Sphere Fluid Research Articles

Double-Hard-Sphere perturbation theory: a perturbation theory that is less dependent on the value of the hard-sphere diameter

Perturbation theories for fluids of molecules with soft-repulsive cores, such as the Lennard-Jones fluid, are usually based on the description of a fluid of hard spheres of temperature-dependent, and sometimes also density-dependent, diameter. The results obtained from such theories are typically rather sensitive towards the value of this diameter. We here derive an alternative implementation of perturbation theory that significantly reduces this sensitivity. The method allows the development of perturbation theories for high-density fluids without necessitating a density-dependent hard-sphere diameter. We refer to the approach as double-hard-sphere (DHS) perturbation theory. When applied using a Weeks-Chandler-Andersen (WCA) division of the intermolecular potential, and considering the expansion up to first order in the Helmholtz energy, we recover the HS-WCA theory of Ben-Amotz and Stell [J. Phys. Chem. B 108, 6877 (2004)] if certain correlation integrals are neglected. The DHS expansion thereby provides a formal basis of the HS-WCA theory, clearly showing the underlying assumptions and how to improve on them. Applying the DHS expansion to a Barker-Henderson division of the Lennard-Jones (or Mie) potential is shown to extend the accuracy of the Barker-Henderson theory to densities up to the freezing density, leading to a substantial improvement in predicted fluid-solid equilibria.

Geometry of static w=-1/5 perfect fluid spheres in general relativity

We discuss the physical features of two recent classes of analytical solutions of the Einstein equations sourced by an exotic perfect fluid with equation of state P=-rho /5. These geometries depend on up to four parameters and are static and spherically symmetric. They describe compact spaces with naked central singularities.

Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids

For the Rayleigh–Taylor unstable arrangement of a viscous fluid sphere embedded in a finite viscous fluid spherical shell with a rigid boundary and a radially directed acceleration, a dispersion relation is developed from a linear stability analysis using the method of normal modes. aR1 is the radially directed acceleration at the interface. ρi denotes the density, μi is the viscosity, and Ri is the radius, where i = 1 is the inner sphere and i = 2 is the outer sphere. The dispersion relation is a function of the following dimensionless variables: viscosity ratio s=μ1μ2, density ratio d=ρ1ρ2, spherical harmonic mode n, B=R1aR1ρ22μ221/3, H=R2R1, and the dimensionless growth rate α=σμ2aR12ρ21/3, where σ is the exponential growth rate. We show that the boundedness provided by the outer spherical shell has a strong influence on the instability behavior, which is reflected not only in the modulation of the growth rate but also in the selection of the most unstable modes that are physically possible. This outer boundary effect is quantified by the relative magnitude of the radius ratio H. We find that when H is close to unity, lower order harmonics are excluded from becoming the most unstable within a vast region of the parameter space. In other words, the effect of H has precedence over the other controlling parameters d, B, and a wide range of s in establishing what the lowest most unstable mode can be. When H ∼ 1, low order harmonics can become the most unstable only for s ≫ 1. However, in the limit when s → ∞, we show that the most unstable mode is n = 1 and derive the dispersion relation in this limit. The exclusion of most unstable low order harmonics caused by a finite outer boundary is not realized when the outer boundary extends beyond a certain threshold length-scale in which case all modes are equally possible depending on the value of B.

Model of hybrid star with baryonic and strange quark matter in Tolman–Kuchowicz spacetime

The purpose of our work is to investigate some new features of a static anisotropic relativistic hybrid compact star composed of strange quark matter (SQM) in the inner core and normal baryonic matter distribution in the crust. Here we apply the simplest form of the phenomenological MIT bag model equation of state [Formula: see text] to correlate the density and pressure of strange quark matter within the stellar interior, whereas radial pressure and matter density due to baryonic matter are connected by the simple linear equation of state [Formula: see text]. In order to obtain the solution of the Einstein field equations, we have used the Tolman–Kuchowicz ansatz [R. C. Tolman, Static solutions of Einstein’s field equations for spheres of fluid, Phys. Rev. 55 (1939) 364–373; B. Kuchowicz, Acta Phys. Pol. 33 (1968) 541] and further derivation of the arbitrary constants from some physical conditions. Here, we examine our proposed model graphically and analytically in detail for physically plausible conditions. In particular, for this investigation, we have reported on the compact object Her [Formula: see text] [[Formula: see text]; [Formula: see text] km] in our paper as a strange quark star candidate. In order to check the physical validity and stability of our suggested model, we have performed various physical tests both analytically and graphically, namely, dynamical equilibrium of applied forces, energy conditions, compactness factor and surface redshift. Finally, we have found that our present model meets all the necessary physical requirements for a realistic model and can be studied for strange quark stars (SQS).

Anisotropic relativistic fluid spheres with a linear equation of state

In this work, we present a class of relativistic and well-behaved solution to the Einstein’s field equations for anisotropic matter distribution. We perform our analysis by using the Buchdahl ansatz for the metric function grr. Three different classes of new exact solution are found for anisotropy factor Δ. We have analyzed our model with various physical aspects such as pressure (radial as well as transverse), energy density, anisotropy factor, mass, compactness parameter, adiabatic index γ and surface redshift. A graphical analysis of energy conditions, TOV equation and causality condition indicates the model is well behaved. The physical acceptability of the model has been verified by considering compact objects with similar mass and radii, such as 4U 1820-30, Vela X-1, PSR J1614-2230, LMC X-4, SMC X-1, 4U 1538-52, Her X-1, Cyg X-2, PSR B1913+16 and PSR J1903+327.

Data-driven closure model for the drag coefficient of the creeping flow past a translating sphere in a shear-thinning viscoelastic fluid

A drag force closure model for particle-laden viscoelastic fluid flows is the key to describing the ensemble-averaged behavior of the mixture. The effects of fluid rheological properties on the flow dynamics of a spherical particle in viscoelastic fluids in the creeping flow regime are parameterized using the Giesekus rheological model. Direct numerical simulations are performed within a large range of Deborah number(0−10).The drag force of a sphere in unbounded Giesekus fluids decreases monotonically with the increase of Deborah number. The negative wake may occur when the viscosity ratio is larger than 0.6 in Giesekus fluids but is absent in Oldroyd-B fluids in all conditions. An explicit closure model for the drag coefficient of a sphere in Giesekus fluids is established using the backpropagation artificial neural network. The drag closure model provides a method for explicitly formulating the momentum exchange model for dilute suspensions of solid particles in shear-thinning viscoelastic fluids.

Experimental study on the entry of solid spheres into Newtonian and non-Newtonian fluids

This study experimentally investigates the entry of hydrophobic/hydrophilic spheres into Newtonian and Boger fluids. By considering solution of 82% glycerin and 18% water and solution of 80% glycerin, 20% water and 100 ppm polyacrylamide, Newtonian and Boger fluids are made, respectively. It has been tried that liquids' surface tension, density, and viscosity are almost the same. Thus, all dimensionless numbers are approximately the same at a similar impact velocity except for the elasticity number. A PcoDimaxS highspeed camera captures the spheres' trajectory from the impact to the end of the path. Regarding the range of released height (0.5–100 cm), the impact velocities are approximately in the range of 0.31–4.43 ms−1. The role of fluid elasticity in combination with the sphere surface wettability on the air cavity formation/evolution/collapse is mainly studied. Also, the kinetics of the sphere motion (velocity, acceleration, and hydrodynamic force coefficient) is studied. The results show that air drawn due to the sphere's impact with the Newtonian liquid is more, and the pinch-off takes place later. Also, shedding bubbles are cusped-shaped in the Boger fluid, while in the Newtonian fluid, they are elliptical. In addition, the most significant impact of surface wettability is observed in the Newtonian fluid. Finally, the results reveal that the sphere in the Newtonian fluid can move faster and travel a longer distance in a specific time interval. The differences observed are closely related to the viscoelastic fluid's elasticity property and extensional viscosity.

Wave Scattering by a Submerged Sphere in Three-Layer Fluid

Wave Scattering by a Submerged Sphere in Three-Layer Fluid

Motion of a sphere in a viscous fluid towards a wall confined versus unconfined conditions

In the present work, we investigate experimentally and numerically the motion of solid macroscopic spheres (Brownian and colloidal effects are negligible) when settling from rest in a quiescent fluid toward a solid wall under confined and unconfined configurations. Particle trajectories for spheres of two types of materials are measured using a high-speed digital camera. For unconfined configurations, our experimental findings are in excellent agreement with well-established analytical frameworks, used to describe the forces acting on the sphere. Besides, the experimental values of the terminal velocity obtained for different confinements are also in very good agreement with previous theoretical formulations. Similar conditions are simulated using a resolved CFD-DEM approach. After adjusting the parameters of the numerical model, we analyze the particle dynamic under several confinement conditions. The simulations results are contrasted with the experimental findings, obtaining a good agreement. We analyze several systems varying the radius of the bead and show the excellent agreement of our results with previous analytical approaches. However, the results indicate that confined particles have a distinct dynamics response when approaching the wall. Consequently, their motion cannot be described by the analytical framework introduced for the infinite system. Indeed, the confinement strongly affects the spatial scale where the particle is affected by the bottom wall and, accordingly, the dimensionless results can not be collapsed in a single master curve, using the particle size as a characteristic length. Alternatively, we rationalize our findings using a kinematic approximation to highlight the relevant scale of the problem. Our outcomes suggest it is possible to determine a new spatial scale to describe the collisional process, depending on the specific confining conditions.

Uniform Flow of Viscous Fluid Past a Porous Sphere Saturated with Micro Polar Fluid

The analytical investigation of a uniform flow of a viscous fluid past a spherical ball filled with porous medium saturated by Micropolar fluid is considered. Velocity function is defined in the form of stream function. The flowing shape is obtained for the outer and inner regions of the sphere. The effects of physical parameters like porosity and micro polarity parameters on the flow and on the drag on the sphere are shown in graphs. It is observed that when the porosity parameter is between 0.05 to 0.2, we find another concentric fluid sphere enclosing the porous sphere. Below and above this range, the fluid sphere disappears.

Unsteady and lineal translation of a sphere through a viscoelastic fluid

Unsteady translation of a sphere in a viscoelastic fluid is studied analytically. General, fully invertible relationships between an imposed time-dependent velocity and the resultant force are described in terms of a Volterra series expansion. These results are used to analyze particle motion in fluids described by the Johnson-Segalman and Giesekus models and to define a general framework for analyzing weakly nonlinear microrheology measurements.

Higher-Dimensional Regular Reissner–Nordström Black Holes Associated with Linear Electrodynamics

Following the interpretation of matter source that the energy-momentum tensor of anisotropic fluid can be dealt with effectively as the energy-momentum tensor of perfect fluid plus linear (Maxwell) electromagnetic field, we obtain the regular higher-dimensional Reissner–Nordström (Tangherlini–RN) solution by starting with the noncommutative geometry-inspired Schwarzschild solution. Using the boundary conditions that connect the noncommutative Schwarzschild solution in the interior of the charged perfect fluid sphere to the Tangherlini–RN solution in the exterior of the sphere, we find that the interior structure can be reflected by an exterior parameter, the charge-to-mass ratio. Moreover, we investigate the stability of the boundary under mass perturbation and indicate that the new interpretation imposes a rigid restriction upon the charge-to-mass ratio. This restriction, in turn, permits a stable noncommutative black hole only in the 4-dimensional spacetime.

CFD to improve the capture rate of CTC microchips with particle tracking

CTC (Circulating Tumor Cell) is a small cancer within blood. By capturing CTCs, it is possible to detect cancer and determine whether cancer treatment is effective earlier than with conventional testing methods. We studied to identify microchip geometries that facilitate contact between the CTC and the wall surface. We have performed CFD using OpenFOAM, considering the interaction between rigid spherical particles and fluid flowing in imitation of a microchip. As a result, we have succeeded in representing rigid spherical particles flowing in a fluid by using a CFD solver called DPMFoam.

Embedding class 1 model of anisotropic fluid spheres in [formula omitted] gravity

In this article, a completely new model for the spherically symmetric anisotropic compact stars presenting class 1 solutions in the background of f(R,T) gravity, where the functional f(R,T) consider as f(R,T)=R+χT, is presented. All the physical parameters, which are obtained by introducing a compatible grr metric function, are regular and physically well-behaved throughout the interior of star i.e. the reported solutions are physically acceptable to present anisotropic fluid spheres. The solutions satisfy all the energy conditions and causality condition i.e. the representing matter configurations are physical in nature. The satisfaction of TOV-equation and Abreu et al. condition, Γr(r)>4/3, Harrison–Zeldovich–Novikov static condition confirm that the matter configurations represented by our solutions are in equilibrium state and stable, respectively. In our solutions, the coupling parameter χ plays the crucial role, the energy density, pressure and mass are larger for lesser values of χ. The M−R graph generated from our solutions indicates the maximum mass under the observational range. The present model ensures that the f(R,T) gravity is enough suitable to study massive stellar objects in the ground of it. Moreover, all the results of our solutions come back in the Einstein gravity for χ=0.

Flow structures, nonlinear inertial waves and energy transfer in rotating spheres

We investigate flow structures, nonlinear inertial waves and energy transfer in a rotating fluid sphere, using a Galerkin spectral method based on helical-wave decomposition (HWD). Numerical simulations of flows in a sphere are performed with different system rotation rates, where a large-scale forcing is employed. For the case without system rotation, the intense vortex structures are tube-like. When a weak rotation is introduced, small-scale structures are reduced and vortex tubes tend to align with the rotation axis. As the rotation rate increases, a large-scale anticyclonic vortex structure is formed near the rotation axis. The structure is shown to be led by certain geostrophic modes. When the rotation rate further increases, a cyclone and an anticyclone emerge from the top and bottom of the boundary, respectively, where two quasi-geostrophic equatorially symmetric inertial waves dominate the flow. Based on HWD, effects of spherical confinement on rotating turbulence are systematically studied. It is found that the forward cascade becomes weaker as the rotation increases. When the rotation rate becomes larger than some critical value, dual energy cascades emerge, with an inverse cascade at large scales and a forward cascade at small scales. Finally, the flow behavior near the boundary is studied, where the average boundary layer thickness gets smaller when system rotation increases. The flow behavior in the boundary layer is closely related to the interior flow structures, which create significant mass flux between the boundary layer and the interior fluid through Ekman pumping.

Anisotropic counterpart of charged Durgapal V perfect fluid sphere

In this paper, we have developed a static charged anisotropic stellar model for a spherically symmetric spacetime geometry. For this, we have considered charged Durgapal V perfect fluid sphere and constructed its anisotropic counterpart by using gravitational decoupling through the minimal geometric deformation (MGD) approach. We have presented physical analysis of the constructed model in details by taking observational data of two different compact stars, namely, SMC X-4 and Vela X-1, into account. All the physical properties such as density, pressure, sound speeds, energy conditions, stability conditions, Tolman–Oppenheimer–Volkoff (TOV) equation, compactness factor, and redshift are found to meet the general criteria required to ensure a well-behaved stellar system.

Three-dimensional quasiperiodic torsional flows in rotating spherical fluids at very low Prandtl numbers

The aim of this study is to determine through numerical simulations the extent and robustness of the three-dimensional torsional dynamics of the thermal convection in rotating spherical fluids at very low Prandtl numbers. It is known that the kinetic energy of the periodic axisymmetric flows propagates latitudinally on the surface of the sphere. Here, it is shown that when the axisymmetry is broken at a secondary Hopf bifurcation, the flow starts to drift in the azimuthal direction giving rise to a quasiperiodic motion that propagates the energy in latitude and longitude. The double direction of propagation gives rise to a meandering path of the kinetic energy, which is still concentrated on the surface, but highly localized. Several new stable states of convection with different symmetries have been identified in a large range of Rayleigh numbers, all of them retaining the torsional motion of the basic velocity field. Particular attention is paid to their dependence on the Rayleigh number and on the values of the frequencies, of the mean zonal flow, and of the kinetic energy of the fluid.

Terminal velocity and drag coefficient for spherical particles

Empirical correlations and experimental works relating the drag coefficient (CD) of spheres to the Reynolds number (Re) and Re to the Archimedes number (Ar) were reviewed with a focus on the correlations applicable to the entire Re range. In addition, experiments with various spherical particles and fluids for the entire range of Re were conducted using high-speed video and added to the literature data. One of the correlations from the literature for Re-Ar and a modified correlation for CD–Re were found to best fit the experimental results. The analysis also established new correlations for Re–Ha (a non-dimensional number for velocity not including particle size) and CD–Ar. The latter is easier to use than the common CD–Re curve.

Counterexamples to the Maximum Force Conjecture

Dimensional analysis shows that the speed of light and Newton’s constant of gravitation can be combined to define a quantity F*=c4/GN with the dimensions of force (equivalently, tension). Then in any physical situation we must have Fphysical=fF*, where the quantity f is some dimensionless function of dimensionless parameters. In many physical situations explicit calculation yields f=O(1), and quite often f≤1/4. This has led multiple authors to suggest a (weak or strong) maximum force/maximum tension conjecture. Working within the framework of standard general relativity, we will instead focus on idealized counter-examples to this conjecture, paying particular attention to the extent to which the counter-examples are physically reasonable. The various idealized counter-examples we shall explore strongly suggest that one should not put too much credence into any truly universal maximum force/maximum tension conjecture. Specifically, idealized fluid spheres on the verge of gravitational collapse will generically violate the weak (and strong) maximum force conjectures. If one wishes to retain any truly general notion of “maximum force” then one will have to very carefully specify precisely which forces are to be allowed within the domain of discourse.

Two-body transient viscous interactions in free space

A generalization of Stokesian dynamics is formulated to describe hydrodynamic interactions between two spheres in a viscous fluid. The analysis quantifies transient mutual interactions in terms of frequency-dependent friction coefficients of both spheres as well as their temporally varying mobility response to an impulsive force. The analysis also contributes to work on many-body unsteady Brownian motions.