Isotropic Fluid Research Articles

Vapour-liquid equilibrium and low-temperature liquid-crystal phase diagram of discotic colloids

Discotic colloids give rise to a paradigmatic family of liquid crystals with sound applications in Materials Science. In this paper, Monte Carlo simulations are employed to characterise the low-temperature liquid crystal phase diagram and the vapour-liquid coexistence of discotic colloids interacting via a Kihara potential. Discoidal particles with thickness-diameter aspect ratios L ∗ ≡ L / D = 0.5 , 0.3, 0.2 and 0.1 are considered. For the less anisotropic particles ( L ∗ ≥ 0.2 ), coexistence of a vapour phase with the isotropic fluid and with the columnar liquid crystal phase is observed. As the particle anisotropy increases, the vapour-liquid coexistence shifts to lower temperatures and its density range diminishes, eventually merging with coexistences involving the liquid crystal phases. The L ∗ = 0.1 fluid displays a rich sequence of mesophases, including a nematic phase and a novel lamellar phase in which particles arrange in layers perpendicular to the nematic director.

Viscous tweezers: Controlling particles with viscosity

Control of particle motion is generally achieved by applying an external field that acts directly on each particle. Here, we propose a global way to manipulate the motion of a particle by dynamically changing the properties of the fluid in which it is immersed. We exemplify this principle by considering a small particle sinking in an anisotropic fluid whose viscosity depends on the shear axis. In the Stokes regime, the motion of an immersed object is fully determined by the viscosity of the fluid through the mobility matrix, which we explicitly compute for a pushpin-shaped particle. Rather than falling upright under the force of gravity, as in an isotropic fluid, the pushpin tilts to the side, sedimenting at an angle determined by the viscosity anisotropy axis. By changing this axis, we demonstrate control over the pushpin orientation as it sinks, even in the presence of noise, using a closed feedback loop. This strategy to control particle motion, that we dub viscous tweezers, could be experimentally realized in systems ranging from polyatomic fluids under external fields to chiral active fluids of spinning particles by suitably changing their direction of global alignment or anisotropy. Published by the American Physical Society 2024

Spherical accretion onto higher-dimensional Reissner–Nordström black hole

Abstract We obtain relativistic solutions of spherically symmetric accretion by a dynamical analysis of a generalised Hamiltonian for higher-dimensional Reissner–Nordström (RN) Black Hole (BH). We consider two different fluids namely, an isotropic fluid and a non-linear polytropic fluid to analyse the critical points in a higher-dimensional RN BH. The flow dynamics of the fluids are studied in different spacetime dimensions in the framework of Hamiltonian formalism. The isotropic fluid is found to have both transonic and non-transonic flow behaviour, but in the case of polytropic fluid, the flow behaviour is found to exhibit only non-transonic flow, determined by a critical point that is related to the local sound speed. The critical radius is found to change with the spacetime dimensions. Starting from the usual four dimensions it is noted that as the dimension increases the critical radius decreases, attains a minimum at a specific dimension (D > 4) and thereafter increases again. The mass accretion rate for isotropic fluid is determined using Hamiltonian formalism. The maximum mass accretion rate for RN BH with different equations of state parameters is studied in addition to spacetime dimensions. The flow behaviour and mass accretion rate for a change in BH charge is also studied analytically. It is noted that the maximum mass accretion rate in a higher-dimensional Schwarzschild BH is the lowest, which however, increases with the increase in charge parameter in a higher-dimensional RN BH.

Hydrodynamic Attractor in Ultracold Atoms.

The hydrodynamic attractor is a concept that describes universal equilibration behavior in which systems lose microscopic details before hydrodynamics becomes applicable. We propose a setup to observe hydrodynamic attractors in ultracold atomic gases, taking advantage of the fact that driving the two-body s-wave scattering length causes phenomena equivalent to isotropic fluid expansions. We specifically consider two-component fermions with contact interactions in three dimensions and discuss their dynamics under a power-law drive of the scattering length in a uniform system. By explicit computation, we derive a hydrodynamic relaxation model. We analytically solve their dynamics and find the hydrodynamic attractor solution. Our proposed method using the scattering length drive is applicable to a wide range of ultracold atomic systems, and our results establish these as a new platform for exploring hydrodynamic attractors.

Electro-Optic Kerr Response in Optically Isotropic Liquid Crystal Phases

The results of an experimental investigation of the temperature and wavelength dependence of the Kerr constant (K) of mixtures with an increasing amount of chiral dopant in an isotropic liquid crystal phase are reported. The material was composed of a nematic liquid crystal (5CB) and a chiral dopant (CE2), which formed non-polymer-stabilized liquid crystalline blue phases with an exceptionally large value of K∼2 × 10−9 mV−2. The measurements were performed on liquid and blue phases at several concentrations covering a range of temperatures and using three wavelengths: 532 nm, 589 nm and 633 nm. The work focused on changes caused by concentration and their impact on the increase in the value of K, and it was found that in the case of the 5CB/CE2 mixture these changes were significant and quite systematic with temperature and wavelength. It is shown that the dispersion relation based on the single-band birefringence model described K well in isotropic liquid crystal phases at all of the measured concentrations. In an isotropic fluid, both temperature-dependent parameters in the dispersion relation had a simple linear form and, therefore, the K-surface could be described by only four constants. In the blue phase, the expression reproducing the temperature variation of K depended on concentration, which could vary from being almost linear to quasi-linear and could be represented well by an inverse exponential analytic expression.

Experimental characterization of the effective acoustic properties of anisotropic porous materials via free-field measurements

Porous media are commonly described as effective isotropic fluid materials, such that their acoustic properties can be adequately determined from their bulk modulus and dynamic density. Most acoustic absorbents, however, possess a marked anisotropy, which influences their acoustical behavior and the parameters necessary to deduce it. Specifically, the influence of anisotropy translates into a full symmetric density tensor (in place of a scalar). This study presents a method for retrieving the bulk modulus and all six components of the density tensor of a layer of porous material from reflection coefficients measured in free field with an array of microphones. The procedure consists in expressing the sound field measured in the vicinity of the layer as a superposition of plane waves, from which the surface impedance and the reflection coefficient are reconstructed. The reflection properties, as well as the pressure at the rigid backing interface, are estimated for various source positions (i.e., various angles of incidence) and an inverse problem is formulated to infer the effective fluid parameters. The validity of the method is examined experimentally on a manufactured porous material, and the resulting fluid parameters compared with experimental results obtained from reflection and transmission coefficients measured in an impedance tube.

Hydrodynamic cloaks with isotropic and homogeneous viscosity for multi-object in collaborative operations

Although significant efforts have been devoted to advancing hydrodynamic cloaks for a single object, limited exploration has focused on cloaking multiple objects. By cloak, we mean a state of hydrodynamic invisibility achieved by eliminating flow disturbances caused by intrusive objects in the surrounding fluids. These gaps in understanding present challenges in developing effective strategies for achieving hydrodynamic stealth for multiple objects in collaborative operations. To address these issues, we propose a multi-object hydrodynamic cloak with isotropic and homogeneous fluid viscosity in viscous potential flows through a combination of neutral inclusion theory and convection-diffusion-balance method. By effectively transforming the intrusive objects into one single object while maintaining the overall invasive volume unchanged—a critical factor in flow disturbances—we successfully derive the analytical solution of fluid viscosity for multi-object hydrodynamic cloaks. Numerical simulations demonstrate the proposed cloaks considerably minimize the hydrodynamic perturbations generated by objects in groups with symmetric or asymmetric distributions, various sizes, and even arbitrary shapes. In addition, we reveal that the antagonism between the defined boundary effect of flow disturbances and vorticity magnitudes primarily determines the effectiveness of the proposed cloaks, laying the foundation for the future development of multi-object hydrodynamic cloaks involving interactions among objects. Hopefully, this research will advance the fields of hydrodynamic metamaterials for multiple objects in collaborative settings and contribute to the broader understanding of complexity science.

Charged analog of anisotropic dark energy star in Rastall gravity

Dark energy is one of the potential strategies for preventing compact objects from gravitationally collapsing into singularities. Because it is the cause of the accelerated expansion of our universe, it has the greatest impact on the cosmos. Thus, it is plausible that dark energy will interact with any stellar object that is compact in the universe [Phys. Rev. D 103 (2021) 084042]. Our main goal in this work is to create a simplified model, in the Rastall gravitational framework, of a charged strange star coupled to anisotropic dark energy in Krori–Barua spacetime [J. Phys. A, Math. Gen. 8 (1975) 508]. Here, we consider a specific strange star object, Her [Formula: see text], with observed values of mass [Formula: see text] and radius [Formula: see text] km, so that we can develop our model. In this context, we began by modeling dark energy using the equation of state (EoS), in which the dark energy density is proportional to the isotropic perfect fluid matter-energy density. The Darmois–Israel condition has been used to calculate the unknown constants that are present in the metric. We perform a detailed analysis of the model’s physical properties, including the mass–radius relation, pressure, density, metric function, and dark energy parameters for different Rastall coupling parameter values. We also examine the stability and force equilibrium of our proposed stellar configuration. Following a comprehensive theoretical analysis, we discovered that our suggested model is both singularity-free and meets all stability requirements needed to be a stable, physically reasonable stellar model.

Role of decoupling process on the configurations of compact stars induced by Thomas-Fermi dark matter with null complexity in f(T) gravity

Our goal in this work is to find an anisotropic solution for a self-bound compact object composed of dark matter with a null complexity factor in f(T)-gravity theory. We use a well-known gravitational decoupling via complete geometric deformation (CGD) technique to examine the role of decoupling parameters on the configuration of compact objects. Initially, we derive the null complexity condition for f(T)-gravity decoupled system which leads to a relation between gravitational potentials. Next, we apply the CGD approach to split the decoupled system into two subsystems. The initial system refers to a pure f(T) gravity system consisting of an isotropic fluid distribution, where the isotropy criterion is equivalent to the condition in Einstein's gravity. The solution of the first system is solved through the Vlasenk-Pronin space-time metrics while the second system associated with the deformation function is solved by the density constraints method by mimicking a new source with Thomas-Fermi dark matter density profile that generates the anisotropy in the decoupled system. The physical validity of the anisotropic solution is checked by the graphical analysis of the pressure, density, energy, and stability conditions. We have also shown the effect of torsion and decoupling parameters on the configuration of anisotropic compact objects. The energy exchange (ΔE) of fluid distribution is also discussed. We found that ΔE is positive throughout the stellar configuration, which implies that energy is effectively transmitted to the surrounding environment.

Cosmological bouncing solutions in f(𝒬,𝒯) theory

This paper examines the behavior of the universe around the bouncing point in the background of [Formula: see text] theory, where [Formula: see text] is the non-metricity and [Formula: see text] is the trace of the energy–momentum tensor. We derive the field equations that describe gravitational phenomena in the existence of non-metricity and matter source terms. By applying the reconstruction method for the Hubble parameter, a phenomenon of the bouncing universe for homogeneous spacetime filled with perfect fluid is studied. We consider specific models of this modified theory to evaluate the behavior of various cosmic parameters such as the Hubble, deceleration, equation of state and fluid parameters. When the null energy condition is violated, it follows a bouncing behavior. It is found that spacetime is composed of isotropic fluid, where a big bounce can occur and the universe turns into extremely unstable. We conclude that [Formula: see text] gravity successfully explains the early and late time cosmic expansion and evolution.

Spontaneous assembly of condensate networks during the demixing of structured fluids

Liquid-liquid phase separation, whereby two liquids spontaneously demix, is ubiquitous in industrial, environmental, and biological processes. While isotropic fluids are known to condense into spherical droplets in the binodal region, these dynamics are poorly understood for structured fluids. Here, we report the unique observation of condensate networks, which spontaneously assemble during the demixing of a mesogen from a solvent. Condensing mesogens form rapidly elongating filaments, rather than spheres, to relieve distortion of an internal smectic mesophase. As filaments densify, they collapse into bulged discs, lowering the elastic free energy. Additional distortion is relieved by retraction of filaments into the discs, which are straightened under tension to form a ramified network. Understanding and controlling these dynamics may provide different avenues to direct pattern formation or template materials.

Ab initio uncertainty quantification in scattering analysis of microscopy.

Estimating parameters from data is a fundamental problem in physics, customarily done by minimizing a loss function between a model and observed statistics. In scattering-based analysis, it is common to work in the reciprocal space. Researchers often employ their domain expertise to select a specific range of wave vectors for analysis, a choice that can vary depending on the specific case. We introduce another paradigm that defines a probabilistic generative model from the beginning of data processing and propagates the uncertainty for parameter estimation, termed the ab initio uncertainty quantification (AIUQ). As an illustrative example, we demonstrate this approach with differential dynamic microscopy (DDM) that extracts dynamical information through minimizing a loss function for the squared differences of the Fourier-transformed intensities, at a selected range of wave vectors. We first show that the conventional way of estimation in DDM is equivalent to fitting a temporal variogram in the reciprocal space using a latent factor model as the generative model. Then we derive the maximum marginal likelihood estimator, which optimally weighs the information at all wave vectors, therefore eliminating the need to select the range of wave vectors. Furthermore, we substantially reduce the computational cost of computing the likelihood function without approximation, by utilizing the generalized Schur algorithm for Toeplitz covariances. Simulated studies of a wide range of dynamical systems validate that the AIUQ method improves estimation accuracy and enables model selection with automated analysis. The utility of AIUQ is also demonstrated by three distinct sets of experiments: first in an isotropic Newtonian fluid, pushing limits of optically dense systems compared to multiple particle tracking; next in a system undergoing a sol-gel transition, automating the determination of gelling points and critical exponent; and lastly, in discerning anisotropic diffusive behavior of colloids in a liquid crystal. These studies demonstrate that the new approach does not require manually selecting the wave vector range and enables automated analysis.

Most general isotropic charged fluid solution for Buchdahl model in ℱ(𝒬) gravity

In this work, we investigated a most general isotropic charged fluid solution for the Buchdahl model via a two-step method in ℱ(𝒬)-gravity framework for the first time. In this context, a linear function of the form ℱ(𝒬) = ζ 1 𝒬 + ζ 2 and a particular transformation is used to solve the Einstein-Maxwell Equations (EMEs) employing the Buchdahl ansatz: e Υ(r) = μ(1+λ r 2)/μ+λ r 2, where ζ 1, ζ 2, λ and μ are constant parameters. The Schwarzschild de Sitter (AdS) exterior solution is joined to the interior solution at the boundary to determine the constant parameters. It should be emphasized that, for a given transformation, the Buchdahl ansatz only offers a mathematically feasible solution in the context of electric charge, where pressure and density are maximum at the center and decrease monotonically towards the boundary when 0 < μ < 1. We taken into account the compact star EX01785-248 with M = (1.3±0.2)M ⊙; Radius = 12.02+0.55 -0.55 km for graphical analysis.The physical acceptability of the model in the context of ℱ(𝒬) gravity has been evaluated by looking at the necessary physical properties, including energy conditions, causality condition, hydrostatic equilibrium, pressure-density ratio, etc. Additionally, we predicted the maximum mass limit of different compact objects for various parameter values along with the mass-radius relation. The maximum masses range (1.927 - 2.321) M ⊙ are obtained for our solution. It can be observed that when the coupling parameter ζ 1 for ℱ(𝒬 gravity is smaller, then our solution yields massive stars. The present investigation provides novel insights and realistic implications regarding the formation of compact astrophysical objects.

Hele-Shaw flow of a nematic liquid crystal.

Motivated by the variety of applications in which nematic Hele-Shaw flow occurs, a theoretical model for Hele-Shaw flow of a nematic liquid crystal is formulated and analyzed. We derive the thin-film Ericksen-Leslie equationsthat govern nematic Hele-Shaw flow, and consider two important limiting cases in which we can make significant analytical progress. First, we consider the leading-order problem in the limiting case in which elasticity effects dominate viscous effects, and find that the nematic liquid crystal anchoring on the plates leads to a fixed director field and an anisotropic patterned viscosity that can be used to guide the flow of the nematic. Second, we consider the leading-order problem in the opposite limiting case in which viscous effects dominate elasticity effects, and find that the flow is identical to that of an isotropic fluid and the behavior of the director is determined by the flow. As an example of the insight which can be gained by using the present approach, we then consider the flow of nematic according to a simple model for the squeezing stage of the one-drop-filling method, an important method for the manufacture of liquid crystal displays, in these two limiting cases.

Rotational dynamics of a disk in a thin film of weakly nematic fluid subject to linear friction

Dynamics at low Reynolds numbers experiences recent revival in the fields of biophysics and active matter. While in bulk isotropic fluids it is exhaustively studied, this is less so in anisotropic fluids and in confined situations. Here, we combine the latter two by studying the rotation of a disk-like inclusion in a uniaxially anisotropic, globally oriented, incompressible two-dimensional fluid film. In terms of a perturbative expansion in parameters that quantify anisotropies in viscosity and in additional linear friction with a supporting substrate or other type of confinement, we derive analytical expressions for the resulting hydrodynamic flow and pressure fields as well as for the resistance and mobility coefficients of the rotating disk. It turns out that, in contrast to translational motion, the solutions remain well-behaved also in the absence of the additional linear friction. Comparison with results from finite-element simulations shows very good agreement with those from our analytical calculations. Besides applications to describe technological systems, for instance, in the area of microfluidics and thin cells of aligned nematic liquid crystals, our solutions are important for quantitative theoretical approaches to fluid membranes and thin films in general featuring a preferred direction.

Accretion mechanism for regular black holes with asymptotically Minkowski Cores and improved Schwarzschild black holes

In this paper, we investigate the fascinating implications of the accretion process for two different kinds of black holes. A detailed analysis of the moving fluid in this accretion process is provided. The radial velocity u(r), the energy density ρ(r), speed of sound a2s and the mass accretion rate Ṁ of the regular black holes and improved Schwarzschild black hole are explored. Interestingly, we consider the most generic black hole space–times with isotropic fluid for this accretion process. The required and necessary physical behaviors around the black holes, such as the radial velocity, the energy density of the moving fluid within the scope of dust, stiff fluid and quintessence, are achieved. Our findings suggest that critical parameters like l in regular black holes, Γ in improved Schwarzschild black holes and the state parameter k are responsible for the accretion mechanism.

Physically viable and stable charged perfect fluid solution within [formula omitted] gravity

In this work, we investigate the physical behavior and stability of compact stars in F(Q) gravity. We employ the Buchdahl metric to examine the dynamics of a relativistic, newly charged, isotropic fluid model. The interplay between gravity and electromagnetism is included in the analysis of the system by taking into account the charged state of the fluid, providing insights into how charged fluids behave in gravitational theories. The exterior solution under Schwarzschild–de Sitter (dS) spacetime is linked to the interior solution at the boundary to identify the constants. It is important to note that the Buchdahl ansatz provides a mathematically viable solution for a given transformation in the context of electric charge when pressure and density are maximum in the center and monotonically fall towards the boundary. We have taken into account the compact star Her X-1 with M=(0.85±0.15)M⊙; Radius =13.26−1.08+1.08 km for graphical analysis. In the context of F(Q), the physical acceptability of the model has been examined by looking at the required physical attributes, such as energy conditions, causality, hydrostatic equilibrium, pressure–density ratio, etc. that are satisfied throughout the stellar configuration. It is concluded that the present approach allows a suitable modeling of astrophysical compact objects in F(Q) gravity.

Imaging flow focusing and isolation of aqueous fluids in synthetic quartzite: implications for permeability and retained fluid fraction in deep-seated rocks

The microstructure of realistic fluid–rock systems evolves to minimize the overall interfacial energy, enabling local variations in fluid geometry beyond ideal models. Consequently, the permeability–porosity relationship and fluid distribution in these systems may deviate from theoretical expectations. Here, we aimed to better understand the permeability development and fluid retention in deep-seated rocks at low fluid fractions by using a combined approach of high-resolution synchrotron radiation X-ray computed microtomography imaging of synthesized rocks and numerical permeability computation. We first synthesized quartzite using a piston-cylinder apparatus at different fluid fractions and wetting properties (wetting and non-wetting systems with dihedral angles of 52° and 61°–71°, respectively) under conditions of efficient grain growth. Although all fluids should be connected along grain edges and tubules in the homogeneous isotropic wetting fluid–rock system enabling segregation by gravitational compaction in natural settings, the fluid connectivity rapidly decreased to ~ 0 when the total fluid fraction decreased to 0.030–0.037, as the non-ideality of quartzite, including the interfacial energy anisotropy (i.e., grain faceting), became critical. In non-wetting systems, where the minimum energy fluid fraction based solely on the dihedral angle is ~ 0.015–0.035, the isolated (disconnected) fractions was 0.048–0.062. A streamline computation in the non-wetting system revealed that with decreasing total porosity, flow focusing into fewer channels maintained permeability, allowing the effective segregation of the connected fluids. These results provide insight into how non-wetting fluids segregate from rocks and exemplify the fraction of retained fluids in non-wetting systems. Thus, the findings suggest a potential way for wetting system fluids to be transported into the deep Earth's interior, and the amount of fluids dragged down to the Earth’s interior could be higher than what was previously estimated.

A molecular perspective on the emergence of long-range polar order from an isotropic fluid

The ferroelectric nematic phase (NF) has quickly become the most studied system in liquid crystal research. In this work, we investigate the origin of such polar structure by studying a compound for which the NF phase directly follows the isotropic liquid phase on cooling, making it a particularly interesting system. Our experimental results evidence the presence of polar correlations already in the high-temperature phase, in which ferroelectric order can be induced under a sufficiently strong electric field. In the NF phase, molecular dynamics and polar correlations are investigated through detailed dynamic dielectric measurements, while second harmonic generation experiments evidence a large value of the main coefficient of the second order dielectric susceptibility tensor. Lastly, experimentally determined parameters are employed for calculations based on a recently proposed theoretical model for the stability of the NF phase. The obtained results suggest that the parallel alignment of dipoles is driven by a subtle interplay between electrostatic and excluded volume interactions.

Static Spherically Symmetric Perfect Fluid Solutions in Teleparallel F(T) Gravity

In this paper, we investigate static spherically symmetric teleparallel F(T) gravity containing a perfect isotropic fluid. We first write the field equations and proceed to find new teleparallel F(T) solutions for perfect isotropic and linear fluids. By using a power-law ansatz for the coframe components, we find several classes of new non-trivial teleparallel F(T) solutions. We also find a new class of teleparallel F(T) solutions for a matter dust fluid. After, we solve the field equations for a non-linear perfect fluid. Once again, there are several new exact teleparallel F(T) solutions and also some approximated teleparallel F(T) solutions. All these classes of new solutions may be relevant for future cosmological and astrophysical applications.