# Latest papers in fluid mechanics

### Effect of honeycomb porous plate on critical heat flux in saturated pool boiling of highly concentrated artificial seawater

To enhance the reliability of in-vessel retention techniques during a nuclear power plant hazard, the viability of seawater as a coolant to flood the reactor pressure vessel was investigated. Pool boiling of distilled water, 3.5 wt. % artificial seawater, and 7.0 wt. % highly concentrated artificial seawater was performed on a 30-mm-diameter Cu bare surface (BS) with a honeycomb porous plate (HPP). The results revealed an increase in the critical heat flux (CHF) with both artificial seawater solutions, on the BS, when compared with distilled water. The improvement of surface wettability by sea salt deposits was assumed as the main reason for the improvement. A significant enhancement in the CHF was achieved with distilled water and 3.5 wt. % artificial seawater owing to the capillary properties of HPP and the separation of the liquid and vapor phases near the heated surface. When the HPP was employed with 7.0 wt. % highly concentrated artificial seawater, the performance did not improve. Although experiments with a honeycomb solid plate suggested that a high concentration of sea salt can clog the micropores in the HPP walls, resulting in loss of its capillary properties, highly concentrated artificial seawater still presented a better performance than distilled water in all cases investigated.

### Compressible flow in a Noble–Abel stiffened gas fluid

While the compressible flow theory has relied on the perfect gas model as its workhorse for the past century, compressible dynamics in dense gases, solids, and liquids have relied on many complex equations of state, yielding limited insight into the hydrodynamic aspect of the problems solved. Recently, Le Métayer and Saurel studied a simple yet promising equation of state owing to its ability to model both the thermal and compressibility aspects of the medium. It is a hybrid of the Noble–Abel equation of state and the stiffened gas model, labeled the Noble–Able Stiffened Gas (NASG) equation of state. In the present work, we derive the closed form analytical framework for modeling compressible flow in a medium approximated by the NASG equations of state. We derive the expressions for the isentrope, sound speed, isentropic exponent, Riemann variables in the characteristic description, and jump conditions for shocks, deflagrations, and detonations. We also illustrate the usefulness by addressing the Riemann problem. The closed form solutions generalize in a transparent way the well-established models for a perfect gas, highlighting the role of the medium’s compressibility.

### Finite amplitude torsional oscillations of shape-morphing plates immersed in viscous fluids

In this paper, we study torsional oscillations of a cross section of a thin plate submerged in a quiescent, Newtonian, incompressible, and viscous fluid. The plate is subjected to a prescribed shape-morphing deformation in phase with the rigid oscillation. The problem is completely described by three nondimensional parameters indicating oscillation frequency and amplitude and intensity of the shape-morphing deformation. We conduct a parametric study to investigate the possibility of controlling hydrodynamic moments and power dissipation through an active time-varying shape-morphing strategy. The problem is studied in both the linear and nonlinear flow regimes, by employing the boundary element method and direct numerical simulations via computational fluid dynamics methods, respectively. Investigation of flow physics demonstrates that, similarly to what is observed for the case of flexural oscillations, the shape-morphing strategy is effective in modulating vortex shedding in torsional oscillations. The results show that hydrodynamic power dissipation can be minimized and hydrodynamic moments can be controlled through an optimal imposed shape-morphing deformation. Findings from this study are directly applicable to torsional oscillation-based underwater energy harvesting or sensing and actuation systems, where control of hydrodynamic moments and reduction of hydrodynamic power losses are necessary for optimal device operation.

### Effect of viscosity ratio on the dynamic response of droplet deformation under a steady electric field

The effect of the fluid viscosity ratio on the transient deformation of a droplet is investigated. A numerical model is developed by employing the phase field method to capture the interface. The model is validated in both steady and transient cases with literature data with good agreement. In the creeping flow regime, the droplet always undergoes monotonic deformation. When the viscosity of the suspending fluid dominates, the transient process of the droplet deformation is nearly independent of the viscosity ratio. When the viscosities of the droplet and suspending fluid are comparable, the damping effect of the droplet viscosity on the deformation is magnified and the time to reach the steady-state deformation increases with viscosity. When the effect of suspending fluid inertia prevails, the droplet will deform to the steady state either in a monotonic way or in an oscillating way depending on the viscosity ratio. A quasi-steady mode, which can be considered as an intermediate mode between the oscillating and the steady mode, is identified for the first time. When the droplet is in the quasi-steady mode, the increase in the electric capillary number can turn it into the steady mode. The flow field evolution is analyzed and it shows that the vortices inside the droplet play an important role in the transient deformation. The deformation process can be determined by the competition between the inner and outer vortices. It is found that the minimum deformation time can be obtained for the quasi-steady mode when the viscosity of the suspending fluid is low.

### Influence of glow discharge on evolution of disturbance in a hypersonic boundary layer: The effect of first mode

The evolution of the first- and second-mode instabilities in a hypersonic flat plate boundary layer is investigated. Experiments are conducted in a Mach 6.5 quiet wind tunnel using particle image velocimetry, Rayleigh-scattering flow visualization, and schlieren methods. Glow discharge is introduced as an artificial disturbance. The results show that an artificially introduced disturbance in the first-mode frequency range can excite a specific second-mode wave that is one of the high-order harmonics of the added disturbance. For the first time, we find a clear harmonic relationship between the first- and second-mode waves, as well as the phase lock phenomenon between them.

### Delay of subsonic choking in slip regime by structured roughness in microchannel

Roughness is an intrinsic property of a surface. Its presence is recognized at the micro-scale due to the high surface area to volume ratio. In the present experimental work, three-dimensional microchannels with structured roughness in the form of cuboidal protrusions called micro-ridges are fabricated. Ridge fraction (δ) is the ratio of the length of the ridge (s) to the distance between the ridges (L). δ is varied as 0.75, 0.50, 0.25, and 0 to check the occurrence of the choking phenomenon and its impact on the frictional resistance in gaseous slip flow. To this end, mass flow controllers, pressure sensors, and thermocouples are employed to explore the dependence of Poiseuille number (fRe) on Mach number (Ma) in the microchannel. It is demonstrated that the smooth microchannel (δ = 0) and the ridge with the shortest length (δ = 0.25) gets choked subsonically, but the longer ridges (δ = 0.50, 0.75) do not choke under the investigated conditions. Interestingly, fRe (δ = 0.50) > fRe (δ = 0.25) > fRe (δ = 0.75) ≈ fRe (δ = 0). Since choking limits the maximum amount of mass flow rate through a microchannel, its occurrence could be counter-productive or could even be beneficially employed, depending on the specific application.

### Automatic triangular and triangular-prism mesh generation for overland and subsurface water flow simulations

In this paper, an automatic mesh generator is developed to simulate density-dependent water flow and transport problems in watershed systems. The two-dimensional (2D) triangular mesh is generated by global Delaunay triangulation, and the three-dimensional (3D) triangular-prism mesh is generated by vertical stretch. The implementation procedures of mesh generation are adjusted according to the interaction options of one-dimensional (1D) river, 2D overland, and 3D subsurface flows. An improved boundary point generation algorithm is proposed to maintain appropriate correspondence of points and edges according to the discrete patterns of river reaches and dead ends. Overlapped nodes are generated on zero-width river reaches and zero-width junctions without storage to construct the numerical models for 2D overland simulations. An additional triangular mesh generation method is proposed to create additional triangles for filling the empty water zones of finite-width river reaches, junctions with storage, finite-width ponds, lakes, and dead ends. The boundary loops bounding each water area are identified correctly, and the additional grids are created compatibly, aiming at the finite-depth and zero-depth patterns of storage zones. The computation equations of relevant parameters used for 3D stretch from triangles to triangular-prisms are built, and the 1D/2D/3D correspondence on river reaches, junctions, ponds, lakes, dead ends, and control structures is established. Finally, practical examples for discretizing real-world water areas are provided to demonstrate the robustness and effectiveness of our developed mesh generator by using the skewness as the mesh quality metric.

### Instabilities, bifurcations, and transition to chaos in electrophoresis of charge-selective microparticle

Electro-hydrodynamic instabilities near a cation-exchange microgranule in an electrolyte solution under an external electric field are studied numerically. Despite the smallness of the particle and practically zero Reynolds numbers, in the vicinity of the particle, several sophisticated flow regimes can be realized, including chaotic ones. The obtained results are analyzed from the viewpoint of hydrodynamic stability and bifurcation theory. It is shown that a steady-state uniform solution is a non-unique one; an extra solution with a characteristic microvortex, caused by non-linear coupling of the hydrodynamics and electrostatics, in the region of incoming ions is found. Implementation of one of these solutions is subject to the initial conditions. For sufficiently strong fields, the steady-state solutions lose their stability via the Hopf bifurcation and limit cycles are born: a system of waves grows and propagates from the left pole, θ = 180°, toward the angle θ = θ0 ≈ 60°. Further bifurcations for these solutions are different. With the increase in the amplitude of the external field, the first cycle undergoes multiple period doubling bifurcation, which leads to the chaotic behavior. The second cycle transforms into a homoclinic orbit with the eventual chaotic mode via Shilnikov’s bifurcation. Santiago’s instability [Chen et al., “Convective and absolute electrokinetic instability with conductivity gradients,” J. Fluid Mech. 524, 263 (2005)], the third kind of instability, was then highlighted: an electroneutral extended jet of high salt concentration is formed at the right pole (region of outgoing ions, θ = 0°). For a large enough electric field, this jet becomes unstable; the perturbations are regular for a small supercriticality, and they acquire a chaotic character for a large supercriticality. The loss of stability of the concentration jet significantly affects the hydrodynamics in this area. In particular, the Dukhin–Mishchuk vortex, anchored to the microgranule at θ ≈ 60°, under the influence of the jet oscillations loses its stationarity and separates from the microgranule, forming a chain of vortices moving off the granule. This phenomenon strongly reminds the Kármán vortices behind a sphere but has another physical mechanism to implement. Besides the fundamental importance of the results, the instabilities found in the present work can be a key factor limiting the robust performance of complex electrokinetic bio-analytical systems. On the other hand, these instabilities can be exploited for rapid mixing and flow control of nanoscale and microscale devices.

### Flow-induced segregation and dynamics of red blood cells in sickle cell disease

Author(s): Xiao Zhang, Christina Caruso, Wilbur A. Lam, and Michael D. Graham

We present cell-scale simulations for an idealized model of blood flow in sickle cell disease (SCD): a confined binary suspension of flexible biconcave discoids and stiff curved prolate spheroids representing healthy and sickle RBCs, respectively. Like white blood cells and platelets, sickle cells are found to be driven from the bulk flow toward the walls (top image), a phenomenon called margination. Marginated sickle cells induce large transient peaks in wall shear stress (bottom image). These large, rapid stress fluctuations may lead to the blood vessel wall damage observed in SCD.

[Phys. Rev. Fluids 5, 053101] Published Mon May 04, 2020

### Method of separation of vibrational motions for applications involving wetting, superhydrophobicity, and microparticle extraction

Author(s): Md Syam Hasan and Michael Nosonovsky

Nonlinear vibrations lead to such effects as the stabilization of an inverted pendulum on a vibrating foundation and size separation of particles of a granular material. When applied to fluid mechanics, unusual effects including jamming holes in a vibrating tank with liquid, vibrational propulsion, and multiphase flow separation are found.

[Phys. Rev. Fluids 5, 054201] Published Mon May 04, 2020

### Compaction front and pore fluid pressurization in horizontally shaken drained granular layers

Author(s): Shahar Ben-Zeev, Einat Aharonov, Renaud Toussaint, Stanislav Parez, and Liran Goren

We numerically simulate a gently shaken fluid-saturated granular layer. Above a critical imposed acceleration an upward moving compaction front forms. The front divides the layer in two: above the front, a compacting fluidlike sublayer with a lithostatic pore pressure gradient (PPG), and under it, a compacted solidlike sublayer with a hydrostatic PPG. This front, and the controlling parameters of the coupled flow (permeability and fluid viscosity, rather than granular parameters), are theoretically predicted. These results can be inputs for saturated soil response to earthquake excitation.

[Phys. Rev. Fluids 5, 054301] Published Mon May 04, 2020

### Non-Kolmogorov scaling for two-particle relative velocity in two-dimensional inverse energy-cascade turbulence

Author(s): Tatsuro Kishi, Takeshi Matsumoto, and Sadayoshi Toh

A conditional sampling method to remove initial separation dependence on the Richardson–Obukhov t3 law of relative separation in two-dimensional inverse energy-cascade turbulence is proposed. The method enables the study of temporal scaling of the Lagrangian velocity increment in a robust way. It is shown that the scaling of the second-order moment of the velocity increment differs from t1, which is the prediction based on Kolmogorov’s phenomenology, and that time evolution of the probability distribution function of the increment is self-similar.

[Phys. Rev. Fluids 5, 054601] Published Mon May 04, 2020

### Pressure distribution and eddies at the periphery of a drop about to shed due to water shear-flow

The physics behind the formation of eddies and their effect on an oil drop about to shed due to water shear flow are investigated. The velocities at the frontal periphery of the drop are measured after visualizing the flow and compared with those obtained numerically. A good comparison is observed. It is found that for oleophilic surfaces, two eddies are formed at the back of the drop, while no eddies are formed at the front side. One eddy at the front and three eddies at the rear are observed for drops shedding from oleophobic surfaces. The observations are the same for both experimental and numerical analyses. Eddies, velocity variation, and peripheral pressure distribution are found to be closely related. The pressure distribution along the periphery is studied. The pressure coefficient and the drag coefficient are observed to be higher for drops shedding from the oleophobic surface than from the oleophilic surface for a given volume. Therefore, less critical velocity is necessary for the drop to shed. The velocity variation along the frontal area is responsible for the drag applied. The drag coefficient is observed to increase with the volume. The formation of various eddies and the distribution of pressure along the drop periphery are responsible for the increase in drag coefficient. The pressure drag is observed to be dominant over the viscous drag for all volumes tested. A novel topology is proposed to explain the observations.

### Analysis of Rayleigh–Taylor instability at high Atwood numbers using fully implicit, non-dissipative, energy-conserving large eddy simulation algorithm

Large eddy simulation of three-dimensional, multi-mode Rayleigh–Taylor instability at high Atwood numbers is performed using a recently developed, kinetic energy-conserving, non-dissipative, fully implicit, finite volume algorithm. The algorithm was especially designed for simulating low-Mach number, variable density/viscosity, transitional, and turbulent flows. No interface capturing mechanism is required. Buoyancy and heat transfer effects can be handled without relying on the Boussinesq assumption. Because of this feature, unlike the pure incompressible ones, it does not suffer from the loss of physical accuracy at high Atwood and Rayleigh numbers. In this study, the mixing phenomenon in Rayleigh–Taylor instability and the effects of high Atwood numbers on the development of the flow are investigated using various diagnostics such as local mole fractions, bubble and spike penetration lengths and growth rates, mixing efficiencies, Taylor micro-scales, and corresponding Reynolds numbers and energy ratios. Additionally, some important terms of the Reynolds stress transport equation are also introduced, such as Reynolds stresses (and their anisotropies) and turbulent production. Results show that Rayleigh–Taylor instability at high Atwood numbers is characterized by rapid development of instability due to the increasing growth rates and higher velocities of spike fronts, larger asymmetry in the mixing region, denser interactions in the non-linear phase, and changes in bubble and spike morphologies. It is also found that interactions of spike-fronts with their surroundings are the primary mechanisms of turbulent production and transition to turbulence. However, late time mean flow measures such as energy ratio and mixedness are not significantly affected. A scaling relation between the spike to bubble penetration ratio and the heavy to light density ratio is also provided.

### Simultaneous measurement of rheological properties in a microfluidic rheometer

Microfluidic rheometry is considered to be a potential alternative to conventional rheometry for the rheological characterization of viscoelastic solutions having relatively low viscoelastic properties. None of the microfluidic platforms introduced so far, however, can be used for the measurements of multiple rheological properties in the same device. In this work, I present the first microfluidic platform, named the “μ-rheometer,” which allows for the simultaneous measurement of zero-shear viscosity η0 and longest shear relaxation time λ. This is achieved by transforming the original “flow rate controlled” platform presented by Del Giudice et al., “Rheometry-on-a-chip: Measuring the relaxation time of a viscoelastic liquid through particle migration in microchannel flows,” Lab Chip 15, 783–792 (2015) into a “pressure drop controlled” microfluidic device, by replacing a syringe pump with a pressure pump. The novel device has been tested by measuring both η0 and λ for a number of polyethylene oxide solutions in glycerol–water 25 wt. % and pure water, respectively. Its effectiveness has been corroborated by means of a direct comparison with a conventional rotational rheometer.

### Closed-form theoretical model of the secondary drop size in partial coalescence—Capturing pertinent timescales and viscous forces

One of the most important outcomes of partial drop coalescence is the ratio of the secondary drop radius to the primary drop radius, known as the drop ratio, ri. This ratio is thought to be approximately constant and independent of physical parameters of the fluids involved. However, this study reveals that ambient fluid viscosity can alter the size of the secondary drop and the drop ratio consequently. Using scaling analysis, we derive a model that predicts the behavior of the drop ratio as a function of the Ohnesorge number, a dimensionless ratio of viscous to inertial forces. In addition, we present our experimental results of coalescing drops on a planar interface under the influence of surface tension gradients. A high-speed digital camera is used to observe the evolution of drops as they coalesce with a bulk liquid. We show that this process is influenced by the surface tension gradient between the drop and the bulk liquid. The ratio of the secondary drop to the primary drop in partial coalescence is smaller than the reported values for coalescence without a surface tension gradient. The analytical model derived through this study is based on a new modified Ohnesorge number that includes surface tension gradients. Our analytical model is compared against other models and the results illustrate good agreement with our experimental findings and experimental data in the literature.

### Liquid bridge length scale based nondimensional groups for mapping transitions between regimes in capillary break-up experiments

Author(s): Karel Verbeke, Susanna Formenti, Francesco Briatico Vangosa, Christos Mitrias, Naveen Krishna Reddy, Patrick D. Anderson, and Christian Clasen

Experiments and theoretical arguments explore different regimes of the capillary breakup of a liquid bridge, depending on the viscosity of the outer fluid and the length of the bridge.

[Phys. Rev. Fluids 5, 051901(R)] Published Fri May 01, 2020

### Evolution of Rayleigh-Taylor instability under interface discontinuous acceleration induced by radiation

Author(s): Ze-Xi Hu, You-sheng Zhang, and Bao-lin Tian

Rayleigh-Taylor instability (RTI) under radiation background is commonly found in both engineering applications and natural phenomena. In the optically thin and incompressible limit, the corresponding problem can be simplified as an interface discontinuous acceleration (IDA) RTI problem, but to date...

[Phys. Rev. E 101, 043115] Published Thu Apr 30, 2020

### Effect of spinning on the shape and stability of a pendent drop

Author(s): P. Lin, X. Lin, L. E. Johns, and R. Narayanan

Assuming that we wish to measure the surface tension between two liquids by running a pendent drop experiment, we present calculations supporting the case for spinning the drop. For bridges, jets, etc., spinning a heavy fluid surrounded by a lighter fluid is strictly destabilizing. But we find that ...

[Phys. Rev. E 101, 043116] Published Thu Apr 30, 2020

### Sediment motion induced by Faraday waves in a Hele-Shaw cell

Author(s): Román Martino, Alejandro Boschan, Diego Barba Maggi, Gustavo Bongiovanni, Jean-Christophe Géminard, and Marcelo Piva

The interaction between the oscillatory boundary-layer flow induced by Faraday waves and a sedimentary granular layer was studied in a Hele-Shaw cell vertically vibrated. The experimental parameters were the vibration frequency f and acceleration a and the particle diameter dp. At a critical value f...

[Phys. Rev. E 101, 043112] Published Wed Apr 29, 2020