Isotropic Fluid Research Articles

Study of isotropic compact stars in $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity

In this paper, we investigate physical behavior and stability of compact stars filled with isotropic fluid in \( f(R,T,R_{\mu\nu}T^{\mu\nu})\) gravity. We consider the static spherically symmetric spacetime and choose the simplest model of this gravity, i.e., \( R+\alpha R_{\mu\nu}T^{\mu\nu}\) . To examine the basic features of compact stars like Her X-1, SAX J 1808.4-3658 and 4U 1820-30, we apply analytic solutions of Krori and Barua metric using the mass-radius relation. We study the behavior of effective energy density, pressure, equation of state parameter and energy conditions in the interior of compact stars. We also explore the stability criteria of compact stars via the speed of sound. It is concluded that all the energy conditions are satisfied and the compact stars are found to be stable at the boundary for this particular model.

Gaseous bubble oscillations in anisotropic non-Newtonian fluids under influence of high-frequency acoustic field

Progress of technology and medicine dictates the ever-increasing requirements (heat resistance, corrosion resistance, strength properties, impregnating ability, etc.) for non-Newtonian fluids and materials produced on their basis (epoxy resin, coating materials, liquid crystals, etc.). Materials with improved properties obtaining is possible by modification of their physicochemical structure. One of the most promising approaches to the restructuring of non-Newtonian fluids is cavitation generated by high-frequency acoustic vibrations. The efficiency of cavitation in non-Newtonian fluid is determined by dynamics of gaseous bubble. Today, bubble dynamics in isotropic non-Newtonian fluids, in which cavitation bubble shape remains spherical, is most full investigated, because the problem reduces to ordinary differential equation for spherical bubble radius. However, gaseous bubble in anisotropic fluids which are most wide kind of non-Newtonian fluids (due to orientation of macromolecules) deviates from spherical shape due to viscosity dependence on shear rate direction. Therefore, the paper presents the mathematical model of gaseous bubble dynamics in anisotropic non-Newtonian fluids. The model is based on general equations for anisotropic non-Newtonian fluid flow. The equations are solved by asymptotic decomposition of fluid flow parameters. It allowed evaluating bubble size and shape evolution depending on rheological properties of liquid and acoustic field characteristics.

On the locally rotationally symmetric Einstein–Maxwell perfect fluid

We examine the stability of Einstein–Maxwell perfect fluid configurations with a privileged radial direction by means of a $$1+1+2$$ -tetrad formalism. We use this formalism to cast in a quasilinear symmetric hyperbolic form the equations describing the evolution of the system. This hyperbolic reduction is used to discuss the stability of linear perturbations in some special cases. By restricting the analysis to isotropic fluid configurations, we assume a constant electrical conductivity coefficient for the fluid. As a result of this analysis we provide a complete classification and characterization of various stable and unstable configurations. We find, in particular, that in many cases the stability conditions are strongly determined by the constitutive equations and the electric conductivity. A threshold for the emergence of the instability appears in both contracting and expanding systems.

Evolution of initially contracting Bianchi class A models in the presence of an ultra-stiff anisotropic pressure fluid

We study the behaviour of Bianchi class A universes containing an ultra-stiff isotropic ghost field and a fluid with anisotropic pressures which is also ultra-stiff on the average. This allows us to investigate whether cyclic universe scenarios, like the ekpyrotic model, do indeed lead to isotropization on approach to a singularity (or bounce) in the presence of dominant ultra-stiff pressure anisotropies. We specialize to consider the closed Bianchi type IX universe, and show that when the anisotropic pressures are stiffer on average than any isotropic ultra-stiff fluid then, if they dominate on approach to the singularity, it will be anisotropic. We include an isotropic ultra-stiff ghost fluid with negative energy density in order to create a cosmological bounce at finite volume in the absence of the anisotropic fluid. When the dominant anisotropic fluid is present it leads to an anisotropic cosmological singularity rather than an isotropic bounce. The inclusion of anisotropic stresses generated by collisionless particles in an anisotropically expanding universe is therefore essential for a full analysis of the consequences of a cosmological bounce or singularity in cyclic universes.

Static spherically symmetric wormholes with isotropic pressure

In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there is no spherically symmetric traversable wormholes sustained by sources with a linear equation of state $p=\omega \rho$ for the isotropic pressure, independently of the form of the redshift function $\phi(r)$. We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.

Fracture stratigraphy and fluid flow properties of shallow-water, tight carbonates: The case study of the Murge Plateau (southern Italy)

The work tackles the control exerted by a sub-seismic fracture network on both secondary porosity and correspondent permeability of outcropping tight carbonates. Taking advantage of excellent 3D exposures, located in the Murge Plateau of southern Italy, the fracture network is investigated at different scales of observation. The rock multi-layer is made up of 10's of cm-thick, sub-horizontal, laterally continuous limestone beds crosscut by stratabound fractures, non-stratabound fractures, and small faults named as persistent fracture zones with low amounts of offset. Stratabound fractures consist of bed-perpendicular joints and sheared joints, non-stratabound fractures of incipient, cm-offset, sub-vertical faults, whereas the 10's of cm-offset persistent fracture zones are made up of 10's of m-high, m-thick fractured damage zones. The aforementioned structural elements localize within discrete carbonate units bounded by primary features such as bed surfaces, prominent surfaces and sedimentary breccia horizons. Such interfaces therefore affected the fracture stratigraphy of the limestone rock, and thus impact the fluid flow properties of the carbonate multilayer by compartmentalizing deformation.In the field, the fracture network is investigated by means of scanline and scan area methodologies to document the orientation, intensity, height distribution, mechanical aperture and roughness of individual fractures exposed along vertical outcrops and pavements of abandoned quarries. Then, Discrete Fracture Network (DFN) models of representative geocellular volumes are built, according to the different scales of analysis, to compute both fracture porosity and correspondent permeability (Kxx, Kyy, Kzz). Results of such a work show that the most prominent non-stratabound fracture set forms the major control on fluid storage and migration at the scales of single beds and bed-packages. At a larger scale, we document that fluid migration mainly occurs along the persistent fracture zones, which enhance the fault-parallel flow. As a whole, the persistent fracture zones form localized fluid conduits embedded within carbonate matrices that show isotropic fluid flow properties.

Frustration of freezing in a two dimensional hard-core fluid due to particle shape anisotropy

The freezing mechanism suggested for a fluid composed of hard disks [Huerta et al., Phys. Rev. E, 2006, 74, 061106] is used here to probe the fluid-to-solid transition in a hard-dumbbell fluid composed of overlapping hard disks with a variable length between disk centers. Analyzing the trends in the shape of second maximum of the radial distribution function of the planar hard-dumbbell fluid it has been found that the type of transition could be sensitive to the length of hard-dumbbell molecules. From the ${NpT}$ Monte Carlo simulations data we show that if a hard-dumbbell length does not exceed 15% of the disk diameter, the fluid-to-solid transition scenario follows the case of a hard-disk fluid, i.e., the isotropic hard-dumbbell fluid experiences freezing. However, for a hard-dumbbell length larger than 15% of disk diameter, there is evidence that fluid-to-solid transition may change to continuous transition, i.e., such an isotropic hard-dumbbell fluid will avoid freezing.

The atmosphere of a black hole

We present a static, isotropic fluid solution around a black hole and its effects on the field equations and the horizon. We offer the solutions, their descriptions and we comment on their shortcomings. We derive from the proposed metric the density, the pressure, the equation of state, the temperature near and far of the black hole and the equation of state parameter. We show that for a special case, when [Formula: see text] the solution behaves as [Formula: see text], the equation of state for radiation and for [Formula: see text] we observe that [Formula: see text], the equation of state for dust.

Mimicking static anisotropic fluid spheres in general relativity

We argue that an arbitrary general relativistic static anisotropic fluid sphere, (static and spherically symmetric but with transverse pressure not equal to radial pressure), can nevertheless be successfully mimicked by suitable linear combinations of theoretically attractive and quite simple classical matter: a classical (charged) isotropic perfect fluid, a classical electromagnetic field and a classical (minimally coupled) scalar field. While the most general decomposition is not unique, a preferred minimal decomposition can be constructed that is unique. We show how the classical energy conditions for the anisotropic fluid sphere can be related to energy conditions for the isotropic perfect fluid, electromagnetic field, and scalar field components of the model. Furthermore, we show how this decomposition relates to the distribution of both electric charge density and scalar charge density throughout the model. The generalized TOV equation implies that the perfect fluid component in this model is automatically in internal equilibrium, with pressure forces, electric forces, and scalar forces balancing the gravitational pseudo-force. Consequently, we can build theoretically attractive matter models that can be used to mimic almost any static spherically symmetric spacetime.

A model of the emergent Universe in inhomogeneous spacetime

The scenario of an emergent Universe is constructed in the background of an inhomogeneous spacetime model with an asymptotically (at spatial infinity) FRW spacetime. The cosmic substratum consists of two non-interacting components, namely (a) homogeneous and isotropic fluid that is dissipative in nature and (b) an inhomogeneous and anisotropic barotropic fluid. In the non-equilibrium thermodynamic prescription (second order deviations), the particle creation mechanism is considered the cause for the dissipative phenomena. It is found that for a constant value of the particle creation rate parameter there exists a scenario of an emergent Universe.

A multi-scale model of Escherichia coli chemotaxis from intracellular signaling pathway to motility and nutrient uptake in nutrient gradient and isotropic fluid environments

This paper presents a multi-scale mathematical model of Escherichia coli chemotaxis in a fluid environment that links the biochemical dynamics of intracellular signaling and flagellar dynamics to the behavior of cells and the surrounding nutrients and fluid flow. We combine the RapidCell model for the intracellular chemotaxis signaling pathway to obtain run and tumble behaviors of cells with the method of regularized Stokeslets to simulate cell motility in Stokes flow and the finite element method to solve the advection–diffusion–reaction equation of nutrients. Simulations were carried out using varying numbers of bacterial cells to ascertain the effects of cell–cell and cell–fluid interactions in isotropic environments and in fluids characterized by chemoeffector nutrient gradients. The resulting feedback between hydrodynamics and chemotaxis not only shows expected run and tumble behaviors of bacterial cells but also depicts the importance of fluid dynamical effects on the transport and consumption of chemoeffectors.

Class of Charged Fluid Balls in General Relativity

In the present study, we have obtained a new analytical solution of combined Einstein-Maxwell field equations describing the interior field of a ball having static spherically symmetric isotropic charged fluid within it. The charge and electric field intensity are zero at the center and monotonically increasing towards the boundary of the fluid ball. Besides these, adiabatic index is also increasing towards the boundary and becomes infinite on it. All other physical quantities such as pressure, density, adiabatic speed of sound, charge density, adiabatic index are monotonically decreasing towards the surface. Causality condition is obeyed at the center of ball. In the limiting case of vanishingly small charge, the solution degenerates into Schwarzchild uniform density solution for electrically neutral fluid. The solution joins smoothly to the Reissner-Nordstrom solution over the boundary. We have constructed a neutron star model by assuming the surface density . The mass of the neutron star comes with radius 14.574 km.

Planar contraction flow of a nematic PPTA solution

Planar contraction flow of a nematic solution of poly-paraphenylene terephthalamide (PPTA) in sulphuric acid (H2SO4) was studied experimentally and compared with the flow of an isotropic model fluid, a poly-ethyleneglycol–poly-ethyleneoxide (PEG-PEO) Boger fluid, in the same geometry. The dimensions and deformation rates in our experiments are relevant for industrial polymer extrusion processes, such as fiber spinning. Under these conditions, viscoelastic lip vortices arise at the re-entrant corners in the nematic flow. The experimental results show that the vortex growth behavior in the nematic PPTA solution closely resembles that in isotropic viscoelastic fluids, such as the PEG-PEO Boger fluid that was used as a reference. The velocity field in the nematic flow is characteristic of Hele-Shaw flow of a shear-thinning power-law fluid, although locally, the influence of the nematic defect structure was observed, especially for the first minutes after starting the flow. Furthermore, the lateral movement of the extruded jet, downstream of the contraction, was shown to be coupled with velocity fluctuations in the upstream flow. Our experiments give detailed insight in the complex flow behavior of a nematic polymer solution under flow conditions that are relevant to practical applications. The results can be applied in the optimization of nematic polymer extrusion processes.

Anisotropy and probe-medium interactions in the microrheology of nematic fluids

A theoretical formalism is presented to analyze and interpret microrheology experiments in anisotropic fluids with nematic order. The predictions of that approach are examined in the context of a simple coarse-grained molecular model which is simulated using nonequilibrium molecular dynamics calculations. The proposed formalism is used to study the effect of confinement, the type of anchoring at the probe-particle surface, and the strength of the nematic field on the rheological response functions obtained from probe-particle active microrheology. As expected, a stronger nematic field leads to increased anisotropy in the rheological response of the material. It is also found that the defect structures that arise around the probe particle, which are determined by the type of anchoring and the particle size, have a significant effect on the rheological response observed in microrheology simulations. Independent estimates of the bulk dynamic modulus of the model nematic fluid considered here are obtained from small-amplitude oscillatory shear simulations with Lees–Edwards boundary conditions. The results of simulations indicate that the dynamic modulus extracted from particle-probe microrheology is different from that obtained in the absence of the particle, but that the differences decrease as the size of the defect also decreases. Importantly, the results of the nematic microrheology theory proposed here are in much closer agreement with simulations than those from earlier formalisms conceived for isotropic fluids. As such, it is anticipated that the theoretical framework advanced in this study could provide a useful tool for interpretation of microrheology experiments in systems such as liquid crystals and confined macromolecular solutions or gels.

Effects of confinement on pattern formation in two dimensional systems with competing interactions.

Template-assisted pattern formation in monolayers of particles with competing short-range attraction and long-range repulsion interactions (SALR) is studied by Monte Carlo simulations in a simple generic model [N. G. Almarza et al., J. Chem. Phys., 2014, 140, 164708]. We focus on densities corresponding to formation of parallel stripes of particles and on monolayers laterally confined between straight parallel walls. We analyze both the morphology of the developed structures and the thermodynamic functions for broad ranges of temperature T and the separation L2 between the walls. At low temperature stripes parallel to the boundaries appear, with some corrugation when the distance between the walls does not match the bulk periodicity of the striped structure. The stripes integrity, however, is rarely broken for any L2. This structural order is lost at T = TK(L2) depending on L2 according to a Kelvin-like equation. Above the Kelvin temperature TK(L2) many topological defects such as breaking or branching of the stripes appear, but a certain anisotropy in the orientation of the stripes persists. Finally, at high temperature and away from the walls, the system behaves as an isotropic fluid of elongated clusters of various lengths and with various numbers of branches. For L2 optimal for the stripe pattern the heat capacity as a function of temperature takes the maximum at T = TK(L2).

Moment tensors of a dislocation in a porous medium

A dislocation can be represented by a moment tensor for calculating seismic waves. However, the moment tensor expression was derived in an elastic medium and cannot completely describe a dislocation in a porous medium. In this paper, effective moment tensors of a dislocation in a porous medium are derived. It is found that the dislocation is equivalent to two independent moment tensors, i.e., the bulk moment tensor acting on the bulk of the porous medium and the isotropic fluid moment tensor acting on the pore fluid. Both of them are caused by the solid dislocation as well as the fluid–solid relative motion corresponding to fluid injection towards the surrounding rocks (or fluid outflow) through the fault plane. For a shear dislocation, the fluid moment tensor is zero, and the dislocation is equivalent to a double couple acting on the bulk; for an opening dislocation or fluid injection, the two moment tensors are needed to describe the source. The fluid moment tensor only affects the radiated compressional waves. By calculating the ratio of the radiation fields generated by unit fluid moment tensor and bulk moment tensor, it is found that the fast compressional wave radiated by the bulk moment tensor is much stronger than that radiated by the fluid moment tensor, while the slow compressional wave radiated by the fluid moment tensor is several times stronger than that radiated by the bulk moment tensor.

Hard convex lens-shaped particles: Densest-known packings and phase behavior.

By using theoretical methods and Monte Carlo simulations, this work investigates dense ordered packings and equilibrium phase behavior (from the low-density isotropic fluid regime to the high-density crystalline solid regime) of monodisperse systems of hard convex lens-shaped particles as defined by the volume common to two intersecting congruent spheres. We show that, while the overall similarity of their shape to that of hard oblate ellipsoids is reflected in a qualitatively similar phase diagram, differences are more pronounced in the high-density crystal phase up to the densest-known packings determined here. In contrast to those non-(Bravais)-lattice two-particle basis crystals that are the densest-known packings of hard (oblate) ellipsoids, hard convex lens-shaped particles pack more densely in two types of degenerate crystalline structures: (i) non-(Bravais)-lattice two-particle basis body-centered-orthorhombic-like crystals and (ii) (Bravais) lattice monoclinic crystals. By stacking at will, regularly or irregularly, laminae of these two crystals, infinitely degenerate, generally non-periodic in the stacking direction, dense packings can be constructed that are consistent with recent organizing principles. While deferring the assessment of which of these dense ordered structures is thermodynamically stable in the high-density crystalline solid regime, the degeneracy of their densest-known packings strongly suggests that colloidal convex lens-shaped particles could be better glass formers than colloidal spheres because of the additional rotational degrees of freedom.

Grain-boundary-induced melting in quenched polycrystalline monolayers.

Melting in two dimensions can successfully be explained with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario which describes the formation of the high-symmetry phase with the thermal activation of topological defects within an (ideally) infinite monodomain. With all state variables being well defined, it should hold also as freezing scenario where oppositely charged topological defects annihilate. The Kibble-Zurek mechanism, on the other hand, shows that spontaneous symmetry breaking alongside a continuous phase transition cannot support an infinite monodomain but leads to polycrystallinity. For any nonzero cooling rate, critical fluctuations will be frozen out in the vicinity of the transition temperature. This leads to domains with different director of the broken symmetry, separated by a defect structure, e.g., grain boundaries in crystalline systems. After instantaneously quenching a colloidal monolayer from a polycrystalline to the isotropic fluid state, we show that such grain boundaries increase the probability for the formation of dislocations. In addition, we determine the temporal decay of defect core energies during the first few Brownian times after the quench. Despite the fact that the KTHNY scenario describes a continuous phase transition and phase equilibrium does not exist, melting in polycrystalline samples starts at grain boundaries similar to first-order phase transitions.

Kerr effect at high electric field in the isotropic phase of mesogenic materials.

The well-known Kerr effect in isotropic fluids consists in the appearance of uniaxial orientational order and birefringence that grows as the square of the applied electric field. We predict and observe that at a high electric field, the Kerr effect displays features caused by the nonlinear dependence of dielectric permittivity on the field-induced orientational order parameter. Namely, the field-induced birefringence grows faster than the square of the electric field and the dynamics of birefringence growth slows down as the field increases. As a function of temperature, the field-induced birefringence is inversely proportional to the departure from an asymptotic critical temperature, but this temperature is no longer a constant (corresponding to the lower limit of the supercooled isotropic phase) and increases proportionally to the square of the electric field.

Role of interfacial friction for flow instabilities in a thin polar-ordered active fluid layer.

We construct a generic coarse-grained dynamics of a thin inflexible planar layer of polar-ordered suspension of active particles that is frictionally coupled to an embedding isotropic passive fluid medium with a friction coefficient Γ. Being controlled by Γ, our model provides a unified framework to describe the long-wavelength behavior of a variety of thin polar-ordered systems, ranging from wet to dry active matter and free-standing active films. Investigations of the linear instabilities around a chosen orientationally ordered uniform reference state reveal generic moving and static instabilities in the system that can depend sensitively on Γ. Based on our results, we discuss estimation of bounds on Γ in experimentally accessible systems.