model of viscoelastic fluid is considered. Constant temperature and concentration differences are maintained between the boundaries. A basic flow is present in the horizontal direction. The governing parameters are the thermal Rayleigh number (RaT), solutal Rayleigh number (RaS), Gebhart number (Ge), Lewis number (Le), Péclet number (Pe), dimensionless relaxation time (λ1), and dimensionless retardation time (λ2). A small perturbation to the basic flow is assumed, and a linear stability analysis is performed. A detailed discussion is carried out considering RaT as the eigenvalue. The critical wave number and frequency are also derived for a wide range of Lewis numbers and solutal Rayleigh numbers. The oscillatory modes are analyzed. It is found that transverse rolls are the preferred mode for the onset of oscillatory convection, except for some special cases. Moreover, a negative solutal Rayleigh number stabilizes the flow. An opposite effect is seen in the presence of a positive solutal Rayleigh number.

### Data-driven order reduction and velocity field reconstruction using neural networks: The case of a turbulent boundary layer

We present a data-driven methodology to achieve the identification of coherent structure dynamics and system order reduction of an experimental turbulent boundary layer flow. The flow is characterized using time-resolved optical flow particle image velocimetry, leading to dense velocity fields that can be used both to monitor the overall dynamics of the flow and to define as many local visual sensors as needed. A Proper Orthogonal Decomposition (POD) is first applied to define a reduced-order system. A non-linear mapping between the local upstream sensors (inputs sensors) and the full-field dynamics (POD coefficients) as outputs is sought using an optimal focused time-delay Artificial Neural Network (ANN). The choices of sensors, ANN architecture, and training parameters are shown to play a critical role. It is verified that a shallow ANN, with the proper sensor memory size, can lead to a satisfying full-field dynamics identification, coherent structure reconstruction, and system order reduction of this turbulent flow.

### Near-wall effect on flow around an elliptic cylinder translating above a plane wall

In this work, the flow over an elliptic cylinder near a moving wall is investigated for Reynolds numbers less than 150. Here, the ratio between the gap (i.e., the distance between the cylinder and the wall) and the length of the semi-major axis of the elliptic cylinder varies from 0.1 to 5. This ratio is hereafter denoted as the gap ratio. The resulting Kármán vortex street, the two-layered wake, and the secondary vortex street have been investigated and visualized. Numerical simulations show that for the steady flow, the wake is composed of two asymmetric recirculation vortices, while a decrease in the gap ratio suppresses the vortex shed from the lower part of the cylinder. For the unsteady flow, the wake can be classified into four different patterns based on the wake structures (the Kármán vortex street, the two-layered wake, and the secondary vortex street). The regions of these wake patterns are given in the gap ratio and Reynolds number space, showing that the critical Reynolds number for the transition between different patterns increases as the gap ratio decreases. An overall increase in the mean drag coefficient with increasing gap ratios is observed, except for a sudden drop that occurs within a small gap ratio range. Moreover, as the gap ratio increases, the onset location of the two-layered wake first decreases due to a decrease in flow velocity in the gap and then increases due to the weakening of the wall suppression effect.

### A dual mesh control domain method for the solution of nonlinear Poisson’s equation and the Navier–Stokes equations for incompressible fluids

In this study, the dual mesh control domain method, which employs the finite element approximation of the primary variables and the finite volume idea of satisfying the governing equations over a control domain, is used for the numerical solution of the Navier–Stokes equations governing the flows of viscous incompressible fluids using the penalty function formulation for two-dimensional analysis. The primal mesh is the mesh of finite elements used to interpolate the velocity field, while the dual mesh of control domains is used to satisfy the integral form of the Navier–Stokes equations, and thus, the method shares certain desirable features of the two popular methods. Numerical examples involving nonlinear Poisson’s equation and the Navier–Stokes equations are presented to illustrate the methodology and accuracy compared to the finite element and finite volume solutions, the latter depending on the scheme used to solve the discretized equations.

### Settling characteristics of bidisperse dilute suspension in the vortex shedding regime

In a fully periodic domain, monodisperse particles form clusters while settling in stagnant fluids at high Reynolds numbers (Re > 250) and dilute suspensions (solid volume fraction less than 1%). This is due to the entrapment of particles in the wakes developed by upstream particles. In this paper, this phenomenon is investigated for suspensions containing particles of different sizes that shed vortices during settling. To model the particle–fluid and particle–particle interactions, the immersed boundary method and discrete element method are used, respectively. Initially, the particles are randomly distributed in the computational domain and allowed to settle under the action of gravity. The gravitational force acting on the particles is adjusted to obtain the desired Reynolds number. The total solid volume fraction used in the simulations is about 0.1%, and the settling Reynolds number, which is based on the Sauter mean diameter, ranges from 250 to 450. Two particle diameter ratios (i.e., diameter of larger particles to smaller particles) of 2:1 and 3:1 are studied. For each particle diameter ratio, the mass fraction for each particle size varies from 0.2 to 0.8. For comparison, simulations of monodisperse particles settling under similar conditions are also conducted, and the average settling velocity, particle velocity fluctuations, and particle microstructures are studied. The simulation results show that, in the case of bidisperse particles, the settling characteristics are dominated by the larger-sized particles. Finally, the physics behind the studied anomalies is discussed in detail.

### A three-dimensional unified gas-kinetic wave-particle solver for flow computation in all regimes

In this paper, the unified gas-kinetic wave-particle (UGKWP) method has been constructed on a three-dimensional unstructured mesh with parallel computing for multiscale flow simulation. Based on the direct modeling methodology, the unified gas-kinetic scheme (UGKS) models the flow dynamics directly on the numerical mesh size and time step scales, and it is able to capture the flow dynamics from the kinetic scale particle transport to the hydrodynamic wave propagation seamlessly according to the local cell Knudsen number. Instead of discretizing the particle velocity space in UGKS, the UGKWP method is composed of evolution of deterministic wave and stochastic particles. With dynamic wave-particle decomposition according to the cell Knudsen number, the UGKWP method is able to capture the continuum wave interaction and rarefied particle transport under a unified framework and achieves high efficiency in different flow regimes. The UGKWP flow solver is constructed in three-dimensional space and is validated by many test cases at different Mach and Knudsen numbers. The examples include a 3D shock tube problem, lid-driven cubic cavity flow, high-speed flow passing through a cubic object, and hypersonic flow around a space vehicle. The parallel performance has been tested on the Tianhe-2 supercomputer, and reasonable parallel performance has been observed up to 1000 cores. With the wave-particle formulation, the UGKWP method has great potential in solving three-dimensional multiscale transport problems with the co-existence of continuum and rarefied flow regimes, especially for the high-speed rarefied and continuum flow simulation around a space vehicle in near-space flight, where the local Knudsen number can vary significantly with five or six orders of magnitude differences.

### Sonneting critical heat flux: New insights in boiling multiphase flow

Boiling—a process widely used for its good heat transferability—is limited by a phenomenon known as critical heat flux (CHF). Our experiments revealed a new CHF mechanism that is different from previously believed theories; we refer to it as “sonneting CHF.” At CHF, the flow pattern changes from bubbly flow to slug/churn flow and then to an unusual reverse annular flow, leading to a significant rise in the heater surface temperature. The reverse annular flow, however, does not sustain but breaks down into a chaotic flow pattern, resulting in unprecedented quenching of the heater surface. The flow pattern shortly reverts back to bubbly flow; this entire process repeats for a few cycles, where the heater surface temperature rises and falls with amplitudes increasing in each cycle until the heater trips. The maximum removal-surface heat flux is significantly higher than the CHF. This new understanding will enable flexible and innovative boiling systems for several energy applications.