Continuum Fluid Research Articles

Proven Distributed Memory Parallelization of Particle Methods

We provide a mathematically proven parallelization scheme for particle methods on distributed-memory computer systems. Particle methods are a versatile and widely used class of algorithms for computer simulations and numerical predictions in various applications, ranging from continuum fluid dynamics to discrete granular flows and molecular dynamics simulations. Particle methods naturally lend themselves to implementation on parallel computing systems. So far, however, a mathematical proof of correctness and equivalence to sequential implementations was only available for shared-memory parallelism. Here, we leverage a formal definition of the algorithmic class of particle methods to provide a proven parallelization scheme for distributed-memory computers. We prove that thus parallelized particle methods on distributed-memory computers are formally equivalent to their sequential counterpart for a well-defined class of particle methods, and we provide analytical expressions for the speed-up and scalability bounds of this class of algorithms in function of their parameters. The parallelization scheme analyzed here is the basis of many real-world software designs for parallel particle methods. The present analysis is, therefore, of direct relevance to existing and new parallel implementations of particle methods and places them on solid theoretical grounds, rationalizing best practices and providing useful scalability and speedup bounds for benchmarking.

Comparisons between full molecular dynamics simulation and Zhang's multiscale scheme for nanochannel flows.

In a very small surface separation, the fluid flow is actually multiscale consisting of both the molecular scale non-continuum adsorbed layer flow and the intermediate macroscopic continuum fluid flow. Classical simulation of this flow often takes over large computational source and is not affordable owing to using molecular dynamics simulation (MDS) to model the adsorbed layer flow, if the flow field size is on the engineering size scale such as of 0.01-10mm or even bigger like occurring in micro or macro hydrodynamic bearings. The present paper uses full MDS to validate Zhang's multiscale flow model, which yields the closed-form explicit flow equations respectively for the adsorbed layer flow and the intermediate continuum fluid flow. Here, full MDS was carried out for the pressure-driven flow of methane in the nano slit pore made of silicon respectively with the channel heights 5.79nm, 11.57nm, and 17.36nm. According to the number density distribution, the flow areas were respectively discriminated as the adsorbed layer zone and the intermediate fluid zone. The values of the characteristic parameters for Zhang's multiscale scheme were extracted from full MDS and input to Zhang's multiscale flow equations respectively for calculating the flow velocity profile and the volume flow rates of the adsorbed layers and the intermediate fluid. It was found that for these three channel heights, the flow velocity profiles calculated from Zhang's model approximate those calculated from full MDS, while the total flow rates through the channel calculated from Zhang's model are close to those calculated from full MDS. The accuracy of Zhang's multiscale flow model is improved with the increase of the channel height. The recent modification of the optimized potential for liquid simulation (MOPLS) model was used to calculate the interaction force between two methane molecules. In order to calculate the interaction force between the wall atoms and the methane molecules accurately, our previous non-equilibrium multiscale MDS was used. The interaction forces between the methane molecule and the wall atom were obtained from the coupled potential function by the L-B mixing rule when the fluid molecules arrived at near wall. The methane molecule diameter was obtained from the radial distribution function by using equilibrium MDS under the same initial conditions. The local viscosities across the adsorbed layer were obtained from the local velocity profile by using the Poiseuille flow method. The motion equation of the methane molecule was solved by the leapfrog method. The temperature of the simulation system was checked by Bhadauria's method, i.e., the system temperature was rectified by the velocities in the y- and z-directions. The flow velocity distributions across the channel height and the volume flow rates through the channel were also calculated from Zhang's closed-form explicit flow equations respectively for the adsorbed layer flow and the intermediate fluid flow. The results respectively obtained from full MDS and Zhang's multiscale flow equations were then compared.

Multiscale Mixed Elastohydrodynamics in Inclined Fixed Pad Thrust Bearing Involving Surface Roughness and Low Clearance

The film pressures, surface separation profiles and carried loads of the hydrodynamic inclined fixed pad thrust bearing with the sandwich films were calculated by the multiscale approach when the bearing clearance was low and the combined effects of the adsorbed layer, the surface roughness and the surface elastic deformation were incorporated; The sandwich film consists of two physically adsorbed layers respectively on the coupled bearing surfaces and the intermediate continuum fluid film. The results show that the surface roughness intrinsically generates the film pressure ripples, but the rough surface is somewhat flattened and the film pressure ripples are a bit reduced by the surface elastic deformation. For a given sliding speed and a given original bearing clearance, the surface elastic deformation results in the significant reductions of both the maximum film pressure and the carried load of the bearing especially for a strong fluid-bearing surface interaction. In spite of this, the slope of the increase of the bearing load with the magnitude () of the surface roughness is nearly the same for the elastic surfaces with that for the rigid surfaces. The presence of the surface roughness does not qualitatively alter the influence of the surface elastic deformation on the performance of the bearing.

Feminine Metaphorical Language: Platonic Resonances in Origen of Alexandria

Abstract This article explores the use of feminine metaphorical language in the works of Plato and Origen. Drawing from Hanne Løland’s definition of gendered metaphorical language, it examines how Plato and Origen both inherit and challenge the stereotypical use of feminine metaphorical language to advance their philosophical and theological agendas. While partially adhering to the stereotypical uses of gendered metaphorical language, both Plato and Origen navigate beyond them to conceptualize a fluid and multifaceted feminine continuum. By anchoring the analysis in Plato’s Symposium and Timaeus and in Origen’s exegetical works, the article demonstrates how both authors represent intellectual ascent and spiritual transformation through feminine metaphors. In this regard, the article suggests the possibility that Origen inherited this feminine continuum from Plato’s philosophy. Through this comparative analysis, the article contributes to a deeper understanding of feminine metaphorical language in ancient philosophy and theology, thus challenging a simplistic interpretation of gendered metaphorical language. Overall, the article underscores the complex interplay between cultural constructs, philosophical frameworks, and gender representations in the intellectual legacies of Plato and Origen.

Revisiting the governing equations of a magnetic suspension of polar particles: From microhydrodynamics analysis to rheological response

In this review, we describe a formulation for the stress tensor of a monodisperse magnetic suspension of polarized neutrally buoyant spheroidal particles suspended in a non-magnetic liquid. A magnetic suspension affords a rare example of a material for which the stress tensor is non-symmetric. The present formulation is based on a microhydrodynamics description of a spherical particle suspended in a Newtonian fluid subjected to magnetic forces and torques. The magnetic suspension is considered statistically homogeneous and treated as being a homogeneous equivalent fluid. Under this condition, a volume average over all particles in the carrier fluid is used in order to obtain the magnetization equation evolution and the constitutive equation for the stress tensor of the magnetic suspension, in particular the magnetic stress contribution. The average effects on the homogeneous continuum fluid due to particle pressure, particle dipole, and the applied magnetic field on each particle are computed by our constitutive equation. In this approach, the particles are not considered force or torque free since their permanent magnetization allows them to experience the effects of an applied magnetic field. The calculated stress tension can be used for modeling common flows of symmetric or non-symmetric magnetic fluids flowing in arbitrary geometries and in rheological applications for determination of important properties such as the rotational viscosity of non-symmetric magnetic fluids. The final expression of the constitutive equation for the stress tensor based on a particle scale approach presents some difference as compared with current constitutive models proposed in the current literature. Our constitutive equation considers the effect of a magnetic particle pressure, the average particle stresslet contribution in terms of an effective viscosity, the average particle rotlet in terms of a rotational viscosity, and a configurational tensor associated with dipole–dipole interactions. In addition, we discuss the situation in which the dipole moment of the particle is not frozen on it which leads to the necessity of an internal balance of angular momentum in a fluid element to close the governing equations of the model. An extension of the model for emulsions of polar deformable droplets is also proposed.

Rate-limiting factors in thin-film evaporative heat transfer processes

In this paper, we present a theoretical study aimed at investigating the rate-limiting factors in thin-film evaporative heat transfer processes, considering the finite-rate evaporation kinetics. The problems of evaporation of a flat thin-film in either pure vapours or vapour-inert-gas mixtures are analysed based on the non-dimensionalised macroscopic transport equations for continuum fluids, coupled with out-of-equilibrium kinetic boundary conditions. Both the full numerical solutions and asymptotic analytical solutions at slow evaporation limit are provided and applied to analyse thin water film evaporation. Existing solutions, assuming negligible heat transfer in the gas domain, or negligible temperature jump across the non-equilibrium kinetic layer, or more boldly a thermodynamically equilibrial interface (i.e. its temperature is at the saturation temperature), can be fully recovered from the more general solutions presented here. Our results show that while these assumptions hold in special cases, they can lead to significant errors in many conditions, especially when the film thickness δ is reduced to a few micrometers or thinner. We show that the conventional views that the rate-limiting factors in thin-film evaporative heat transfer is either the heat diffusion through the liquid film or the mass transfer in the gas domain only apply to thick film (i.e. δ≫λ where λ is the mean free path in the vapour phase). As δ decreases to a few micrometer or smaller (more precisely when the Knudsen number Kn increases beyond O(1) in an pure vapour environment or when the kinetic Peclet number Pe is reduced below O(1) in inert gases), the interfacial thermal resistance due to the evaporation kinetics can be on the same orders of magnitude as the thermal resistance in the liquid film. The analysis also allow us to compare the heat transfer processes during the evaporation of a thin-film in pure vapours to those in inert gases, providing deeper insight into the effectiveness of various strategies for exploring the evaporation process in practical thermal management.

Experimental and Theoretical Insights into Interfacial Properties of 2D Materials for Selective Water Transport Membranes: A Critical Review.

Interfacial properties, such as wettability and friction, play critical roles in nanofluidics and desalination. Understanding the interfacial properties of two-dimensional (2D) materials is crucial in these applications due to the close interaction between liquids and the solid surface. The most important interfacial properties of a solid surface include the water contact angle, which quantifies the extent of interactions between the surface and water, and the water slip length, which determines how much faster water can flow on the surface beyond the predictions of continuum fluid mechanics. This Review seeks to elucidate the mechanism that governs the interfacial properties of diverse 2D materials, including transition metal dichalcogenides (e.g., MoS2), graphene, and hexagonal boron nitride (hBN). Our work consolidates existing experimental and computational insights into 2D material synthesis and modeling and explores their interfacial properties for desalination. We investigated the capabilities of density functional theory and molecular dynamics simulations in analyzing the interfacial properties of 2D materials. Specifically, we highlight how MD simulations have revolutionized our understanding of these properties, paving the way for their effective application in desalination. This Review of the synthesis and interfacial properties of 2D materials unlocks opportunities for further advancement and optimization in desalination.

Computational fluid dynamics method for determining the rotational diffusion coefficient of cells

This work presents a straightforward computational method to estimate the rotational diffusion coefficient (Dr) of cells and particles of various sizes using the continuum fluid mechanics theory. We calculate the torque (Γ) for cells and particles immersed in fluids to find the mobility coefficient μ and then obtain the Dr by substituting Γ in the Einstein relation. Geometries are constructed using triangular mesh, and the model is solved with computational fluid dynamics techniques. This method is less intensive and more efficient than the widely used models. We simulate eight different particle geometries and compare the results with previous literature.

Predicting lift and drag coefficients during hypersonic Mars reentry using hyStrath

During hypersonic reentry, a spacecraft experiences several different fluid flow regimes, which usually require the application of different software frameworks to simulate the respective regimes. This study aims to evaluate the hyStrath library for predicting aerodynamic lift and drag coefficients of complex three-dimensional (3D) geometries during hypersonic Mars reentry, using flight data of the Viking 1 mission as reference. A range of altitudes (h=30−140 km) and Mach numbers (M=13−24) where flight data is available is considered, covering the rarefied, transitional, and continuum fluid flow regimes. The hyStrath library contains a set of modified solvers and state-of-the-art thermophysical and chemistry models within the framework of OpenFOAM, dedicated to modeling high-enthalpy hypersonic flow problems. Depending on the flow regime, the computational fluid dynamics solver hy2Foam or direct-simulation Monte Carlo solver dsmcFoam+ are employed in the study. Because hyStrath is based on OpenFOAM, it allows the use of an unstructured adaptive mesh refinement approach for arbitrary geometries. We obtain excellent results throughout all investigated flow regimes and Mach numbers with an average deviation of 1.5% and 2% from the measured lift and drag coefficients, respectively. The applicability of the framework for accurately modeling both rarefied and continuum Mars reentry problems of complex 3D geometries such as the Viking capsule is demonstrated.

Numerical study of Two-Phase flow behavior during dryout in a Two-Phase closed thermosyphon under thermal boundary conditions

This paper presents a two-dimensional axisymmetric two-phase closed thermosyphon (TPCT) model filled with R-134a refrigerant using the Volume of Fluid (VOF) method, Lee model, and Continuum Surface Force (CSF) method within Computational Fluid Dynamics (CFD) and simulates the flow characteristics inside the TPCT during the occurrence of dry out. Specifically, it discusses the two-phase flow in the condensation and evaporation sections when dry out occurs. The results indicate that the condensation section exhibits varying forms of vapor–liquid interface waves at different times. Phenomena such as liquid carryover and entrainment become increasingly prominent over time, contributing significantly to refrigerant blockages and dryout in the evaporation section. The mechanism behind dryout in the evaporation section is revealed to be the result of the initially continuous falling film being disrupted by fluctuations in the liquid–vapor interface, leading to the premature drying of thin liquid films in the troughs of these waves.

Statistical characterization of the collective synchrotron radiation power emitted by non-ideal magnetized plasma fluids in relativistic jets

The problem of determining the collective synchrotron radiation power emitted by non-ideal magnetized plasma fluids at kinetic equilibrium in relativistic jets is addressed. A covariant statistical kinetic approach is implemented based on a novel solution for the corresponding non-isotropic kinetic distribution function (KDF). This is expressed by a Gaussian-like solution that is consistent with relativistic magnetic moment conservation holding in collisionless magnetized plasmas and predicts tensorial equation of state and pressure anisotropy which are specific for these systems. Notably, the same equilibrium admits also a convergent integrable Chapman–Enskog series expansion around a leading-order Juttner distribution, which affords the analytical calculation of continuum fluid fields. In this reference, it is shown that the statistical average of total synchrotron power evaluated over the non-isotropic KDF differs significantly from the corresponding ensemble estimate that would be trivially obtained if the underlying velocity distribution were purely isotropic. It is pointed out that the knowledge of such a statistical discrepancy on the radiation-power curve could provide an independent framework for the characterization of the physical properties of the relativistic plasma state or of the background magnetic field that permeates these astrophysical scenarios.

Multiscale Elastohydrodynamic Wedge-Platform Thrust Bearing with Ultra Low Clearance

The effect of the surface elastic deformation is investigated by the multiscale approach in the hydrodynamic wedge-platform thrust bearing with the ultra low clearance on the 1nm scale, by incorporating both the non-continuum pure adsorbed layer flow and the multiscale “sandwich” film flow. The pure adsorbed layer flow in ultra small surface separations is described by the non-continuum nanoscale flow equation; The “sandwich” film flow is described by the multiscale flow equations respectively for the adsorbed layer flow and the intermediate continuum fluid flow. The numerical calculation results show that in the studied bearing, the effect of the surface elastic deformation is normally significant, it pronouncedly reduces the maximum film pressure, greatly changes both the film pressure profile and the surface separation profile, and considerably increases the minimum surface separation, which occurs on the exit of the bearing. The effect of the surface elastic deformation is shown to be obviously dependent on the fluid-bearing surface interaction.

The Sentient Cell: Implications for Osteopathic Medicine.

The Foundation of Osteopathic Research and Clinical Endorsement (FORCE) is an organization that includes various figures involved in clinical and non-profitresearch and does not depend on any private or government body. To better understand how the human body behaves, we need to observe cellular behavior. Considering the human body as layers, districts, and regions, or just as a machine, is severely limiting to understanding the systemic mechanisms that are implemented to maintain bodily health. For some years, FORCE has contributed several articles to the literature to support the view of a human body as a unit, a fascial continuum (solid and fluid fascia) capable of interacting consciously, and not as a passive mirror, with respect to external stresses. The article reviews the tensegrity theory applied to the cell, trying to bring to light that the mechanistic vision on which this theory is based does not meet biological reality. We review some concepts related to biology, the science that studies life, and quantum physics, the science that studies the invisible physical phenomena that underlie life. Understanding that the cells and tissues are aware of the therapeutic approaches they receive could better guide the decisions of the osteopathic clinician.

What Is the Nexus between Migration and Mobility? A Framework to Understand the Interplay between Different Ideal Types of Human Movement

Categorising certain forms of human movement as ‘migration’ and others as ‘mobility’ has far-reaching consequences. We introduce the migration–mobility nexus as a framework for other researchers to interrogate the relationship between these two categories of human movement and explain how they shape different social representations. Our framework articulates four ideal-typical interplays between categories of migration and categories of mobility: continuum (fluid mobilities transform into more stable forms of migration and vice versa), enablement (migration requires mobility, and mobility can trigger migration), hierarchy (migration and mobility are political categories that legitimise hierarchies of movement) and opposition (migration and mobility are pitted against each other). These interplays reveal the normative underpinnings of different categories, which we argue are too often implicit and unacknowledged.

Grad's 13 moments-based gas kinetic flux solver with triangle unstructured meshes for simulating continuum and rarefied fluid flows

A numerical framework based on the gas kinetic flux solver (GKFS) with unstructured meshes of triangle cells has been proposed and assessed in this work. Like conventional GKFS, the present scheme only updates the cell-average macroscopic conservative variables in time, thereby saving computational costs. At each cell interface, the numerical normal flux is computed with the GKFS scheme proposed by Liu et al. [J. Comput. Phys. 415, 109548 (2020)], in which the distribution functions at the surrounding points are reconstructed with the Grad's 13 moments (G13). Additionally, a solid wall boundary condition treatment has been proposed in the present G13-GKFS framework, which allows one to model from purely specular to perfectly thermalized solid walls. The present framework has been validated with the steady cylindrical Couette flow, the lid-driven cavity flow, the unsteady Rayleigh flow, and the rarefied flow around the NACA0012 airfoil test-cases, where good agreements are found with references for a quite wide range of flow regimes, from continuum to transitional flow regimes.

Effect of inhomogeneous structure on the water desalination performance of graphitic carbon nitride nanochannels: A molecular dynamics study

The transport behaviors of aqueous solution in two-dimensional (2D) nanomaterial-based separation membranes are correlated with the structure of the nanoconfined geometry. However, little is known about the impact of asymmetric structures on the transport behavior of aqueous solutions in membranes. In this work, we use molecular dynamics (MD) simulations to investigate the transport behaviors of aqueous solution in non-parallel stacked graphitic carbon nitride (g-C3N4) nanochannels. Interestingly, the non-parallel stacking of g-C3N4 could lead to the local aggregation of water, resulting in an inhomogeneous density distribution within the nanochannel. The high-density region in g-C3N4 nanochannel significantly disrupted the continuum fluid of water. Moreover, the inhomogeneous density distribution of water could impede ion transport in the non-parallel g-C3N4 nanochannel. It was found that ions cannot maintain compact hydration structures in the high-density region. This work reveals the unique properties of slightly tilted membrane structures, providing novel perspective for the design of next-generation nanofluidic devices.

The Transformation of the Ottoman State’s Relationship with the Nusayri/ʿAlawi Community in the Nineteenth Century

ABSTRACT This article aims to examine the changing nature of the Ottoman central administration’s policies towards Nusayris in the nineteenth century. In different contexts of space and time, the Ottoman authorities employed different measures of collaboration, oppression and persecution, while the Nusayris responded to these policies by either resistance or accommodation. Drawing on various sources from the Ottoman archives, the article singles out various contexts in time and space, in which the Ottoman state – both centrally and locally – condemned them as ‘heretics’ or, alternatively within this fluid continuum, accommodated them to local political and administrative practice and needs. A close analysis of the practices and the terminology brought to bear in dealing with the Nusayris suggests an adaptive, ever changing and dynamic relationship of the state to these parts of the population. The findings presented here thus urge the historicization of instances of persecution and marginalization in order to come to terms with complex religio-political entanglements and, finally, to delineate a more nuanced perspective on the history of this community in the late Ottoman Empire.

Estimating water transport in carbon nanotubes: a critical review and inclusion of scale effects.

The quasi-frictionless water flow across graphitic surfaces offers vast opportunities for a wide range of applications from biomedical science to energy. However, the conflicting experimental results impede a clear understanding of the transport mechanism and desired flow control. Existing literature proposes numerous modifications and updated boundary conditions to extend classical hydrodynamic theories for nanoflows, yet a consensus or definitive conclusion remains elusive. This study presents a critical review of the proposed modifications of the pressure driven flow or the Hagen-Poiseuille (HP) equations to estimate the flow enhancement through carbon nanotubes (CNTs). For such a case, we performed (semi-)classical molecular dynamics simulations of water flow in various sizes of CNTs, applied the different forms of boundary definitions from the literature, and derived HP equation models by implementing these modifications. By aggregating seven distinct experimental datasets, we tested various flow enhancement models against our measurements. Our findings indicate that including the interfacial layering-based dynamic slip-definition in the proposed HP equations yields accurate estimations. While considering interfacial viscosity predicts the individual CNT experiments well, using the experimental viscosity yields better estimations of measurements for the water flow enhancement through membranes of CNTs. This critical review testing existing literature demonstrates how to refine continuum fluid mechanics to predict water flow enhancement at the nanoscale providing holistic multiscale modeling.

MULTISCALE SIMULATION OF HYDRODYNAMIC STEP BEARING WITH ULTRA-LOW CLEARANCE INVOLVING SURFACE ROUGHNESS

The numerical calculation was carried out for the multiscale hydrodynamic step bearing with ultra-low clearance and nanoscale surface roughness based on the newly developed multiscale approach. The moving surface was assumed as perfectly smooth and the stationary surface was imposed with the sinusoidal surface roughness. Due to the surface roughness, locally the physically adsorbed boundary layer may be only present, while in other areas, the sandwich films consisting of both the adsorbed boundary layers and the intermediate continuum fluid film may be present. In this bearing, the fluid film may be locally severely squeezed so that the local film pressure is very high. In this circumstance, the influences of the film pressure on both the film viscosity and density were considered. The results show that with the increase of the surface roughness, the hydrodynamic pressure and carried load of the bearing are very significantly increased especially for a stronger fluid-bearing surface interaction; the fluid piezo-viscous effect becomes stronger with the increases of both the surface roughness and the fluid-bearing surface interaction strength.

Overcoming passivation through improved mass transport in dense ionic fluids.

Deep Eutectic Solvents (DESs) have recently been shown to be part of a dense ionic fluid continuum between ionic liquids and concentrated aqueous brines. Charge transport was shown to be governed by fluidity, with no discontinuity between molar conductivity and fluidity irrespective of cation, charge density or ionic radius. By adjusting the activity of water and chloride ions, mass transport, speciation and reactivity can be altered. It has been shown that while brines provide a high chloride content at a lower viscosity than DESs, unlike DESs, brines are unable to prevent metal passivation due to their high water content. This results in the possibility to impart a level of selectivity towards metal dissolution (or passivation) when processing mixed metal materials. Forced convection can be used to avoid the issue of slow mass transport in viscous media, and the use of jets or targeted ultrasound are effective methods for overcoming this issue. High-powered ultrasound was applied to copper, cobalt, and aluminium electrodes undergoing anodic dissolution, and linear sweep voltammetry showed a linear current-voltage response at potentials anodic of the oxidation potential under sonication, with total charge passed being 5 to 134 times greater than under silent conditions. Application of ultrasound to silver and nickel electrodes displayed an initial linear current-voltage response, but the increased water content of the brines resulted in passivation. Mass transport throughout the bulk solution is governed by the forced convection imparted by the ultrasound and ionic species must only migrate across the electrical double layer. It is shown that the anodic dissolution of a range of metals classically expected to passivate, e.g. aluminium, can be significantly accelerated under insonation conditions.