# Latest papers in fluid mechanics

### Thermodynamic effects on Venturi cavitation characteristics

In this paper, the thermodynamic effect is systematically studied by Venturi cavitation in a blow-down type tunnel for the first time, using water at temperatures up to relatively high levels and at controlled dissolved gas contents in the supply reservoir (measured by dissolved oxygen, DO). The mean attached cavity length [math] is chosen to reveal the thermodynamic effect, and the cavitation characteristics are analyzed from the experiments. With an increase in the thermodynamic parameter Σ*, a decrease in [math] vs the pressure recovery number κ is observed, which is consistent with suppression of cavitation by the thermodynamic effect, but the decrease is related not only to this effect. Based on the experimental results, a model is presented of the attached cavity cloud that develops from the Venturi throat. It is found that either the length of this cloud oscillates stably around a mean value or the cloud breaks regularly at some upstream position, allowing that a detached cavity cloud is shed, flows downstream, and collapses while the remaining attached cloud regenerates. Applying this model to experimental results obtained first with cold water, then with hot water, we find that when the mean length of the attached cavity cloud oscillates stably, temperature increase causes reduction of the mean cavitation length. This is interpreted to be a consequence of the thermodynamic effect. When detachment of large cavity clouds occurs, the mean length is increased at temperature increase. This is a consequence of cloud configuration changes being superposed on changes due to the thermodynamic effect. These observations explain conflicting results reported for attached cavity clouds in relation to the thermodynamic effect. The gas content in the water is found to be without significance within the range of DO tested.

### Turbulent transport and mixing in the multimode narrowband Richtmyer-Meshkov instability

The mean momentum and heavy mass fraction, turbulent kinetic energy, and heavy mass fraction variance fields, as well as the budgets of their transport equations are examined several times during the evolution of a narrowband Richtmyer-Meshkov instability initiated by a Mach 1.84 shock traversing a perturbed interface separating gases with a density ratio of 3. The results are computed using the “quarter scale” data from four algorithms presented in the θ-group study of Thornber et al. [“Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer-Meshkov instability: The θ-group collaboration,” Phys. Fluids 29, 105107 (2017)]. The present study is inspired by a previous similar study of Rayleigh-Taylor instability and mixing using direct numerical simulation data by Schilling and Mueschke [“Analysis of turbulent transport and mixing in transitional Rayleigh-Taylor unstable flow using direct numerical simulation data,” Phys. Fluids 22, 105102 (2010)]. In addition to comparing the predictions of the data from four implicit large-eddy simulation codes, the budgets are used to quantify the relative importance of the terms in the transport equations, and the balance of the terms is employed to infer the numerical dissipation. Terms arising from the compressibility of the flow are examined, in particular the pressure-dilatation. The results are useful for validation of large-eddy simulation and Reynolds-averaged modeling of Richtmyer-Meshkov instability.

### Determination of the volume fraction in (water-gasoil-air) multiphase flows using a simple and low-cost technique: Artificial neural networks

The precise prediction of the volume fraction in three-phase flows plays an important role in the petroleum and process industries. In this study, attenuation gamma rays (single pencil beam) and multilayer perceptron neural networks were used to precisely predict the volume fraction percentage in water-gasoil-air three-phase flows. The detection system uses just one 137Cs source (single energy of 662 keV) and one NaI(Tl) detector in order to calculate the transmitted beams. The experimental setup was simulated using the MCNPX code to provide the required data for the neural network. The volume fraction percentage was measured with a root mean square error of 2.48 and a mean relative error percentage of less than 7.08%. The proposed setup is the best and simplest design for reducing radiation hazards and cost.

### The effect of deformability on the microscale flow behavior of red blood cell suspensions

Red blood cell (RBC) deformability is important for tissue perfusion and a key determinant of blood rheology. Diseases such as diabetes, sickle cell anemia, and malaria, as well as prolonged storage, may affect the mechanical properties of RBCs altering their hemodynamic behavior and leading to microvascular complications. However, the exact role of RBC deformability on microscale blood flow is not fully understood. In the present study, we extend our previous work on healthy RBC flows in bifurcating microchannels [Sherwood et al., “Viscosity and velocity distributions of aggregating and non-aggregating blood in a bifurcating microchannel,” Biomech. Model. Mechanobiol. 13, 259–273 (2014); Sherwood et al., “Spatial distributions of red blood cells significantly alter local hemodynamics,” PLoS One 9, e100473 (2014); and Kaliviotis et al., “Local viscosity distribution in bifurcating microfluidic blood flows,” Phys. Fluids 30, 030706 (2018)] to quantify the effects of impaired RBC deformability on the velocity and hematocrit distributions in microscale blood flows. Suspensions of healthy and glutaraldehyde hardened RBCs perfused through straight microchannels at various hematocrits and flow rates were imaged, and velocity and hematocrit distributions were determined simultaneously using micro-Particle Image Velocimetry and light transmission methods, respectively. At low feed hematocrits, hardened RBCs were more dispersed compared to healthy ones, consistent with decreased migration of stiffer cells. At high hematocrit, the loss of deformability was found to decrease the bluntness of velocity profiles, implying a reduction in shear thinning behavior. The hematocrit bluntness also decreased with hardening of the cells, implying an inversion of the correlation between velocity and hematocrit bluntness with loss of deformability. The study illustrates the complex interplay of various mechanisms affecting confined RBC suspension flows and the impact of both deformability and feed hematocrit on the resulting microstructure.

### The effect of deformability on the microscale flow behavior of red blood cell suspensions

Red blood cell (RBC) deformability is important for tissue perfusion and a key determinant of blood rheology. Diseases such as diabetes, sickle cell anemia, and malaria, as well as prolonged storage, may affect the mechanical properties of RBCs altering their hemodynamic behavior and leading to microvascular complications. However, the exact role of RBC deformability on microscale blood flow is not fully understood. In the present study, we extend our previous work on healthy RBC flows in bifurcating microchannels [Sherwood et al., “Viscosity and velocity distributions of aggregating and non-aggregating blood in a bifurcating microchannel,” Biomech. Model. Mechanobiol. 13, 259–273 (2014); Sherwood et al., “Spatial distributions of red blood cells significantly alter local hemodynamics,” PLoS One 9, e100473 (2014); and Kaliviotis et al., “Local viscosity distribution in bifurcating microfluidic blood flows,” Phys. Fluids 30, 030706 (2018)] to quantify the effects of impaired RBC deformability on the velocity and hematocrit distributions in microscale blood flows. Suspensions of healthy and glutaraldehyde hardened RBCs perfused through straight microchannels at various hematocrits and flow rates were imaged, and velocity and hematocrit distributions were determined simultaneously using micro-Particle Image Velocimetry and light transmission methods, respectively. At low feed hematocrits, hardened RBCs were more dispersed compared to healthy ones, consistent with decreased migration of stiffer cells. At high hematocrit, the loss of deformability was found to decrease the bluntness of velocity profiles, implying a reduction in shear thinning behavior. The hematocrit bluntness also decreased with hardening of the cells, implying an inversion of the correlation between velocity and hematocrit bluntness with loss of deformability. The study illustrates the complex interplay of various mechanisms affecting confined RBC suspension flows and the impact of both deformability and feed hematocrit on the resulting microstructure.

### Manipulation of jet breakup length and droplet size in axisymmetric flow focusing upon actuation

External sinusoidal actuation is employed in the axisymmetric flow focusing (AFF) for generating uniform droplets in the jetting mode. The perturbations propagating along the meniscus surface can modulate the rupture of the liquid jet. Experiments indicate that the jet breakup length and the resultant droplet size can be precisely controlled in the synchronized regime, which are further confirmed by the scaling law. The finding of this study can help for better understanding of the underlying physics of actuation-aided AFF, and this active droplet generation method with fine robustness, high productivity, and nice process control would be advantageous for various potential applications.

### Nonaxisymmetric simulations of the Princeton magnetorotational instability experiment with insulating and conducting axial boundaries

Author(s): Dahan Choi, Fatima Ebrahimi, Kyle J. Caspary, Erik P. Gilson, Jeremy Goodman, and Hantao Ji

Stability and nonlinear evolution of rotating magnetohydrodynamic flows in the Princeton magnetorotational instability (MRI) experiment are examined using three-dimensional non-axisymmetric simulations. In particular, the effect of axial boundary conductivity on a free Stewartson-Shercliff layer (SS...

[Phys. Rev. E 100, 033116] Published Tue Sep 24, 2019

### Kolmogorov or Bolgiano-Obukhov scaling: Universal energy spectra in stably stratified turbulent fluids

Author(s): Abhik Basu and Jayanta K. Bhattacharjee

We set up the scaling theory for stably stratified turbulent fluids. For a system having infinite extent in the horizontal directions, but with a finite width in the vertical direction, this theory predicts that the inertial range can display three possible scaling behavior, which are essentially pa...

[Phys. Rev. E 100, 033117] Published Tue Sep 24, 2019

### Liquid plug formation in an airway closure model

Author(s): F. Romanò, H. Fujioka, M. Muradoglu, and J. B. Grotberg

A numerical study finds that bifrontal plug growth leading to the closure of a human lung airway induces high stress levels on the wall, which is the location of airway epithelial cells. Postcoalescence wall stresses can be from 300% to 600% greater than precoalescence values.

[Phys. Rev. Fluids 4, 093103] Published Tue Sep 24, 2019

### Thermoelectric convection in a dielectric liquid inside a cylindrical annulus with a solid-body rotation

Author(s): Changwoo Kang, Antoine Meyer, Harunori N. Yoshikawa, and Innocent Mutabazi

We study thermoelectric convection in a cylindrical annulus of dielectric liquid under rotation and a fixed temperature gradient. Convection onset is delayed and stationary helical vortices become oscillatory columnar vortices for a rotation rate above a value dependent on the radius ratio.

[Phys. Rev. Fluids 4, 093502] Published Tue Sep 24, 2019

### Cospectral budget model describes incipient sediment motion in turbulent flows

Author(s): Shuolin Li and Gabriel Katul

Incipient motion of sediment particles is analyzed using a relation between a densimetric Froude number (Fr) and 6 decades of relative roughness (N). The universal character of the Fr-N relation was recovered from the vertical velocity energy spectrum using a cospectral budget model.

[Phys. Rev. Fluids 4, 093801] Published Tue Sep 24, 2019

### Connectivity enhancement due to film flow in porous media

Author(s): Marcel Moura, Eirik Grude Flekkøy, Knut Jørgen Måløy, Gerhard Schäfer, and Renaud Toussaint

An experimental investigation shows that thin liquid films can interconnect different parts of a porous network (like wet soils or rocks) and effectively enhance the overall connectivity of the system. The effect is large enough to allow for the drainage of fluid clusters that otherwise would be entirely trapped in the matrix.

[Phys. Rev. Fluids 4, 094102] Published Tue Sep 24, 2019

### Simulation of blood flow past a distal arteriovenous-graft anastomosis at low Reynolds numbers

Patients with end-stage renal disease are usually treated by hemodialysis while waiting for a kidney transplant. A common device for vascular access is an arteriovenous graft (AVG). However, AVG failure induced by thrombosis has been plaguing dialysis practice for decades. Current studies indicate that the thrombosis is caused by intimal hyperplasia, which is triggered by the abnormal flows and forces [e.g., wall shear stress (WSS)] in the vein after AVG implant. Due to the high level of complexity, in almost all of the existing works of modeling and simulation of the blood-flow vessel-AVG system, the graft and blood vessel are assumed to be rigid and immobile. Very recently, we have found that the compliance of graft and vein can reduce flow disturbances and lower WSS [Z. Bai and L. Zhu, “Three-dimensional simulation of a viscous flow past a compliant model of arteriovenous-graft anastomosis,” Comput. Fluids 181, 403–415 (2019)]. In this paper, we apply the compliant model to investigate possible effects of several dimensionless parameters (AVG graft-vein diameter ratio [math], AVG attaching angle θ, flow Reynolds numbers Re, and native vein speed [math]) on the flow and force fields near the distal AVG anastomosis at low Reynolds numbers (up to several hundreds). Our computational results indicate that the influences of the parameters [math], θ, and Re lie largely on the graft and the influence of [math] lies largely on the vein. In any case, the WSS, wall shear stress gradient, and wall normal stress gradient and their averaged values on the graft are significantly greater than those on the vein.

### Comparison of the quasi-steady-state heat transport in phase-change and classical Rayleigh-Bénard convection for a wide range of Stefan number and Rayleigh number

We report the first comparative study of the phase-change Rayleigh–Bénard (RB) convection system and the classical RB convection system to systematically characterize the effect of the oscillating solid-liquid interface on the RB convection. Here, the role of Stefan number Ste (defined as the ratio between the sensible heat to the latent heat) and the Rayleigh number based on the averaged liquid height Raf is systematically explored with direct numerical simulations for low Prandtl number fluid (Pr = 0.0216) in a phase-change RB convection system during the stationary state. The control parameters Raf (3.96 × 104 ≤ Raf ≤ 9.26 × 107) and Ste (1.1 × 10−2 ≤ Ste ≤ 1.1 × 102) are varied over a wide range to understand its influence on the heat transport and flow features. Here, we report the comparison of large-scale motions and temperature fields, frequency power spectra for vertical velocity, and a scaling law for the time-averaged Nusselt number at the hot plate [math] vs Raf for both the RB systems. The intensity of solid-liquid interface oscillations and the standard deviation of Nuh increase with the increase in Ste and Raf. There are two distinct RB flow configurations at low Raf independent of Ste. At low and moderate Raf, the ratio of the Nusselt number for phase-change RB convection to the Nusselt number for classical RB convection [math] is always greater than one. However, at higher Raf, the RB convection is turbulent, and [math] can be less than or greater than one depending on the value of Ste. The results may turn out to be of immense consequence for understanding and altering the transport characteristics in the phase-change RB convection systems.

### Determination of the transmissivity of a heterogeneous anisotropic fracture in slip flow conditions

Author(s): Tony Zaouter, Didier Lasseux, and Marc Prat

Rough fractures often exhibit a broad spectrum of defect length scales ranging from the microscopic (roughness) scale to a macroscopic one (waviness) and further to the megascopic scale corresponding to the entire fracture. The influence of these multiple scales and their reciprocal interactions are...

[Phys. Rev. E 100, 033115] Published Mon Sep 23, 2019

### Directionally controlled open channel microfluidics

Free-surface microscale flows have been attracting increasing attention from the research community in recent times, as attributable to their diverse fields of applications ranging from fluid mixing and particle manipulation to biochemical processing on a chip. Traditionally, electrically driven processes governing free surface microfluidics are mostly effective in manipulating fluids having characteristically low values of the electrical conductivity (lower than 0.085 S/m). Biological and biochemical processes, on the other hand, typically aim to manipulate fluids having higher electrical conductivities (>0.1 S/m). To circumvent the inherent limitation of traditional electrokinetic processes in manipulating highly conductive fluids in free surface flows, here we experimentally develop a novel on-chip methodology for the same by exploiting the interaction between an alternating electric current and an induced thermal field. We show that the consequent local gradients in physical properties as well as interfacial tension can be tuned to direct the flow toward a specific location on the interface. The present experimental design opens up a new realm of on-chip process control without necessitating the creation of a geometric confinement. We envisage that this will also open up research avenues on open-channel microfluidics, an area that has vastly remained unexplored.

### On gravity currents of fixed volume that encounter a down-slope or up-slope bottom

We consider a gravity current released from a lock into an ambient fluid of smaller density, that, from the beginning or after some horizontal propagation X1, propagates along an inclined (up- or down-) bottom. The flow (assumed in the inertial-buoyancy regime) is modeled by the shallow-water (SW) equations with a jump condition applied at the nose (front). The behavior of the current is dominated by the slope angle, θ, but is also affected by additional dimensionless parameters: the aspect ratio of the lock x0/h0, the height ratio of the ambient to lock, H/h0, and the distance of the backwall from the beginning of the slope, X1/x0. We show that the stability of the interface, reflected by the value of the bulk Richardson number, Ri, is essential in the interpretation and modeling. In the upslope flow, Ri increases and hence entrainment/mixing effects are unimportant. In the downslope flow, the current first accelerates and Ri decreases; this enhances entrainment and drag, which then decelerate the current. We show that the accelerating-decelerating downstream current is reproduced well by a SW model combined with a simple closure for the entrainment and drag. A comparison of the theoretical results with previously published experimental data for both upslope flow and downslope flow show fair agreement.

### Cahn-Hilliard mobility of fluid-fluid interfaces from molecular dynamics

The Cahn-Hilliard equation is often used to model the temporospatial evolution of multiphase fluid systems including droplets, bubbles, aerosols, and liquid films. This equation requires knowledge of the fluid-fluid interfacial mobility γ, a parameter that can be difficult to obtain experimentally. In this work, a method to obtain γ from nonequilibrium molecular dynamics is presented. γ is obtained for liquid-liquid and liquid-vapor interfaces by perturbing them from their equilibrium phase fraction spatial distributions, using molecular dynamics simulations to observe their relaxation toward equilibrium, and fitting the Cahn-Hilliard model to the transient molecular simulations at each time step. γ is then compared to a different measure of interfacial mobility, the molecular interfacial mobility M. It is found that γ is proportional to the product of M, the interface thickness, and the ratio of thermal energy to interfacial energy.

### Direct methods for solving the Boltzmann equations: Comparisons with direct simulation Monte Carlo and possibilities

The possibilities of direct methods for solving the Boltzmann equation in comparison with direct simulation Monte Carlo are discussed. The general features of these different methods are considered, in particular, from the point of view of application of different variants of discretization in phase space. The advantages and disadvantages of both approaches are clarified. Comparative solutions of some simple problems are given. An important issue concerns anomalous heat transfer and validation of the effect by calculations based on these two methods. The solutions of the stationary one-dimensional heat transfer problem between two infinite plates with nonclassical nonequilibrium reflection from the surface are obtained; the anomalous heat transfer with a temperature gradient and a heat flux having the same sign is observed. One-dimensional and two-dimensional (in the square domain) problems with nonequilibrium “membranelike” boundary conditions are solved numerically; the anomalous heat transfer for all the considered cases is demonstrated.

### Initial coalescence of a drop at a planar liquid surface

Author(s): Qindan Zhang, Xiaofeng Jiang, David Brunello, Taotao Fu, Chunying Zhu, Youguang Ma, and Huai Z. Li

The initial coalescence of a pendant drop at bulk liquid was jointly investigated by an ultrahigh-speed DC electrical device, a high-speed camera, and a fast micro-Particle Image Velocimetry (micro-PIV). Extended to highly viscous non-Newtonian liquids, the variation of the coalescing width vs time ...

[Phys. Rev. E 100, 033112] Published Fri Sep 20, 2019