# Latest papers in fluid mechanics

### Evaporation from arbitrary nanoporous membrane configurations: An effective evaporation coefficient approach

Thin-film evaporation from nanoporous membranes is a promising cooling technology employed for the thermal management of modern electronic devices. We propose an effective one-dimensional analytical approach that can accurately predict the temperature and density jump relations, and evaporation rates, for arbitrary nanoporous membrane configurations. This is accomplished through the specification of an effective evaporation coefficient that encompasses the influence of different system parameters, such as porosity, meniscus shape, evaporation coefficient, and receding height. Our proposed approach can accurately predict all the typical output evaporation parameters of interest like mass flux, and temperature and density jumps, without the need to carry out computationally demanding numerical simulations. Several exemplar cases comprising of nanoporous configurations with a wide range of parameters have been considered to demonstrate the feasibility and accuracy of this analytic approach. This work thus enables a quick, efficient, and accurate means of aiding the design and engineering analysis of nanoporous membrane-based cooling devices.

### Energy efficiency analysis of mass transport enhancement in time-periodic oscillatory electroosmosis

The streamwise mass transport of passive, neutral non-reacting solutes in oscillatory electroosmotic microchannel flows is theoretically investigated from an energy consumption and efficiency perspective for general asymmetric wall zeta potentials and slip velocities. Analytical solutions to the averaged mass transport and total power input (consisting of Joule heating, viscous dissipation, and sliding friction) are obtained and expressed in terms of the relevant parameters governing the system. Particularly, we define a “[math]-parameter” to quantify the mass transport gained (excluding pure diffusion) per total power input in our analysis and discussions. While the no-slip, symmetric potential [math]-performances agree with the mass transport results reported in previous literature, a “resonance like” behavior in the [math]-performances is identified for large enough Womersley numbers and symmetric slip lengths despite the extra sliding friction, viscous dissipation, and Joule heating consumptions in the symmetric zeta potential configuration. When favorable asymmetries in the wall potentials and slip lengths are introduced, the [math]-performances are not only considerably improved, but also highly correlated with the magnitudes of the velocity gradients in the oscillatory velocity profiles, hence reinforcing the physical picture of Taylor–Aris dispersion. Geometric symmetry can be identified among distinct velocity profiles which yield the same [math]-performance. These profiles are generally associated with particular families of wall potential and/or slip length combinations also exhibiting symmetry among one another. Finally, the aspect ratio of the slit microchannel (width divided by length) is found to play a crucial role in significantly improving the [math]-energy efficiency of mass transport in time-periodic electroosmosis.

### Natural modes of the two-fluid model of two-phase flow

A physically based method to derive well-posed instances of the two-fluid momentum transport equations from first principles is presented. The basic tools used in this endeavor are the variational principles of field theory, namely, the Hamilton principle and the virtual power principle. The state of the two-fluid flow is represented by the superficial velocity and the drift flux, instead of the average velocities of each fluid. This generates the conservation equations of the two principal motion modes naturally: the global center-of-mass flow and the relative velocity between fluids. Well-posed equations can be obtained by modeling the storage and exchange of kinetic energy in fluctuations structures induced by the interaction between fluids, like wakes and vortexes. In this way, the equations can be regularized without losing in the process the kinetic instabilities responsible for flow-patterns formation and transition. A specific case of vertical air–water flow is analyzed showing the capability of the present model to predict the formation of the slug flow regime as a train of solitons.

### Numerical investigation of multistability in the unstable flow of a polymer solution through porous media

Author(s): Manish Kumar, Soroush Aramideh, Christopher A. Browne, Sujit S. Datta, and Arezoo M. Ardekani

The accumulation of stresses as polymeric chains cross successive pores creates streaks of high polymeric stress. Highly stretched polymeric chains in the regions of high polymeric stress resist the flow crossing these streaks, leading to eddy formation in the different regions of the pores. Multiple distinct unstable flow structures occur inside the pore above a critical Weissenberg number.

[Phys. Rev. Fluids 6, 033304] Published Thu Mar 25, 2021

### Revealing the state space of turbulence using machine learning

Author(s): Jacob Page, Michael P. Brenner, and Rich R. Kerswell

We train deep convolutional autoencoders to learn highly efficient embeddings of two-dimensional turbulence. We define a new technique, latent Fourier analysis, that decomposes these representations into a set of interpretable recurrent patterns, and show how these recurrent patterns are closely related to the simple invariant solutions populating the turbulent attractor. By examining a series of bursting episodes with this framework we are able to identify large numbers of new simple invariant solutions that characterize these events and which have avoided previous detection methods.

[Phys. Rev. Fluids 6, 034402] Published Thu Mar 25, 2021

### Reynolds number dependence of Lyapunov exponents of turbulence and fluid particles

Author(s): Itzhak Fouxon, Joshua Feinberg, Petri Käpylä, and Michael Mond

The Navier-Stokes equations generate an infinite set of generalized Lyapunov exponents defined by different ways of measuring the distance between exponentially diverging perturbed and unperturbed solutions. This set is demonstrated to be similar, yet different, from the generalized Lyapunov exponen...

[Phys. Rev. E 103, 033110] Published Wed Mar 24, 2021

### Maximum run-up produced by tsunami wave trains entering bays of variable cross section

Author(s): N. Postacioglu and M. S. Özeren

Tsunami run-up in bays is essentially a wave diffraction problem in three dimensions. In this work we are showing that it is possible to treat the problem in one dimension and still obtain satisfactory results for the run-up.

[Phys. Rev. Fluids 6, 034803] Published Wed Mar 24, 2021

### Controlling structure of materials derived from spinodally decomposing liquids

Arresting morphological evolution of spinodally decomposing heterogeneous mixtures via the addition of colloidal particles has resulted in the discovery of new classes of bicontinuous materials, viz., bicontinuous interfacially jammed emulsion gels (bijels) and most recently bicontinuous intraphase jammed emulsion gels (bipjels). Here, we demonstrate how the extent of particle wettability and particle–particle interactions govern the ultimate structure formed. We present the multi-phase lattice Boltzmann method (LBM) integrated with a discrete particle model with two particle–particle collision models, the classic hard-sphere model and a new bonding collision model, to predict the final state of spinodally decomposing fluid mixtures containing solid particles. We show that the elastic collision model yields either the formation of emulsions or bijels, while only the bonding collision model on particles with preferential wettability for one phase can predict bipjels formation. In the case of bipjels, a delicate balance between the dynamics of evolving interface and the strength of particle–particle aggregates is required to restrict the interfacial motion. These results are consistent with experimental findings, suggesting that the presence of smaller particles with high particle–particle interactions can yield the formation of bipjels and consequent isolation of hierarchically porous materials.

### An implicit discontinuous Galerkin finite element discrete Boltzmann method for high Knudsen number flows

Simulations of the discrete Boltzmann Bhatnagar–Gross–Krook equation are an important tool for understanding fluid dynamics in non-continuum regimes. Here, we introduce a discontinuous Galerkin finite element method for spatial discretization of the discrete Boltzmann equation for isothermal flows with high Knudsen numbers [[math]]. In conjunction with a high-order Runge–Kutta time marching scheme, this method is capable of achieving high-order accuracy in both space and time, while maintaining a compact stencil. We validate the spatial order of accuracy of the scheme on a two-dimensional Couette flow with [math] and the D2Q16 velocity discretization. We then apply the scheme to lid-driven micro-cavity flow at [math], and we compare the ability of Gauss–Hermite (GH) and Newton–Cotes (NC) velocity sets to capture the high non-linearity of the flow-field. While the GH quadrature provides higher integration strength with fewer points, the NC quadrature has more uniformly distributed nodes with weights greater than machine-zero, helping to avoid the so-called ray-effect. Broadly speaking, we anticipate that the insights from this work will help facilitate the efficient implementation and application of high-order numerical methods for complex high Knudsen number flows.

### Sinking bubbles in a fluid under vertical vibration

The special nonlinear effect of sinking bubbles is observed when the container partially filled with a liquid is excited by vibration. This paper is concerned with this interesting phenomenon in an incompressible viscous fluid under vertical vibration. We construct the theoretical model from the view of vibration mechanics and fluid mechanics. According to theoretical analysis, we derive the accurate model of the bubble moving in the liquid and the added mass caused by it. After that, the control equation of the bubble is given by the force analysis and the differential equation of variable-mass systems. Besides, the critical depth of the sinking bubble is derived based on the method of direct separation of motions. We further explore and analyze the specific reasons why the bubbles sink. At the same time, the conditions where the variable mass has a significant influence on the motion of the object are given. The main factors affecting the sinking of bubbles, density, frequency, and amplitude are numerically simulated and analyzed with different conditions. To prevent or weaken the effect of sinking bubbles in the oscillating fluid, feasible approaches are proposed. Meanwhile, the theory is validated experimentally.

### Compressible effects modeling for turbulent cavitating flow in a small venturi channel: An empirical turbulent eddy viscosity correction

The Reynolds-averaged Naviers-Stokes (RANS) method coupling with cavitation model is still a practical tool to predict cavitating flows, particularly in industrial applications, due to its computational efficiency. However, the compressibility effects induced by cavitation are not well considered in conventional RANS methods, which often causes the blockage of the reentrant jet and the total steadiness of the simulated cavity. To this end, modeling of compressibility effects becomes critical to predict the characteristics of unsteady cavitating flows. An empirical eddy viscosity correction [Reboudet al., “Two phase flow structure of cavitation: experiment and modeling of unsteady effects,” in 3rd International Symposium on Cavitation CAV1998, Grenoble, France (1998), Vol. 26.] was proposed to consider the compressibility effects induced by cavitation. Although this modification is able to capture unsteady behaviors of cavitating flows in various configurations, it is still not fully analyzed in terms of the turbulent quantities, e.g., Reynolds shear stress. In this work, we investigate the effects of this compressibility correction on the Reynolds shear stress, by comparing with x-ray experimental data in a small Venturi channel. It is shown that the Reboud correction reduces the eddy viscosity in the entire cavity region, which improves the prediction of Reynolds shear stress near the wall significantly. However, the correction depends only on the simulated mixture density, leading to poor predictions near the phase interface where the simulated mixture density has large discrepancies. Based on the results, we propose an empirical eddy viscosity limiter to confine the original correction beneath the cavitating layer and demonstrate the merits of the proposed correction by comparing with experimental measurements.

### A new soft computing approach for studying the wire coating dynamics with Oldroyd 8-constant fluid

In this paper, a mathematical model for wire coating in the presence of pressure type die along with the bath of Oldroyd 8-constant fluid is presented. The model is governed by a partial differential equation, transformed into a nonlinear ordinary differential equation in dimensionless form through similarity transformations. We have designed a novel soft computing paradigm to analyze the governing mathematical model of wire coating by defining weighted Legendre polynomials based on Legendre neural networks (LeNN). Training of design neurons in the network is carried out globally by using the whale optimization algorithm (WOA) hybrid with the Nelder–Mead (NM) algorithm for rapid local convergence. Designed scheme (LeNN-WOA-NM algorithm) is applied to study the effect of variations in dilating constant (α), pressure gradient (Ω), and pseudoplastic constant β on velocity profile w(r) of fluid. To validate the proposed technique's efficiency, solutions and absolute errors are compared with the particle swarm optimization algorithm. Graphical and statistical performance of fitness value, absolute errors, and performance measures in terms of minimum, mean, median, and standard deviations further establishes the worth of the designed scheme for variants of the wire coating process.

### Solitary-wave loads on a three-dimensional submerged horizontal plate: Numerical computations and comparison with experiments

A parallelized three-dimensional (3D) boundary element method is used to simulate the interaction between an incoming solitary wave and a 3D submerged horizontal plate under the assumption of potential flow. The numerical setup follows closely the setup of laboratory experiments recently performed at Shanghai Jiao Tong University. The numerical results are compared with the experimental results. An overall good agreement is found for the two-dimensional wave elevation, the horizontal force and the vertical force exerted on the plate, and the pitching moment. Even though there are some discrepancies, the comparison shows that a model solving the fully nonlinear potential flow equations with a free surface using a 3D boundary element method can satisfactorily capture the main features of the interaction between nonlinear waves and a submerged horizontal plate.

### An off-lattice Boltzmann method for blood flow simulation through a model irregular arterial stenosis: The effects of amplitude and frequency of the irregularity

In this work, a finite-difference-based axisymmetric off-lattice Boltzmann solver is developed to simulate blood flow through pathological arteries. The proposed solver handles arterial geometries using a body-fitted curvilinear mesh. The axisymmetric nature of the flow and the non-Newtonian behavior of blood are incorporated using external source terms. The solver is verified for spatially developing pulsatile inflow through an abdominal aortic aneurysm using reference data from literature. Thereafter, the effects of amplitude and frequency of an irregular-shaped stenosed artery are systematically studied. The results are analyzed using the instantaneous vorticity contours, streamlines, cycle-averaged and phase-averaged profiles of wall shear stress (WSS), and oscillatory shear index. Further, the correlation between the luminal surface concentration (LSC) of low-density lipoproteins and the WSS is studied to predict potential disease initiation and progression locations. It is noted that an increase in the amplitude of irregularity of the stenosis increases the magnitudes of maxima and minima of WSS profiles without altering their locations. On the other hand, an increase in the frequency of irregularity increases the magnitudes of WSS extrema while bringing the peaks closer together. Further, a positive correlation is found between the degree of irregularity as well as the number of locations of elevated LSC. The presence of irregularity creates additional vortices in the upstream section of the stenosis. Both the upstream and downstream sections of the stenosis are subjected to the opposing shear-layers with higher magnitudes, which may lead to endothelial damage. Finally, the shear-thinning effect of blood is studied using the power-law model. The magnitudes of the maxima and minima in WSS have a lower value for the shear-thinning model than the Newtonian case. Also, the vortices that were produced in the upstream section because of the irregularity get suppressed by the shear-thinning effect of the blood.

### Multiscale instabilities of Magnus–Robins effect for compressible flow past rotating cylinder

In the present research, the instability suffered by flow past a rotating cylinder with very high rotation rates is studied. Special emphasis is given on exploring the effects of compressibility by solving two-dimensional Navier–Stokes equations. The first account of this instability has been provided in “T. K. Sengupta, K. Gupta, and M. T. Nair, “Lift generation and limiting mechanism via unsteady flow development for Magnus-Robins effect,” Proceedings of the 8th Asian Congress of Fluid Mechanics, Shenzhen, China (1999).” Subsequently, there have been other efforts on the same with different numerical models based on incompressible and compressible flow formulation. Apart from the efforts reported by the present group, other reported results did not identify this as a phenomenon of flow instability. The perceived temporal variations of lift and drag by both the incompressible and compressible flow formulation have been correlated with each other, without highlighting the role of compressibility in triggering the flow instability. Here, we report the sensitive dependence of the temporal instability on the accuracy of the simulation for the growth of the disturbance field during the transient monotonic variations of lift and drag. Of specific interest is the role of compressibility in promoting the disturbance growth and limiting the maximum lift that is generated. The compressibility effects have been incorporated by considering lower Mach numbers for the oncoming uniform flow, so that nowhere in the flow field there is the formation of a supersonic pocket.

### Insights into low Reynolds flow past finite curved cylinders

Spectral proper orthogonal decomposition (SPOD) is applied to experimental digital visualizations to scrutinize the properties of the wake flow behind curved cylinders. This technique has been applied to the image data of Shang et al. [“Flow past finite cylinders of constant curvature,” J. Fluid Mech. 837, 896–915 (2018)] to emphasize the main features of the flow and to extract the most energetically and dynamically relevant space-time coherent structures. The study considers different Reynolds numbers and angles of curvature for two cylinder aspect ratios. It is first shown that the SPOD structures reproduce the base flow topology of the digital visualizations, confirming the presence of a single oblique shedding regime for a low aspect ratio and both normal and oblique regimes for a high aspect ratio. The appearance of the instabilities typical of straight cylinders, usually referred to as type-A and -B in literature, is identified as well. As principal results obtained for curved cylinders, increasing the Reynolds number the analysis of SPOD spectra has revealed two reductions in the oscillation frequency of the leading coherent structures, attributed to the occurrence of type-A instability when the wake is still laminar, and to the development of a one-sided vortex dislocation in turbulent regime. The study has also highlighted the gradual transfer of energy between flow structures during the transition from type-A to type-B instabilities, accompanied by high-frequency scales excitement. Some peculiar aspects of SPOD field reconstruction are outlined here, which are suggested by the physical characteristics of the flow.

### Well-balanced lattice Boltzmann model for two-phase systems

The standard two-phase lattice Boltzmann equation (LBE) method usually fails to capture the physical equilibrium state (zero velocity and constant chemical potential). Consequently, spurious velocities and inconsistent thermodynamic density properties are frequently encountered in LBE simulations. In this work, based on a rigorous analysis of the discrete balance equation of LBE, the structure of force imbalance due to discretization errors is identified. Then, a well-balanced LBE model is proposed, which can achieve the discrete equilibrium state. The well-balance properties of the model are confirmed by simulating a flat interface problem and a droplet system.

### A study of the natural convection of water-AA7075 nanoliquids in low-porosity cylindrical annuli using a local thermal non-equilibrium model

Natural convection in nanoliquid-saturated porous cylindrical annuli due to uniform heat and mass influxes from the solid cylinder and effluxes from the outer hollow cylinder is investigated analytically. The Darcy model and the modified version of the Buongiorno two-phase model are used, and local thermal non-equilibrium between the phases is assumed. A nanoliquid-saturated porous medium made up of glass balls with a dilute concentration of AA7075 alloy nanoparticles well-dispersed in water is considered. Out of three types of annuli considered, shallow annuli provide the best heat transport and tall annuli show the worst performance. The presence of a dilute concentration of nanoparticles significantly enhances the heat transport in the system. Of nine nanoparticle shapes considered, lamina-shaped nanoparticles enhance heat transport the most. Heat transport is enhanced in the case of heat-and-mass-driven convection compared to the case of purely heat-driven convection. The results for a rectangular enclosure are obtained as a particular case of the present study. Two asymptotic routes that take us to the results of thermal equilibrium are shown. The vanishing limit of the concentration Rayleigh number yields the result for a single-phase model. Results for the base-liquid-saturated porous medium form a limiting case of the present study. We conclude that a shallow cylindrical annulus saturated with water-AA7075 lamina-shaped alloy nanoparticles is best suited for heat transfer due to its high effective thermal conductivity in comparison with that of other shaped nanoparticles and a tall rectangular enclosure saturated by water is best suited for heat storage applications.

### The change in the wetting regime of a nanodroplet on a substrate with varying wettability: A molecular dynamics investigation

The effect of the triple-phase contact line (TPCL) on the wetting phenomenon has been extensively discussed during the past decade. Numerous attempts have also been made to quantify its characteristics based on thermodynamic or mechanical definitions. In this research, molecular dynamics simulation was used to define the term “vicinity of the TPCL” and its effect on the hydrophilic and hydrophobic behaviors of a water nanodroplet. A nanodroplet was placed on a substrate that was modified in a stepwise manner by growing a patch of heterogeneity from either the center of the substrate or from the sides. The relative direction of motion of the TPCL and the patch determined the pathway that the nanodroplet chooses in order to change its wetting regime from hydrophilic to hydrophobic and vice versa. A gradual change occurs when the TPCL and the heterogeneity move in the same direction, and an abrupt change takes place otherwise. In addition to the insights into the wetting phenomenon, the width of the TPCL is also discussed. The obtained data suggest that the effective width of the TPCL, δ, is different inside the perimeter of the nanodroplet from outside of it. Moreover, the value of δ for the abrupt pathway is twice as large as the gradual one. In conclusion, the width, or vicinity, of the TPCL depends on the type of the pathway and the configuration of the substrate-patch system and cannot be treated similarly in both cases.

### Experimental and numerical modeling of a sloshing problem in a stepped based rectangular tank

In this study, the two-dimensional sloshing of water in a stepped based tank partially filled was analyzed using an arbitrary Lagrangian–Eulerian adaptive fixed-mesh method and including the Smagorinsky turbulence model. The numerical model is verified by contrasting the predictions made by the model with experimental results. The tank was subjected to controlled one-directional motion imposed using a shake table. The free surface evolution was followed using ultrasonic sensors, and a high-speed camera was used to record the experiments. The experimental and numerical analyses include a comparison of the wave height at different control points and snapshots of the free surface evolution for two imposed frequencies. Also, a detailed numerical study of the effects of the frequency of the imposed movement, the step height, and the fluid volume on the wave dynamics was performed. Moreover, the effect of fluid viscosity on the dynamics of the free surface was also studied. In brief, the numerical method proved to be accurate, experimental data were reported, and the effects on the numerical results of different physical and numerical aspects were exhaustively analyzed. The proposed results help to understand the sloshing of stepped geometries.