# Latest papers in fluid mechanics

### Bouncing, chasing, or pausing: Asymmetric collisions of active droplets

Author(s): Kevin Lippera, Michael Benzaquen, and Sébastien Michelin

Small differences in the size of colliding chemically active droplets lead to three strikingly different dynamic behaviours: (i) an asymmetric rebound where both droplets reverse directions, (ii) a chasing regime leading to a bound state with both droplets swimming together, and (iii) a pausing regime where the larger droplet is temporarily stopped. Such diversity and sensitivity of the exact droplet properties may influence the complex collective dynamics of chemically active droplets.

[Phys. Rev. Fluids 5, 032201(R)] Published Tue Mar 10, 2020

### Retraction dynamics of water droplets after impacting upon solid surfaces from hydrophilic to superhydrophobic

Author(s): Fujun Wang and Tiegang Fang

The retraction dynamics of water droplets impacting on surfaces with different wettabilities is studied. Three modes of droplet retractions can be classified as inertial, capillary, and spherical-cap. A new model is proposed to predict the inertial-mode retraction rate of water droplets on different surfaces. The scaling of retraction curves is revised to reveal the similarity behavior of droplet retraction dynamics.

[Phys. Rev. Fluids 5, 033604] Published Tue Mar 10, 2020

### Role of all jet drops in mass transfer from bursting bubbles

Author(s): Alexis Berny, Luc Deike, Thomas Séon, and Stéphane Popinet

When a bubble bursts at a liquid surface, it creates a jet that destabilizes into an aerosol of a few droplets. The gigantic number of bubbles that burst every second at the surface of the oceans form the sea spray. By evaporating, this spray plays a key role in the exchange between the ocean and the atmosphere. The dynamics and the evaporation of the drops generated by a large range of bubbles bursting are presented, and it is shown that they all have to be taken into account in the evaporation process.

[Phys. Rev. Fluids 5, 033605] Published Tue Mar 10, 2020

### Lattice Boltzmann simulations of droplet breakup in confined and time-dependent flows

Author(s): Felix Milan, Luca Biferale, Mauro Sbragaglia, and Federico Toschi

A multicomponent lattice Boltzmann algorithm shows that droplet breakup in a generic time-dependent flow is highly dependent on the flow startup conditions. Confinement plays a crucial role as well. For a system with strong confinement, an adiabatic increase of the maximum shear intensity may drive the system into a metastable state, which has a much higher critical capillary number than the stable state.

[Phys. Rev. Fluids 5, 033607] Published Tue Mar 10, 2020

### Towards an improved spatial representation of a boundary layer from the attached eddy model

Author(s): Felix Eich, Charitha M. de Silva, Ivan Marusic, and Christian J. Kähler

Synthetic turbulent boundary flow fields generated based on the attached eddy model are compared to experimental data in wall-parallel and wall-normal planes. In doing so, a modification to the placement of the representative eddies in the attached eddy model is proposed that incorporates the meandering of the flow structures. Results reveal that this subtle modification provides a superior spatial representation of a turbulent boundary layer from the attached eddy model.

[Phys. Rev. Fluids 5, 034601] Published Tue Mar 10, 2020

### Data-driven recovery of hidden physics in reduced order modeling of fluid flows

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model the remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and a Galerkin projection (GP) as a model to build the dynamical core of the system. Our proposed methodology, hence, compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmann manifold approach is also adopted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system’s behavior is, thus, implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is then discussed through illustrative examples that are generated synthetically to take hidden physics into account. Our approach, thus, provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.

### Experimental study on secondary flow in turbulent boundary layer over spanwise heterogeneous microgrooves

Convergent–divergent riblets (C–D riblets) are a type of grooved surface pattern with directionality and spanwise heterogeneity. In the cross-stream plane, we apply stereoscopic particle image velocimetry to study the characteristics of the secondary flow over C–D riblets. Three different heights of h+ = 8, 14, and 20 are applied in the turbulent boundary layers at Reθ = 723 to reveal the effect of riblet height on the flow field. In the cross-stream plane, increasing the riblet height intensifies the heterogeneity of turbulent properties, i.e., a wider downwelling region, a stronger spanwise flow, a narrower upwelling region, and a stronger deceleration effect. Compared with the smooth-wall case, the magnitude of spanwise velocity fluctuations is larger over the converging region. The dispersive momentum transfer is primarily contributed by the secondary-flow-induced stress compared with the roughness-induced stress, and it becomes more intense as the riblet height increases. Compared with the smooth-wall case, the near-wall streamwise turbulent events are slightly wider over the diverging region and much narrower over the converging region. Overall, the higher C–D riblets generate a more intense secondary flow, and the mechanism of an increasing riblet height is attributed to the greater capability of deeper yawed microgrooves. In light of the results from our study, we propose a different way of categorizing the surface patterns with spanwise heterogeneity from the perspectives of surface geometry, roll mode, and secondary flow generation mechanisms.

### Evaporation-induced transport of a pure aqueous droplet by an aqueous mixture droplet

Transport of droplets on surfaces is important for a variety of applications such as micro liquid handling and biochemical assays. Here, we report evaporation-induced attraction, chasing, and repulsion between a target pure aqueous (water) droplet and a driver aqueous mixture droplet comprising water and a lower surface tension and lower vapor pressure liquid on a high energy surface. It is observed that for a fixed concentration of the mixture droplet, attraction/chasing or repulsion can be achieved by varying the relative time instants at which the drops are dispensed. Our study reveals that if the water droplet is dispensed within a critical time after dispensing the mixture droplet, the latter will get attracted to and chase the water droplet. On the other hand, if the water droplet is dispensed after this critical time, then it would get repelled from the mixture droplet. We explain the underlying mechanisms that govern the phenomena and demonstrate continuous transport of liquid/cell sample droplets/plugs.

### Laser-induced fluorescence velocimetry for a hypersonic leading-edge separation

Two-dimensional mapping of the velocity distribution for a hypersonic leading-edge separation flowfield generated by a “tick” shaped geometry is presented for the first time. Discrete measurements of two velocity components were acquired at a flow condition having a total specific enthalpy of 3.8 MJ/kg by imaging nitric oxide fluorescence over numerous runs of the hypersonic tunnel at the Australian Defence Force Academy (T-ADFA). The measured freestream velocity distribution exhibited some non-uniformity, which is hypothesized to originate from images acquired using a set of ultraviolet specific mirrors mounted on the shock tunnel deflecting under load during a run of the facility, slightly changing the laser sheet orientation. The flow separation point was measured to occur at 1.4 ± 0.2 mm from the model leading edge, based on the origin of the free shear layer emanating from the expansion surface. Reattachment of this free shear layer on the compression surface occurred at 59.0 ± 0.2 mm from the model vertex. Recirculating the flow bound by the separation and reattachment points contained supersonic reverse flow and areas of subsonic flow aligned with the location of three identified counter-rotating vortices. A comparison of the recirculation flow streamline plots with those computed using Navier–Stokes and direct simulation Monte Carlo (DSMC) codes showed differences in flow structures. At a flow time close to that produced by the facility, flow structures generated by the DSMC solution were seen to agree more favorably with the experiment than those generated by the Navier–Stokes solver due to its ability to better characterize separation by modeling the strong viscous interactions and rarefaction at the leading edge. The primary reason for this is that the no-slip condition used in the Navier–Stokes solution predicts a closer separation point to the leading edge and structures when compared to the DSMC solution, which affects surface shear stress and heat flux, leading to a difference in flow structures downstream of the separation.

### Numerical design of a highly efficient microfluidic chip for blood plasma separation

Blood plasma separation may be one of the most frequent operations in daily laboratory analysis so that a highly efficient separation could save time, cost, and labor for laboratory operators. A numerical technique is demonstrated in this work to design a highly efficient microfluidic chip that can separate 64% plasma from blood with 100% purity. Simulations are carried out for the blood flow by a hybrid method of smoothed dissipative particle dynamics and immersed boundary method (SDPD-IBM). SDPD is used to model the motion of blood flow, while IBM is used to handle the interaction between cells and plasma. A single bifurcation, as the elementary component of the microfluidic chip, is first examined to find an optimal parameter group of flow rate and branch angle, which can generate a maximum separation efficiency on the premise of 100% purity. Then, the microfluidic chip is designed based on the optimal parameter group and compared with the existing experimental chip to analyze its performance. It is shown that the designed chip has a separation efficiency about 40% larger than the experimental one. Finally, the performance of the designed chip is analyzed by investigating the parameter dependence, and two critical parameters are studied, the cell hematocrit and inflow rate. The results provide an optimal hematocrit of 10.4% and an optimal inflow rate of 13.3 μl/h in order to obtain a high efficiency and 100% purity, which provides guidance for the level of diluting blood and the speed of injecting blood in experiments.

### Droplet impact onto a solid sphere in mid-air: Effect of viscosity, gas density, and diameter ratio on impact outcomes

Collision of a droplet and a hydrophobic particle in mid-air was investigated. To study the impact outcomes, specifically the lamella formation, a numerical simulation tool was developed and verified with impact experiments (water droplets and glass particles, ρrel = 0.41). The velocity field within the lamella showed that the flow inside the liquid film moves in two opposite directions along the lamella axis of symmetry: one is generated through the momentum transfer from the particle, and the other is due to the droplet initial velocity. This causes the lamella to be stretched in the same direction as the particle moves and forms a rim at the end of the lamella. Although a larger droplet-to-particle diameter ratio (Dr) increased the impact duration, it did not change the collision outcomes and two opposite flows still exist inside a thicker liquid film. However, the liquid viscosity affects impact outcomes; as viscosity increased, a thicker film remained on the particle, the liquid film became shorter, and the lamella formation was hindered accordingly. The pressure of the ambient gas also affects the liquid film formation. Unlike the literature of the drop impact on a flat surface, our results indicate that by increasing the ambient pressure, the lamella formation will be suppressed (hence chance of splashing). The pressure gradient around the liquid film creates a downward force that hinders the stretching of the liquid film. The effect of the ambient pressure on lamella formation is only significant for relatively higher gas pressures (i.e., Pamb > 2 Patm).

### Contact-line behavior in boiling on a heterogeneous surface: Physical insights from diffuse-interface modeling

Author(s): Biao Shen, Jiewei Liu, Gustav Amberg, Minh Do-Quang, Junichiro Shiomi, Koji Takahashi, and Yasuyuki Takata

Capitalizing on the full potential of latent heat of vaporization, boiling is among the most efficient heat transfer schemes. Further enhancement of boiling heat transfer relies on precise control of bubble dynamics, which can be realized on a surface endowed with heterogeneous wettabilities. However, such ordered bubble behavior could fail when the triple-phase contact line gets dislodged from the hydrophilic-hydrophobic border by accelerated bubble expansion. Here, a numerical study of the critical condition for the transition between the pinned- and depinned-contact-line modes is presented.

[Phys. Rev. Fluids 5, 033603] Published Mon Mar 09, 2020

### Fingering patterns in hierarchical porous media

Author(s): Si Suo, Mingchao Liu, and Yixiang Gan

Fingering during fluid-fluid displacement in porous media can be governed by two primitive parameters—capillary number and mobility ratio. Here, for porous media consisting of two or more distinguishable scales of pores, the dynamics of immiscible fingering under the influences of hierarchical structures are unravelled. In particular, the conditions under which the fingering pattern mode can be switched and controlled as a result of secondary pore structures are presented.

[Phys. Rev. Fluids 5, 034301] Published Mon Mar 09, 2020

### Defect-mediated turbulence in bubbly Taylor-Couette flow

Author(s): Bruno Van Ruymbeke, Noureddine Latrache, Céline Gabillet, and Catherine Colin

The defect-mediated turbulence occurring in the bubbly Taylor-Couette ﬂow patterns is investigated experimentally and discussed in the framework of the Ginzburg-Landau theory using a new control parameter α, which is the ratio between the Reynolds number of the gas and the Reynolds number of the liquid.

[Phys. Rev. Fluids 5, 034302] Published Mon Mar 09, 2020

### Rotary atomization of Newtonian and viscoelastic liquids

Author(s): Bavand Keshavarz, Eric C. Houze, John R. Moore, Michael R. Koerner, and Gareth H. McKinley

We study rotary fragmentation dynamics and final droplet size distributions with a simple physical model. From animals drying their wet fur by rapidly shaking their body to automated rotary atomization in paint coating, centripetal acceleration is widely used to disintegrate liquid films into smaller fragments. However, little is known about the underlying physics and the liquid property effects on overall droplet size distributions. By performing a series of fragmentation tests with various viscous and viscoelastic liquids we are able to construct a simple and accurate physical model.

[Phys. Rev. Fluids 5, 033601] Published Thu Mar 05, 2020

### Effects of settling particles on the bubble formation in a gas-liquid-solid flow system studied through a coupled numerical method

Author(s): Na Zhao, Bo Wang, Qianqian Kang, and Jingtao Wang

The generation and rise of bubbles in gas-liquid-solid flow systems are investigated by employing a coupled discrete element model and volume of fluid method. The calculation results disclose that the existence of solid particles has an important effect on the formation of bubbles. The causes of these results are analyzed through a velocity vector diagram of the flows, and the factors affecting the detachment time of the first bubble are also investigated.

[Phys. Rev. Fluids 5, 033602] Published Thu Mar 05, 2020

### Synergy in the organization of near-wall and bulk turbulence structures in viscoelastic turbulent channel flow in the high drag reduction regime

Structures in polymer drag-reduced turbulence have been examined by using a direct numerical simulation of viscoelastic turbulent channel flow for a high drag reduction (HDR) rate of ∼60%. In drag-reduced flow, the length scale of turbulence structures significantly increases, especially in the streamwise direction. Moreover, the outer turbulence structures in the viscoelastic flow differ from those in Newtonian flow. Two-point correlations and conditionally averaged flow fields suggest that in HDR flow, near-wall structures for both upper and lower walls can be organized by an outer-region co-supporting cycle whose wall-normal extent is approximately equal to the height of the whole channel.

### Collision cross sections and nonequilibrium viscosity coefficients of N2 and O2 based on molecular dynamics

This study examines the collision dynamics of atom–atom, atom–molecule, and molecule–molecule interactions for O–O, N–N, O2–O, N2–N, O2–N, N2–O, O2–O2, N2–N2, and N2–O2 systems under thermal nonequilibrium conditions. Investigations are conducted from a molecular perspective using accurate O4, N4, and N2O2 ab initio potential energy surfaces and by performing Molecular Dynamics (MD) simulations. The scattering angle and collision cross sections for these systems are determined, forming the basis for better collision simulations. For molecular interactions, the effect of the vibrational energy on the collision cross section is shown to be significant, which in turn has a profound effect on nonequilibrium flows. In contrast, the effect of the rotational energy of the molecule is shown to have a negligible effect on the cross section. These MD-based cross sections provide a theoretically sound alternative to the existing collision models, which only consider the relative translational energy. The collision cross sections reported herein are used to calculate various transport properties, such as the viscosity coefficient, heat conductivity, and diffusion coefficients. The effect of internal energy on the collision cross sections reflects the dependence of these transport properties on the nonequilibrium degree. The Chapman–Enskog formulation is modified to calculate the transport properties as a function of the trans-rotational and vibrational temperatures, resulting in a two-temperature nonequilibrium model. The reported work is important for studying highly nonequilibrium flows, particularly hypersonic re-entry flows, using either particle methods or techniques based on the conservation laws.

### Free surface effects on spanwise turbulent structure in the far-field of submerged jets

The flow structure in the cross-sectional and spanwise planes of a turbulent round jet interacting with a free surface has been studied using planar particle image velocimetry. The submerged jet was positioned at an offset height of 5d below the free surface, where d is the nozzle diameter. Measurements were conducted in both streamwise-surface-normal (x-y) and nine streamwise-spanwise (x-z) planes (−4 ≤ y/d ≤ 4) located in the far-field (x/d = 42–62) at an exit Reynolds number of 28 000. To highlight the effects of the free surface, measurements were also performed to evaluate the characteristics of a reference free jet at similar initial conditions. For each jet, the spanwise planes were used to reconstruct the three-dimensional (3D) averaged velocity field to reveal the salient flow features in the cross section of the jet. The reconstruction shows the presence of the well-known surface current, which is usually prominent in the far-field of surface jets. The spanwise development of the surface current is found to reduce the streamwise and spanwise Reynolds normal stresses in the upper shear layer of the surface jet, but the Reynolds shear stress and its associated dominant quadrant motions in the spanwise plane are enhanced near the free surface. As the free surface is approached, the spanwise spread rate increases, but the local vorticity thickness decreases due to the enhancement of the mean shear in the spanwise direction. Two-point spatial correlations are used to show that the large-scale structures near the free surface undergo oblique stretching in the spanwise plane to augment the wider spanwise growth of the surface current. The spatial distributions of the energetic modes based on proper orthogonal decomposition also reveal interesting features near the free surface that are consistent with the inclination of the turbulent structures relative to the flow direction.

### Thermohaline convective instability in an inclined porous layer with permeable boundaries

This study aims at investigating the onset of thermohaline convective instability in an inclined porous layer of finite width confined between two permeable boundaries. The instability in the flow is driven by the combined effect of temperature and solute concentration gradients acting vertically across the layer, and it depends on the angle of inclination at which that layer is inclined to the horizontal. This work complements previous studies on the double-diffusive convective instability by extensively discussing the effect of the solute concentration gradient for the case when the thermal and solutal buoyancy forces have comparable magnitudes and they act in the same and opposite directions. The investigation is illustrated by the results associated with the cases when the diffusivity ratio is thermally dominant, when the diffusivity ratio is thermally suppressed, and when the two components diffuse with the same intensity. A wide spectrum of the neutral stability curves are presented at different inclinations, which depict the instability in the basic state prevailing in the form of stationary and oscillatory modes. The neutral stability curves are seen to exhibit some exceptional behavior in the case when the thermal buoyancy and the solutal buoyancy act in the opposite directions. It is observed that the instability is always initiated by the non-traveling modes, except in the case when the thermal diffusivity is reasonably higher than the solutal diffusivity and when the two buoyant forces are acting in the opposite directions. The ratio of the two buoyant forces has an exceptionally non-monotonic impact on the instability, if considered in the vertical porous layer.