# Latest papers in fluid mechanics

### Fragmentation of a liquid metal droplet falling in a water pool

This paper focuses on the experimental investigation of breakup regimes of a molten fusible metallic droplet in water, at intermediate Weber numbers with emphasis on mass and energy balance. The experiment consists in impacting perpendicularly a molten drop onto the interface of a deep water pool, at a controlled temperature. Using a drop-on-demand device and high-speed shadowgraph, a single drop can be visualized during its evolution. There is a noticeable velocity jump when the droplet crosses the interface that can be modeled using an unsteady Bernoulli equation. As observed for liquid–gas systems, the drop experiences different regimes of fragmentation, depending on its Weber number: oscillations, bag oscillations, prolate drop stretching breakup, and then bowl-shaped bag breakup. However, opposite to the gas–liquid case, a Rayleigh–Taylor instability mechanism seems to be absent and this seems related to the bowl-shaped bag breakup mechanism when compared to the dome-shaped gas–liquid case. Statistics of the daughter droplets are then given, using either image analysis for large droplets size distribution or sieving and weighting of the solidified fragments for measurement of the Sauter mean diameter and surface energy creation. Finally, a simple relation between the Sauter mean diameter and the Weber number is presented based on the energy and mass balances. When comparing with previous higher Weber number results, a viscous transition corresponding to a strong increase in the energy loss is also shown to occur for the higher Weber number.

### Theory of freezing point depression in charged porous media

Author(s): Tingtao Zhou, Mohammad Mirzadeh, Roland J.-M. Pellenq, Dimitrios Fraggedakis, and Martin Z. Bazant

Freezing in charged porous media can induce significant pressure and cause damage to tissues and functional materials. We formulate a thermodynamically consistent theory to model freezing phenomena inside charged heterogeneous porous space. Two regimes are distinguished: free ions in open pore space...

[Phys. Rev. E 104, 045102] Published Wed Oct 13, 2021

### Wave damping by flexible marsh plants influenced by current

Author(s): Xiaoxia Zhang and Heidi Nepf

We develop a wave damping model based on a prediction of current- and wave-induced force on individual plants. The model captures the influence of reconfiguration on wave forces, the impact of current on wave group velocity, and the modification of in-canopy time-mean and wave orbital velocity associated with canopy drag, all of which affect the wave dissipation by vegetation. The model explains why weak current reduces wave dissipation while strong current increases wave dissipation, as observed both in the present and previous studies. Further, we explore the impact of plant flexibility and leaf morphology on wave dissipation over a wide range of current to wave velocity ratio.

[Phys. Rev. Fluids 6, 100502] Published Wed Oct 13, 2021

### Impact of viscosity ratio on falling two-layer viscous film flow inside a tube

Author(s): H. Reed Ogrosky

A two-layer falling film consisting of two viscous fluids with identical density but different viscosity lining the interior of a vertical tube is studied using a long-wave asymptotic model. The impact of the viscosity ratio on the film linear stability and nonlinear dynamics are explored. It is shown that a less viscous outer layer can decrease the total film thickness required for plugs to form; the significance of this study for applications, including human airways, is briefly discussed.

[Phys. Rev. Fluids 6, 104005] Published Wed Oct 13, 2021

### Irreversibility and rate dependence in sheared adhesive suspensions

Author(s): Zhouyang Ge, Raffaella Martone, Luca Brandt, and Mario Minale

Experiments and simulations of a non-Brownian suspension of particles demonstrate that weak van der Waals (adhesive) interactions induce rate dependence of the rheological response in oscillatory shear flow, with enhanced particle diffusivities and cluster formations below a critical shear rate, even though the steady shear behavior remains rate-independent. Phase diagrams showing the influence of volume fraction, strain amplitude, and oscillation frequency, for a given Hamaker constant, highlight the connection between irreversibility and suspension rheology.

[Phys. Rev. Fluids 6, L101301] Published Wed Oct 13, 2021

### Experimental analysis of temperature effects in supercritical-assisted atomization

Supercritical CO2 is proved as an excellent choice in supercritical-assisted atomization of nanoparticle suspensions for fabrication of micro/nano-powders. As the rheological properties of the supercritical fluids are strongly dependent on the temperature, the breakup mechanism of the CO2-liquid mixture upon injection is significantly affected by crossing the critical temperature of the binary mixture. In this study, we investigate the breakup of CO2-water mixture (CO2-A) at subcritical, critical, and supercritical states and compare it with the cases where N2 is utilized as the assisting fluid (N2-A) at the same injection conditions. High-speed imaging and laser diffraction systems are utilized to analyze the primary and secondary atomization of the injected CO2-water mixture (over 20 to 40 °C injection temperature range). In general, CO2-A showed smaller and more homogenous droplets compared to N2-A. Therefore, the use of CO2 as the atomization gas is superior to N2. The underlying mechanism in primary breakup of CO2-A involves the emergence, expansion, and burst of CO2 bubbles and formation of ligaments that break up into droplets. The core of the jet in CO2-A system expands up to 50% due to emergence of gas bubbles, while the expansion ratio remains unchanged in the N2-A jet. The finest and most homogenous droplet sizes are achieved by operating near the critical point at 31.5 °C and 7.5 MPa. High solubility of CO2 in water and low interfacial tension of the CO2-water mixture are the main contributors.

### Effect of co-flow on fluid dynamics of a cough jet with implications in spread of COVID-19

We discuss the temporal evolution of a cough jet of an infected subject in the context of the spread of COVID-19. Computations were carried out using large eddy simulation, and, in particular, the effect of the co-flow (5% and 10% of maximum cough velocity) on the evolution of the jet was quantified. The Reynolds number (Re) of the cough jet, based on the mouth opening diameter (D) and the average cough velocity, is 13 002. The time-varying inlet velocity profile of the cough jet is represented as a combination of gamma-probability-distribution functions. Simulations reveal the detailed structure of cough jet with and without a co-flow for the first time, to the best of our knowledge. The cough jet temporal evolution is similar to that of a continuous free-jet and follows the same routes of instability, as documented for a free-jet. The convection velocity of the cough jet decays with time and distance, following a power-law variation. The cough jet is observed to travel a distance of approximately 1.1 m in half a second. However, in the presence of 10% co-flow, the cough jet travels faster and covers the similar distance in just 0.33 s. Therefore, in the presence of a co-flow, the probability of transmission of COVID-19 by airborne droplets and droplet nuclei increases, since they can travel a larger distance. The cough jet without the co-flow corresponds to a larger volume content compared to that with the co-flow and spreads more within the same range of distance. These simulations are significant as they help to reveal the intricate structure of the cough jet and show that the presence of a co-flow can significantly augment the risk of infection of COVID-19.

### Simultaneous impact of twin drops on a semi-infinite liquid target

We take the enduring topic of drop impact on a deep pool of similar liquid further by allowing twin drops to impact simultaneously. Impacts are sufficiently proximal that impact crowns and craters interact, distorting and merging craters, and creating previously undocumented supersurface fluid interactions. The unique features of twin impacts occur when crowns collide to create a central veil that bifurcates the two craters and the expulsion of jet-like features atop colliding crowns. The emergence of a plethora of splash features is dependent on the Froude number ([math]) and drop separation distance. We analyze proximal crater evolution using theory developed for singular drops and develop scaling relations to predict crown and jet height. Crater and jet energies are compared for various impact velocities and drop separation distances. We find that craters close enough to merge produce thicker, but not higher, rebound jets.

### Friction factor for steady periodically developed flow in micro- and mini-channels with arrays of offset strip fins

In this work, the friction factor for steady periodically developed flow through micro- and mini-channels with periodic arrays of offset strip fins is analyzed. The friction factor is studied numerically on a unit cell of the array for Reynolds numbers ranging from 1 to 600, and fin height-to-length ratios below 1. It is shown that the friction factor correlations from the literature, which primarily focus on larger conventional offset strip fin geometries in the transitional flow regime, do not predict the correct trends for laminar flow in micro- and mini-channels. Therefore, a new friction factor correlation for micro- and mini-channels with offset strip fin arrays is constructed from an extensive set of numerical simulations through a least squares fitting procedure. The suitability of this new correlation is further supported by means of the Bayesian approach for parameter estimation and model validation. The correlation predicts an inversely linear relationship between the friction factor and the Reynolds number, in accordance with our observation that a strong inertia regime prevails over nearly the entire range of investigated Reynolds numbers. Yet, through a more detailed analysis, also the presence of a weak inertia regime and a transitional regime is identified, and the transitions from the strong inertia regime are quantified by means of two critical Reynolds numbers. Finally, the new correlation also incorporates the asymptotic trends that are observed for each geometrical parameter of the offset strip fin array, and whose origins are discussed from a physical perspective.

### A fast and efficient tool to study the rheology of dense suspensions

A cutting-edge software that adopts an optimized searching algorithm is presented to tackle the Newton–Euler equations governing the dynamics of dense suspensions in Newtonian fluids. In particular, we propose an implementation of a fixed-radius near neighbors search based on an efficient counting sort algorithm with an improved symmetric search. The adopted search method drastically reduces the computational cost and allows an efficient parallelization even on a single node through the multi-threading paradigm. Emphasis is also given to the memory efficiency of the code since the history of the contacts among particles has to be traced to model the frictional contributions, when dealing with dense suspensions of rheological interest that consider non-smooth interacting particles. An effective procedure based on an estimate of the maximum number of the smallest particles surrounding the largest one (given the radii distribution) and a sort applied only to the surrounding particles only is implemented, allowing us to effectively tackle the rheology of non-monodispersed particles with a high size-ratio in large domains. Finally, we present validations and verification of the numerical procedure, by comparing with previous simulations and experiments, and present new software capabilities.

### Pressure reconstruction of a planar turbulent flow field within a multiply connected domain with arbitrary boundary shapes

This paper reports for the first time the implementation procedures and validation results for pressure reconstruction of a planar turbulent flow field within a multiply connected domain that has arbitrary inner and outer boundary shapes. The pressure reconstruction algorithm used in this study is the rotating parallel-ray omni-directional integration algorithm that offers high-level of accuracy in the reconstructed pressure. While preserving the nature and advantage of the parallel ray omni-directional pressure reconstruction at places with flow data, the new implementation of the algorithm is capable of processing an arbitrary number of inner void areas with arbitrary boundary shapes. Validation of the multiply connected domain pressure reconstruction code is conducted using the Johns Hopkins DNS (Direct Numerical Simulation) isotropic turbulence databases [J. Graham et al., J. Turbul. 17(2), 181 (2016)], with 1000 statistically independent pressure gradient field realizations embedded with random noise used to gauge the code performance. For further validation, the code is also applied for pressure reconstruction from the DNS data [E. Johnsen and T. Colonius, J. Fluid Mech., 629, 231 (2009)] about a shock-induced non-spherical bubble collapse in water. It is demonstrated that the parallel-ray omni-directional integration algorithm outperforms the Poisson equation approach in terms of the accuracy for the pressure reconstruction from error embedded pressure gradients in both simply connected and multiply connected domains.

### Evolution mechanism of a prototype pump turbine after pump power-off

This study aimed to analyze the time–frequency characteristics of pressure fluctuations and reveal their underlying flow mechanisms during the unavoidable guide vane closing process after a pump power-off in a pumped-storage hydropower plant. In this study, the weak compressibility model, one- and three-dimensional (1D–3D) coupling simulation method, and dynamic mesh technology were adopted simultaneously to accurately simulate the transient flow in a prototype pump turbine during the guide vane closure process after the pump power-off. According to the analysis results of the short-time Fourier transformation for the pressure fluctuations, apart from the familiar runner blade passing frequency and its harmonics, this study found a new component that is five times the runner rotation frequency as well as components that are lower than 4.5 times the runner rotation frequency and correspond to severe fluctuations in the pressure. Internal flow analysis suggests that the former is induced by unstable vortices near the trailing edges of the runner blades, whereas the latter ones are induced by local backflow vortices near the runner inlet. Additionally, these severe pressure fluctuation components were significantly large closer to the maximum reverse discharge of the pump brake mode. This finding indicates that these severe unsteady pressure fluctuation components can be suppressed by optimizing the reduction in the maximum reverse discharge in the pump brake mode.

### Nonlinear wave propagation in dense vapor of Bethe–Zel'dovich–Thompson fluids subjected to temperature gradients

Flows of fluids made of complex organic molecules exhibit unconventional fluid dynamic behavior in the vapor phase if their thermodynamic state is close to that of the vapor–liquid critical point. If the molecule is sufficiently complex, this thermodynamic domain is characterized by negative values of the fundamental derivative of gasdynamics Γ, the fluid is called Bethe–Zel'dovich–Thompson (BZT) fluid, and atypical phenomena, such as rarefaction shockwaves, are theoretically admissible. The nature of the steepening of nonlinear waves in dense vapor flows of organic fluids evolving in this thermodynamic region can be significantly affected by the presence of temperature gradients in the flow. This study investigates the evolution of finite-amplitude acoustic waves in these conditions. The steepening of the wavefront is analyzed using the wavefront expansion technique, and the deformation of the wavefront is simulated numerically by solving the Westervelt equation. The results of simulations of wave propagation in dense vapors indicate that, though Γ governs the nature of steepening waves, local gradients in sound speed and density can alter the rate of steepening and can enhance or delay shock formation in the medium, a result relevant also to the envisaged experiments aimed at proving the existence of nonclassical gasdynamics phenomena in BZT vapors.

### On the relationships between different vortex identification methods based on local trace criterion

Vortical flow is generally considered to be a flow with a rotational trend, but vortex regions vary depending on the vortex identification methods by which they are extracted. In this paper, theoretical relationships between commonly used [math] series vortex criteria, eigenvalue-based vortex criteria, and the Rortex method are analytically derived and built based on the local trace (LT) criterion ([math]). The projections of vortex regions extracted by different vortex criteria onto the LT-plane constructed by [math] are presented to graphically discuss their physical meanings and interrelations. The [math]-based method reflects the local swirling patterns of flow and provides new interpretations of various vortex criteria in terms of local flow patterns. The simple vortex models, including Rankin vortex and Burgers' vortex, forced isotropic turbulence flow, and a compressor corner separation flow case with a practical Mach number, are tested and analyzed. The potential of the [math]-based method is shown both by analyzing vortex dynamic properties and by distinguishing the different swirling patterns of complex vortices in tangle. This contributes to the exploration of flow mechanisms and furthers investigations into vortex dynamics.

### An investigation of droplet mobility and the ultra-mild internal mechanical microenvironment in cylindrical microchannels

The mechanical microenvironment inside droplets acts directly on encapsulated cells and reactive substances. We used microparticle image velocimetry to explore the flow characteristics inside droplets moving in cylindrical microchannels. Two kinds of flow behaviors were found inside droplets with increasing capillary number Ca. When Ca < 5.73 × 10−3, the oil phase cannot bypass droplets forward or backward because there is no gutter flow around the droplets, the droplets move in cylindrical microchannels in the form of rigid bodies, and the difference in velocity and gradients inside the droplets is very low. The fluids inside the droplets remain almost stationary with respect to the surrounding oil phase, and the droplets are driven only by compression. When Ca > 1.43 × 10−2, the droplets move faster than the oil phase, which creates a pair of counter-rotating eddies in the front of droplets, and the droplets are driven by both compression and shearing. The critical Ca range for the two flow behaviors is from 5.73 × 10−3 to 1.43 × 10−2 in this study. Comparisons are made between droplet behaviors in rectangular and cylindrical channels; in the latter, the shear and strain rate inside droplets are reduced by factors of 5.02 and 6.86, respectively, and acceleration and viscous dissipation are reduced by even greater factors of 42.53 and 41.56, respectively.

### Computational fluid dynamics analysis of droplet generation in microfluidic multi-cell coupled systems

Multi-cell coupled droplet generator systems have been used for high-throughput production of microdroplets. However, the coupling effects of intercellular geometry and flow parameters can produce complex hydrodynamic phenomena that affect droplet generation processes and properties. In this study, a computational model of droplet generation in a multi-cell parallel geometry was developed based on the phase field method, and the droplet formation process and hydrodynamic properties in a multi-cell coupled droplet generator were investigated. The coupling effects of flow parameters (e.g., capillary number, continuous and dispersed phase flow rates and flow ratios) on the droplet generation process were systematically analyzed to investigate droplet characteristics and mechanisms in the multi-cell coupled droplet generator system. The causes of synchronous and asynchronous droplet generation patterns in multi-cell coupled systems are also analyzed over a range of capillary numbers. It is found that the droplet generation frequency increases with increasing continuous-phase flow velocity while the size decreases; the droplet size is smaller and the frequency is larger in multi-cell coupled systems than in stand-alone systems at the same flow velocity ratio; the difference between synchronous and asynchronous droplet generation patterns is closely related to the geometric coupling of continuous-phase flow channels and the uneven flow field distribution. This work will provide useful insights into droplet generation in multi-cell coupled systems and provide useful guidance for the structural design of multi-cell coupled systems.

### An experimental study on aquatic collapses of bidisperse granular deposits

A laboratory experiment is conducted to study the mobility and the segregation of aquatic bidisperse granular columns. The effects of the ambient fluid, the particle composition, and the initial geometry on the dynamics of bidisperse granular columns are investigated. It is identified that the ambient fluid plays diverse roles in the phenomenon but is to retard the collapsing process in an overall sense. The instantaneous frontal positions of the granular mass in a bidisperse collapsing case could be shorter or longer than in a monodisperse case under the aquatic condition, but its final run-out is always longer. Compared to dry cases, particle segregations in aquatic cases are found to be more pronounced with columns composed of fine and coarse particles than with columns composed of fine and medium-sized particles. In general, the segregation phenomenon becomes less obvious at relatively large values of the finer-particle fraction and in cases with relatively small particle size difference. It is demonstrated that particle segregation contributes to an increased mobility of the bidisperse granular mass, probably due to the fact that smaller particles fall downward through the gaps between larger particles as the mixture deforms continuously, leading to an increased possibility for large particles to be separated by isolated small particles or an increased possibility for the rolling friction to take place of the sliding friction between large particles.

### Tracking the vortex motion by using Brownian fluid particles

In this paper, we propose a simple yet powerful vortex method to numerically approximate the dynamics of an incompressible flow. The idea is to sample the distribution of the initial vortices of the fluid flow in question and then follow vortex dynamics along Taylor's Brownian fluid particles. The weak convergences of this approximation scheme are obtained for both two-dimensional (2D) and three-dimensional (3D) fluid flows, though only for small time in 3D case. Based on our method, the simulation results are quite attracting.

### Movement and acoustic radiation of a rising bubble from combustion of pyrotechnic mixtures using experiment and image processing method

Bubble volume and bubble geometry are key parameters that affect the movement and acoustic radiation performance of bubble columns. This paper proposes an image processing method to study the movement and acoustic radiation characteristics of the rising bubbles originating from the combustion of a pyrotechnic composition based on high-speed photography. Results showed that during the rise of bubbles, their shape gradually changed from spherical to irregular, and their rising trajectory presented a curvilinear form. After the rising velocities of the bubbles in the z and x directions were compared, the results revealed that the rising velocity of the bubbles was unstable. The velocity of the rising bubbles in the direction of the z axis was much higher than that of the x axis. Meanwhile, the acceleration of bubble volume decreased first and then increased. This process was repeated; however, the amplitude of increase or decrease was inconsistent, which led to the generation of a certain amount of acoustic radiation effect, and it had a similar trend of change with the acceleration of bubble volume.

### Optical flow method for neutron radiography flow diagnostics

The principle of an optical flow method is formulated for neutron radiography (NR) flow diagnostics to determine high-resolution velocity fields of two-phase flows. This method is based on solving an optical flow equation derived from the continuous equation for NR image analysis as an inverse problem using a variational method. The mathematical definition and physical meaning of the optical flow in NR images of a two-phase flow are clarified. As an example, the optical flow method is used to extract complex velocity fields from a time sequence of dynamic NR images acquired in an air–water two-phase flow in a flat bubbler.