# Latest papers in fluid mechanics

### Synthetic turbulent inflow generator using machine learning

Author(s): Kai Fukami, Yusuke Nabae, Ken Kawai, and Koji Fukagata

Machine-learning-based turbulence generators are developed to generate unsteady inflow conditions for turbulent flow simulations. The proposed method can provide inflow conditions with reasonable turbulence statistics without spurious periodicity and at a low computational cost.

[Phys. Rev. Fluids 4, 064603] Published Tue Jun 04, 2019

### Direct simulation Monte Carlo applications to liquid-vapor flows

The paper aims at presenting Direct Simulation Monte Carlo (DSMC) extensions and applications to dense fluids. A succinct review of past and current research topics is presented, followed by a more detailed description of DSMC simulations for the numerical solution of the Enskog-Vlasov equation, applied to the study of liquid-vapor flows. Results about simulations of evaporation of a simple liquid in contact with a dense vapor are presented as an example.

### Deformation, speed, and stability of droplet motion in closed electrowetting-based digital microfluidics

Electrowetting-based microdrop manipulation has received considerable attention owing to its wide applications in numerous scientific areas based on the digital microfluidics (DMF) technology. However, the techniques for highly precise droplet handling in such microscopic systems are still unclear. In this work, the deformation, speed, and stability of droplet transporting in closed electrowetting-based DMF systems are comprehensively investigated with both theoretical and numerical analyses. First, a theoretical model is derived which governs the droplet motion and includes the influences of the key electrowetting system parameters. After that, a finite volume formulation with a two-step projection method is used for solving the microfluidic flow on a fixed numerical domain. The liquid-gas interface of the droplet is tracked by a coupled level-set and volume-of-fluid method, and the surface tension at the interface is computed by the continuum surface force scheme. A parametric study has been carried out to examine the effects of the static contact angles (θs,ON and θs,OFF), hysteresis effect (Δθ), channel height (H), and electrode size (LE) on droplet shape, speed, and deformation during transport, which unanimously shows that droplet length, neck width, and transport stability are directly related to a dimensionless parameter [math] that only comprises θs,ON, θs,OFF, H, LE, and the hysteresis angle Δθ. Based on the results, the scaling laws for estimating droplet shape and stability of the transport process have been developed, which can be used for promoting the accuracy and efficiency of droplet manipulation in a large variety of droplet-based DMF applications.

### Asymptotics of a catenoid liquid bridge between two spherical particles with different radii and contact angles

A liquid bridge between two neighboring particles is commonly observed in nature and various industrial processes. An accurate prediction of the profile of a liquid bridge is significantly important in particulate flows, while it is an analytically challenging task as well. In this paper, we develop an asymptotic solution for a catenoid liquid bridge profile, which is the minimal surface ensuring the minimum total surface energy. Our asymptotic solution is based on a rapid convergent predictor-corrector algorithm that considers different factors including boundary conditions, volume conservation, and geometrical relations while providing the relationship between the liquid bridge profile, bridge radius, half-filling angles, and creeping distances. Therefore, this asymptotic solution of the catenoid of the liquid bridge is applicable to general scenarios of any two neighboring particles of either equal or different sizes having identical or different contact angles. In order to validate the proposed asymptotic solution, we performed comprehensive experiments where the observed and predicted liquid bridge profiles and the resultant capillary forces from both the approaches are found closely matching. Moreover, we also investigate and report the influence of the radii ratio, contact angles, particle distances, and the liquid bridge volumes on its profiles.

### Stochastic flow approach to model the mean velocity profile of wall-bounded flows

Author(s): Benoît Pinier, Etienne Mémin, Sylvain Laizet, and Roger Lewandowski

There is no satisfactory model to explain the mean velocity profile of the whole turbulent layer in canonical wall-bounded flows. In this paper, a mean velocity profile expression is proposed for wall-bounded turbulent flows based on a recently proposed stochastic representation of fluid flows dynam...

[Phys. Rev. E 99, 063101] Published Mon Jun 03, 2019

### Coalescence-induced droplet detachment on low-adhesion surfaces: A three-phase system study

Author(s): Mostafa Moradi, Mohammad Hassan Rahimian, and Seyed Farshid Chini

Coalescing water droplets on superhydrophobic surfaces can detach from the surface without the aid of any external forces. This self-propelled droplet detachment mechanism is useful in many applications, such as phase change heat transfer enhancement, self-cleaning surfaces, and anti-icing and antid...

[Phys. Rev. E 99, 063102] Published Mon Jun 03, 2019

### Faraday waves on band pattern under zero gravity conditions

Author(s): T. Lyubimova, A. Ivantsov, Y. Garrabos, C. Lecoutre, and D. Beysens

Coupled Faraday waves can develop under weightlessness on liquid-vapor bands induced by vibrations. The instability appears above a threshold that is determined by theoretical analysis and numerical simulation. It compares well with sounding rocket experiments in CO2 near its critical point.

[Phys. Rev. Fluids 4, 064001] Published Mon Jun 03, 2019

### Transport across a bathymetric interface in quasi-two-dimensional flow

Author(s): Lei Fang and Nicholas T. Ouellette

In many geophysical situations, variable bathymetry can affect surface transport and mixing. Experiments show that the effect of bathymetry is to produce a porous transport barrier leading to asymmetric transport. These results may help to explain the dynamics of phenomena such as ocean dead zones.

[Phys. Rev. Fluids 4, 064501] Published Mon Jun 03, 2019

### Statistical properties of an incompressible passive vector convected by isotropic turbulence

Author(s): Jingyuan Yang, Toshiyuki Gotoh, Hideaki Miura, and Takeshi Watanabe

Statistical properties of an incompressible passive vector in isotropic turbulence are compared with the velocity and passive scalar in order to explore the physics behind their differences and similarities.

[Phys. Rev. Fluids 4, 064601] Published Mon Jun 03, 2019

### Emergence of skewed non-Gaussian distributions of velocity increments in isotropic turbulence

Author(s): W. Sosa-Correa, R. M. Pereira, A. M. S. Macêdo, E. P. Raposo, D. S. P. Salazar, and G. L. Vasconcelos

A theoretical framework, the H-theory, is applied to describe the skewed non-Gaussian distribution of velocity increments as a weighted mixture of asymmetric Gaussians. The weighing distribution is obtained from a hierarchical stochastic model of intermittency. Good agreement with direct numerical simulation data is found.

[Phys. Rev. Fluids 4, 064602] Published Mon Jun 03, 2019

### Bowling water drops on water surface

In our daily experience, the drops falling on a water pool usually immediately merge into water. The liquid drops floating at different environments are fascinating but attract less attention. Here, we report that the water drops are capable of floating on a water surface without heating, shearing, or oscillating the water pool. Water drops are generated from a beveled needle and fall on the clean water in an acrylic container. Water drops released from a beveled needle are found to travel on the water surface in a speed of tens of millimeter/second for several centimeters, which can be adjusted by the injection rate. A particle image velocimetry (PIV) technique is employed on the air, water drop, and water pool to confirm the rotation-induced shear effect for the delay coalescence. TiO2 particles and water aerosols served as visualized particles for PIV measurements in air, drop, and water pool. We show that the water drop can float on the water surface if it rotates or slides fast enough. The relative motion of the drop and the underneath surface plays an important role in the delay coalescence. The flow in the air layer between the drop and water pool not only shears the drop but also replenishes the loss of squeeze-out air in the thin layer.

### Passive vortical flows enhance mass transport in the interior of a coral colony

Corals exchange nutrients and dissolved gases with the surrounding environment for metabolic purposes. A recent study demonstrated that corals can actively stir quiescent water columns and produce vortical flows that enhance mass transfer rates by up to 400%. Here, three-dimensional immersed-boundary simulations of the flow through a Pocillopora meandrina colony demonstrate that the passive geometric features of the branching colony produce highly vortical internal flows that enhance mass transfer at the interior of the colony, compensating almost exactly for flows speed reductions there of up to 64% so that the advection time scale remains roughly constant throughout the colony.

### Numerical study of thermocapillary migration of a bubble in a channel with an obstruction

Fully resolved numerical simulations are used to examine the thermocapillary motion of a two- and three-dimensional fully deformable bubble in a channel with an obstruction. A front-tracking/finite volume method is used to solve the Navier-Stokes equations coupled with the energy conservation equation. The results show that, for a fixed obstruction and channel size, the influence coefficient α, defined as the ratio of arrival time in channels with and without an obstruction, increases with increasing Marangoni (Ma) number for both two- and three-dimensional flows, whereas an increase in the Reynolds (Re) number leads to an increase in the influence coefficient in two-dimensional flows but a decrease in three-dimensional flows. Moreover, a change in the Capillary (Ca) number does not have a visible effect on the thermocapillary motion if the width of the narrow part of the channel is larger than the bubble diameter. Results for both two- and three-dimensional flows show that the influence coefficient increases dramatically with an increase in the obstruction size W, and a larger obstruction makes the dependence of α on the fluid parameters more obvious.

### Fluid dynamics of oscillatory flow in three-dimensional branching networks

The present study is aimed at understanding and thoroughly documenting the complex unsteady fluid dynamics in six generations of a model human bronchial tree, comprising 63 straight sections and 31 bifurcation modules, during a complete breathing cycle. The computational task is challenging since the complexity of an elaborate network is augmented with adopted stringent criteria for spatial and temporal accuracy and convergence at each time step (10−8 for each scaled residual). The physical understanding of the fluid dynamics of steady expiratory flow is taken to a similar level of fine details that have been previously established for steady inspiratory flow in earlier publications of the authors. The effects of three-dimensional arrangement of the same branches on the oscillatory flow structure are determined. It is found that the quasisteady assumption is approximately valid in the neighborhood of the peak flow rate, both during inspiration and expiration. Unsteady effects are at their maximum during the changeover from expiration to inspiration and inspiration to expiration. At these time instants, regions of bidirectional flow are observed in all branches with significant secondary motion at various cross sections (none of these features can be predicted by steady state simulations). It is described how the symmetry of the solution with respect to both space and time—found in the oscillating, fully developed flow in a pipe—are destroyed in the unsteady effects that occur in the oscillating flow in a branching network. As the Womersley number is increased, the unsteady effects at all branches increase, and bidirectional flow exists over a greater portion of a cycle. The flow division at a bifurcation module during inspiratory flow generates large asymmetry in the flow field with nonuniform mass flow distribution among the branches of a generation (even in a geometrically symmetric network), whereas flow combination at the same bifurcation module during expiratory flow tends to produce more symmetry in the flow field, displaying essential irreversibility of fluid dynamics.

### Pressure-driven flow focusing of two miscible liquids

Flow focusing consists in injecting a core liquid into another surrounding flowing sheath liquid. Here we investigate experimentally the influence of imposing pressure to generate coflow of two miscible liquids. We inject water in the central inlet of a cross-junction microfluidic device and different mixtures of glycerol-water in the two lateral inlets. A pressure generator is used to control the flows, and the established flow rates are monitored in both inlets. We draw a state diagram that delimits the regions of the coflow, the inner and outer back flows. We measure the width of the jet as a function of different control parameters: the inlet pressures, the flow rates, the viscosity contrast, and the channel aspect ratio. We show that the jet width can be controlled by tuning the internal to external pressure ratio solely, provided that the viscosity contrast is low. We discuss the possibility to use such a system to center particles in a channel.

### Stability of inclined flow of a liquid film with soluble surfactants and variable mass density

Author(s): J. P. Pascal, S. J. D. D'Alessio, and E. Ellaban

Adding surfactant to clean fluid stabilizes the inclined flow. A theoretical study shows that beyond a critical level the flow is destabilized as more surfactant is added due to desorption from the surface. If the mass density of the fluid increases with surfactant concentration in the bulk, a later stabilizing stage occurs.

[Phys. Rev. Fluids 4, 054004] Published Fri May 31, 2019

### Counterflow and wall stagnation flow with three-dimensional strain

Three-dimensional (3D) viscous counterflows and wall stagnation flows are analyzed with differing normal strain rates in each of the three directions. Reduction of the equations to a similar form is obtained allowing for variations in density due to temperature and composition, heat conduction, and, for the counterflow, mass diffusion and the presence of a flame. Solutions to the Navier-Stokes equations are obtained without the boundary-layer approximation. For the steady and unsteady incompressible counterflows, analytical solutions are obtained for the flow field and the scalar fields subject to heat and mass transfer. In steady, variable-density configurations, a set of ordinary differential equations (ODEs) governs the two transverse velocity and the axial velocity profiles as well as the scalar-field variables. Diffusion rates for mass, momentum, and energy depend on the two normal strain rates parallel to the counterflow interface or the wall and thereby not merely on the sum of those two strain rates. For thin diffusion flames, the location, burning rate, and peak temperature are readily obtained. Solutions for planar flows and axisymmetric flows are obtained as limits here. Results for the velocity and scalar fields are found for a full range of the distribution of normal strain rates between the two transverse directions, various Prandtl number values, and various ambient (or wall) temperatures. For counterflows with flames and stagnation layers with hot walls, velocity overshoots are seen in the viscous layer, yielding an important correction of theories based on a constant-density assumption.

### Dispersion due to combined pressure-driven and electro-osmotic flows in a channel surrounded by a permeable porous medium

The combined electro-osmotic and pressure-driven flows (PDFs) have pronounced impacts on the solute transport in permeable porous media, particularly mixing and separation processes. However, the relationship between the physical properties of the permeable porous media and the combined electro-osmotic and PDFs still needs further investigation. This study focuses on the transport of a neutral nonreacting solute in a channel with permeable porous walls under the combined effects of electro-osmotic and PDFs. With the aid of perturbation theory and asymptotic analysis, the equivalent one-dimensional equations governing the solute concentrations in the channel and permeable porous medium under the combined velocity are derived. Based on this, an exact analytical expression relating the dispersion coefficient with the physical properties of the permeable porous medium and the combined flow is obtained. The model parameters exerting the most influence on the results are identified through sensitivity analysis. The proposed model is compared and validated with several previously developed models in the literature. The findings of this study can pave the way for the quantitatively design of solute transport through microporous coatings and porous microfluidic membranes.

### Kinetic modeling of unsteady hypersonic flows over a tick geometry

Hypersonic separated flows over the so-called “tick” geometry have been studied using the time-accurate direct simulation Monte Carlo (DSMC) method and global linear theory. The free stream condition for two experimental cases studied in the free-piston shock tunnel (named T-ADFA) was modeled. These two cases span a Knudsen number from transitional to continuum, a Mach number of about 10, a free stream enthalpy from 10 to 3 MJ/kg, a Reynolds number varying by a factor of four, and a leading edge geometry varied from sharp to one with a bevel of 0.2 mm. For the first time, the time dependence of flow macroparameters on the leading edge nose radius and the Reynolds number are studied using global linear theory. High-fidelity DSMC simulations showed that the temporal behavior of the separation region, which has significant effects on the surface parameters, depends closely on the leading edge bluntness and wall temperature. The formation of a secondary vortex was seen in about 2 ms for the sharp leading edge, whereas in the rounded leading edge geometry, it formed at earlier 0.7 ms. At a steady state, the size and structure of the separation zone, vortex structures, and surface parameters predicted by DSMC were found to be in good agreement with computational fluid dynamics for the higher density case. Finally, linear stability theory showed that for some leading edge shapes and flow densities, the time to reach the steady state was longer than the facility measurement time.

### Dynamics of particle migration in confined viscoelastic Poiseuille flows

Author(s): Antoine Naillon, Clément de Loubens, William Chèvremont, Samuel Rouze, Marc Leonetti, and Hugues Bodiguel

Quantitative experimental measurements are used to test the ability of theoretical development to predict the transverse velocity migration of particles in a confined Poiseuille flow, according to the viscoelastic constitutive parameters of dilute polymer solutions.

[Phys. Rev. Fluids 4, 053301] Published Thu May 30, 2019