Classical Fluid Research Articles

A transition point for the blood flow wall shear stress environment in the human fetal left ventricle during early gestation

Development of the fetal heart is a fascinating process that involves a tremendous amount of growth. Here, we performed image-based flow simulations of 3 human fetal left ventricles (LV), and investigated the hypothetical scenario where the sizes of the hearts are scaled down, leading to reduced Reynolds number, to emulate earlier fetal stages. The shape and motion of the LV were retained over the scaling to isolate and understand the effects of length scaling on its fluid dynamics. We observed an interesting cut-off point in Reynolds number (Re), across which the dependency of LV wall shear stress (WSS) on Re changed. This was in line with classical fluid mechanic theory where skin friction coefficient exhibited first a decreasing trend and then a plateauing trend with increasing Re. Below this cut-off point, viscous effects dominated, stifling the formation of LV diastolic vorticity structures, and WSS was roughly independent of Reynolds number. However, above this cut-off, inertial effects dominated to cause diastolic vortex ring formation and detachment, and to cause WSS to scale linearly with Reynolds number. Results suggested that this transition point is found at approximately 11 weeks of gestation. Since WSS is thought to be a biomechanical stimuli for growth, this may have implications on normal fetal heart growth and malformation diseases like Hypoplastic Left Heart Syndrome.

Superdiffusion of quantized vortices uncovering scaling laws in quantum turbulence

Generic scaling laws, such as Kolmogorov's 5/3 law, are milestone achievements of turbulence research in classical fluids. For quantum fluids such as atomic Bose-Einstein condensates, superfluid helium, and superfluid neutron stars, turbulence can also exist in the presence of a chaotic tangle of evolving quantized vortex lines. However, due to the lack of suitable experimental tools to directly probe the vortex-tangle motion, so far little is known about possible scaling laws that characterize the velocity correlations and trajectory statistics of the vortices in quantum-fluid turbulence, i.e., quantum turbulence (QT). Acquiring such knowledge could greatly benefit the development of advanced statistical models of QT. Here we report an experiment where a tangle of vortices in superfluid 4He are decorated with solidified deuterium tracer particles. Under experimental conditions where these tracers follow the motion of the vortices, we observed an apparent superdiffusion of the vortices. Our analysis shows that this superdiffusion is not due to Lévy flights, i.e., long-distance hops that are known to be responsible for superdiffusion of random walkers. Instead, a previously unknown power-law scaling of the vortex-velocity temporal correlation is uncovered as the cause. This finding may motivate future research on hidden scaling laws in QT.

Electrically isolated propagating streamer heads formed by strong electron attachment

Streamer discharges occur in the early stages of electric breakdown of gases in lightning, as well as in plasma and high voltage technology. They are growing filaments characterized by a curved charge layer at their tip that enhances the electric field ahead of them. In this study, we analyze the effect of strong electron attachment on the propagation of positive streamers. Strong attachment occurs in insulating gases like sulphur hexafluoride (SF6) or in air at increased density. We use the classical fluid approximation with photo-ionization for streamers in ambient air, and we artificially increase the electron attachment rate where the field is below the breakdown value. This modification approximates air pressures above 1 bar at room temperature. We find that the streamer head can keep propagating even though the ionized channel loses its conductivity closely behind the head; hence, even if it is electrically isolated. We describe how, depending on the attachment rate, the streamer propagation in a constant electric field can be accelerating, uniformly translating, or stagnating.

Universal relations for dipolar quantum gases

We establish that two-dimensional dipolar quantum gases admit a universal description, i.e., their thermodynamic properties are independent of details of the interaction at short distances. The only relevant parameters are the dipole length as well as the scattering length of the combined short-range plus dipolar interaction potential. We derive adiabatic relations that link the change in the thermodynamic potentials with respect to the scattering length and the dipole length to a generalized Tan contact parameter and a new dipolar contact, which involves an integral of a short-distance regularized pair distribution function. These two quantities determine the scale anomaly in the difference between pressure and energy density and also the internal energy in the presence of a harmonic confinement. For a weak transverse confinement, configurations with attractive interactions appear, which lead to a density-wave instability beyond a critical strength of the dipolar interaction. We show that this instability essentially coincides with the onset of a roton minimum in the excitation spectrum and may be understood in terms of a quantum analog of the Hansen-Verlet criterion for freezing of a classical fluid.

Nonequilibrium ensemble derivation of hydrodynamic heat transport and higher-order generalizations

Thermal transport in classical fluids is analyzed through higher-order generalized hydrodynamics (or mesoscopic hydrothermodynamics) depending on the evolution of the energy density and its fluxes of all orders. It is derived by a kinetic theory based on the nonequilibrium statistical ensemble formalism. A general system of coupled evolution equations is derived. Maxwell times, which are of significance to determine the character of the motion, are derived. They also have an important role in the choice of the contraction of description (limitation in the number of fluxes to be retained) in the studies on hydrodynamic motions. In a description of order 1, an analysis of the technological process of thermal prototyping is presented.

Combined testing of cerebrospinal fluid IL-12 (p40) and serum C-reactive protein as a possible discriminator of acute bacterial neuroinfections

IntroductionCentral nervous system infections (CNS) are life-threatening diseases, with meningitis being the most common. Viral infections are usually self-limiting diseases but bacterial pathogens are associated with higher mortality rates and persistent neurological sequelae. We aimed to study the role of IL-6, IL-8, IL-10, IL-12(p40), TNF-α cytokines, classical cerebrospinal fluid (CSF) parameters, and serum C-reactive protein levels (CRP) for discriminating bacterial from viral central nervous system infections. Material and methodsThis prospective study included 80 patients with clinical signs and abnormal cerebrospinal fluid laboratory findings typical for neuroinfection admitted to St. George University Hospital-Plovdiv. Routine methods such as direct microscopy, culturing and identification were used for microbiological analysis as well as latex-agglutination test and multiplex PCR. Cytokines' concentrations were measured by ELISA. CRP and CSF parameters were collected from the patients' medical records. ResultsWe observed the highest discriminatory power among cytokines for cerebrospinal IL-12(p40) (AUC = 0.925; p = 0.000). CSF protein levels were the best predictor for bacterial neuroinfection (AUC = 0.973; p = 0.000). The AUC for the serum CRP as a stand-alone biomarker was estimated to be 0.943. The discriminatory power can be increased up to 0.995 (p = 0.000) when combining cerebrospinal fluid IL-12(p40) and serum CRP, with an optimal cut-off value of 144 (Sensitivity 100%; Specificity 90.9%). ConclusionThe combined testing of CSF IL-12(p40) and serum CRP is associated with the highest diagnostic accuracy.

Some applications of extended calculus to non-Newtonian flow in pipes

Fractional and non-Newtonian calculus are an extension of classical calculus, usually known for providing new mathematical tools useful in science, developed from alternative approaches. Among fractional calculus, Riemann-Liouville and Caputo fractional derivatives have been the most popular operators employed in spite of their complexity. In this work, two novel and compact methods are presented as an alternative to the fractional calculation options. To test the feasibility of proposed methods, three classical fluid mechanic problems are studied: the flow through circular pipe, parallel plates and annulus, by modifying the constitutive equations into their fractional equivalent. On the other hand, a new weighted non-Newtonian derivative is proposed to extend the possibilities to model fluid viscosity based on the influence of nonadjacent layers, using the pipe flow as an example. Results show that proposed fractional models can describe shear-thinning and shear-thickening behaviors depending on the fractional order of the derivative, while the weighted derivative allows to expand the way viscosity is modeled, demonstrating the suitability of these approaches to describe physical problems.

Particle size and phase equilibria in classical logarithmic fluid

An interparticle interaction potential has been recently proposed in studies of condensate-like systems described by logarithmically nonlinear equations, such as the superfluid helium-4 and Korteweg-type melts. It has the shape of a Gaussian multiplied by a linear function and can switch between the attraction and repulsion regimes as the distance varies. We consider a classical fluid model with a discretized version of this potential in Monte Carlo molecular simulations in the Gibbs ensemble. We demonstrate a two-phase system consisting of a dense “liquid” phase in coexistence with a significantly less dense “vapour” phase. For computations, the particle size term in the potential was varied to determine its effect on both the phase envelope and the critical point of the system. It is found that the logarithm of the dimensionless critical temperature decreases in a sigmoid fashion with increasing particle size, while the critical density may be directly proportional to the particle size.

Numerical study of flow and heat transfer in a porous medium between two stretchable disks using quasi-linearization method

In this study, the flow as well as heat transfer of a classical Newtonian fluid of constant density and viscosity in a porous medium between two radially stretching disks is explored. The role of the porosity of the medium, the stretching of the disks, the viscous dissipation, and radiation on the flow and temperature fields is taken into account. The flow and heat equations are transformed into non-linear ODE by invoking the classical similarity transformations. These non-linear differential equations were linearized using Quasi linearization method. Further the linearized equations were discretized by employing the finite differences which were then solved numerically using the successive over relaxation parameter method. Some features of the flow and temperature are discussed in detail in the form of tables and graphs. The present study may be beneficial in lubricants and computational storage devices as well as fluid-flows and heat transmission in rotor-stator systems.

On the Use of Perturbation Theory in Eigenvalue Problems

The importance of perturbation theory in many fields is very clear through almost a century or even more. Its importance was exemplified in solving many problems in physics and other applied fields. A great deal of applications arose in dealing with eigenvalue problems especially in quantum mechanics in conjunction with the field of atomic physics. Accordingly, it came to our mind to write a brief review article on the subject. At the beginning, we give some important definitions to do with various eigenvalue problems; then we introduce concepts that have to do with perturbation theory and the techniques used in such a theory, beginning with the algebraic perturbation theory giving a good number of examples from the literature on the use of the theory in solving integral equation, algebraic equations and differential equations. Few applications are then given in applied fields such as classical mechanics, quantum mechanics and fluid mechanics. Finally, a concluding discussion is given which is related to the use of the theory.

Quantum Fluctuations of Energy in Subsystems of a Hot Relativistic Gas

We derive a formula that defines quantum fluctuations of energy in subsystems of a hot relativistic gas. For small subsystem sizes we find substantial increase of fluctuations compared to those known from standard thermodynamic considerations. However, if the size of the subsystem is sufficiently large, we reproduce the result for energy fluctuations in the canonical ensemble. Our results are subsequently used in the context of relativistic heavy-ion collisions to introduce limitations of the concepts such as classical energy density or fluid element. In the straightforward way, our formula can be applied in other fields of physics, wherever one deals with hot and relativistic matter.

Time-dependent study of blood flow in an aneurysmic stenosed coronary artery with inelastic walls

Coronary arteries are a family of arteries that are indulged in the supply of oxygenated blood to the muscles of the heart. These blood vessels envelop the entire heart. These blood vessels encounter a common disturbance in which the vessel wall gets thickened leading to the blockage of the vessel lumen. Also, an uncommon condition seen is the development of a protruding bulging structure outward the lumen. The common disturbance seen is the stenosis of the artery whereas the uncommon bulging is the aneurysm. In the present paper, a discussion on the two-dimensional simulation of blood flow across the computationally constructed coronary arterial domain with clinical measurements is made. The arterial segment is assumed to have an aneurysm protrusion as well as a plaque developed due to stenosis. The velocity profile, pressure profile, and the wall shear stress patterns observed are enunciated by treating blood as a classical Newtonian fluid. The results show that the spots below the aneurysm are prone to develop new sacs and lesions. The main innovations of this study are: a) identifying the most probable spots for new plaque development; b) the interrelation between the flow characteristics due to the presence of stenosis and the aneurysm sac.

Grid-algorithm improvements for dense suspensions of discrete element particles in finite element fluid simulations

For homogeneous systems like classical fluid dynamics and structural mechanics, finite element method (FEM) grid generation has reached a mature state. On the other hand, for multi-physics-problems like fluids with a high density of immersed particles, many researchers may not even be aware of the types of instabilities which may be triggered by unsuitable meshes. We review common types of grid generation, point out previously unrecognised types of instabilities for particles in fluids as well as remedies to obtain particle-fluid simulations with higher stability and fewer redundant degrees of freedom.

Generalized Van der Waals Equation for Liquid-Vapor Equilibria in a Stationary Gravitational Field

The behavior of liquids undergoing phase transition in the gravitational field is studied by considering the generalized Van der Waals equation. Considering the two simple models for liquid-vapor boundary of a pure classical fluid, the generalized Van der Waals equation shows how the three critical parameters (critical temperature, critical volume and critical pressure), suffice to describe the reduced state parameters (reduced temperature, reduced volume and reduced pressure), the concentration profile and the liquid-vapor boundary position, which can be used to observe transition phenomenon. This model shows how the form of the equation can influence the vertical phase separation induced by the stationary gravitational field, and on the gas condensation effects.

Magneto-hydrodynamic flow of Reiner-Philippoff fluid: Stability analysis

Analysis of magneto-hydrodynamic flow of classical non-Newtonian fluid, Reiner-Philippoff fluid, over magnetized plate is conducted numerically in this article. The mathematical model incorporates the non-linear stress deformation behavior of Reiner-Philippoff fluid and set of Maxwell’s equations to discuss the behavior of non-Newtonian fluid in a magnetic field. Boundary layer equations are obtained assuming the Reynolds and magnetic Reynolds numbers to be large enough for magnetic and momentum boundary layers to have developed. The correlation expressions for skin friction and magnetic flux on the surface for different flow and magnetic field parameters are developed by performing linear regression on numerical data. Stability analysis is conducted as well to analyze the effects of magnetic field and fluid nature on the stability of the flow.

On the flow of MHD generalized maxwell fluid via porous rectangular duct

Abstract The purpose of this proposed investigation is to study unsteady magneto hydrodynamic (MHD) mixed initial-boundary value problem for incompressible fractional Maxwell fluid model via oscillatory porous rectangular duct. Considering the modified Darcy’s law, the problem is simplified by using the method of the double finite Fourier sine and Laplace transforms. As a limiting case of the general solutions, the same results can be obtained for the classical Maxwell fluid. Also, the impact of magnetic parameter, porosity of medium, and the impact of various material parameters on the velocity profile and the corresponding tangential tensions are illuminated graphically. At the end, we will give the conclusion of the whole paper.

Topological transition from superfluid vortex rings to isolated knots and links

Knots and links are fundamental topological objects play a key role in both classical and quantum fluids. In this research, we propose a novel scheme to generate torus vortex knots and links through the reconnections of vortex rings perturbed by Kelvin waves in trapped Bose-Einstein condensates. We observe a new phenomenon in a confined superfluid system in which the transfer of helicity between knots/links and coils can occur in both directions with different pathways. The pathways of topology transition can be controlled through designing specific initial states. The generation of a knot or link can be achieved by setting the parity of the Kelvin wave number. The stability of knots/links can be improved greatly with tunable parameters, including the ideal relative angle and the minimal distance between the initial vortex rings.

Hybrid continuum-molecular modeling of fluid slip flow

Experiments on fluid systems in micro-/nano-scale solid conveyors have shown a violation of the no-slip assumption that has been adopted by the classical fluid mechanics. To correct this mechanics for the fluid slip, various approaches have been proposed to determine the slip boundary conditions. However, these approaches have revealed contradictory results for a variety of systems, and a debate on the mechanisms and the conditions of the fluid slip/no-slip past solid surfaces is sustained for a long time. In this paper, we establish the hybrid continuum-molecular modeling (HCMM) as a general approach of modeling the fluid slip flow under the influence of excess fluid–solid molecular interactions. This modeling approach postulates that fluids flow over solid surfaces with/without slip depending on the difference between the applied impulse on the fluid and a drag due to the excess fluid–solid molecular interactions. In the HCMM, the Navier–Stokes equations are corrected for the excess fluid–solid interactions. Measures of the fluid–solid interactions are incorporated into the fluid’s viscosity. We demonstrate that the correction of the fluid mechanics by the slip boundary conditions is not an accurate approach, as the fluid–solid interactions would impact the fluid internally. To show the effectiveness of the proposed HCMM, it is implemented for the water flow in nanotubes. The HCMM is validated by an extensive comparison with over 90 cases of experiments and molecular dynamics simulations of different fluid systems. We foresee that the HCMM of the fluid slip flow will find many important implementations in fluid mechanics.

Lbmpy: Automatic code generation for efficient parallel lattice Boltzmann methods

Lattice Boltzmann methods are a popular mesoscopic alternative to classical computational fluid dynamics based on the macroscopic equations of continuum mechanics. Many variants of lattice Boltzmann methods have been developed that vary in complexity, accuracy, and computational cost. Extensions are available to simulate multi-phase, multi-component, turbulent, and non-Newtonian flows. In this work we present lbmpy, a code generation package that supports a wide variety of different lattice Boltzmann methods. Additionally, lbmpy provides a generic development environment for new schemes. A high-level domain-specific language allows the user to formulate, extend and test various lattice Boltzmann methods. In all cases, the lattice Boltzmann method can be specified in symbolic form. Transformations that operate on this symbolic representation yield highly efficient compute kernels. This is achieved by automatically parallelizing the methods, and by various application-specific automatized steps that optimize the resulting code. This pipeline of transformations can be applied to a wide range of lattice Boltzmann variants, including single- and two-relaxation-time schemes, multi-relaxation-time methods, as well as the more advanced cumulant methods, and entropically stabilized methods. lbmpy can be integrated into high-performance computing frameworks to enable massively parallel, distributed simulations. This is demonstrated using the waLBerla multiphysics package to conduct scaling experiments on the SuperMUC-NG supercomputing system on up to 147 456 compute cores.

Mean-field theory of inhomogeneous fluids.

The Barker-Henderson perturbation theory is a bedrock of liquid-state physics, providing quantitative predictions for the bulk thermodynamic properties of realistic model systems. However, this successful method has not been exploited for the study of inhomogeneous systems. We develop and implement a first-principles "Barker-Henderson density functional," thus providing a robust and quantitatively accurate theory for classical fluids in external fields. Numerical results are presented for the hard-core Yukawa model in three dimensions. Our predictions for the density around a fixed test particle and between planar walls are in very good agreement with simulation data. The density profiles for the free liquid vapor interface show the expected oscillatory decay into the bulk liquid as the temperature is reduced toward the triple point, but with an amplitude much smaller than that predicted by the standard mean-field density functional.