Hydrodynamic response and free surface modes for two immiscible fluids

We consider a system consisting of two immiscible fluids and their interface. The equilibrium interface is assumed to be planar. The velocity fields in the fluids are described by the linearized Navier-Stokes equations with appropriate boundary conditions at the interface. Explicit expressions for the response of the system to arbitrary bulk and/or surface forces are derived. In particular, we consider the transmission and reflection of sound modes and conclude that ultrasonic techniques can be used to measure the coefficient of sliding friction between fluids. In addition, we obtain dispersion relations for the free surface modes.     

Resonance line transfer and transport of excited atoms—II. Self-consistent solutions (1)

This second part of our study of non-LTE line transfer with convective transport of excited atoms presents self-consistent solutions of the radiative transfer equation and the kinetic equation of the excited two-level atoms, for the limiting case of no elastic velocity-changing collisions of the excited atoms. Pure Doppler broadening of the spectral line is assumed. We investigate reflecting and destroying boundaries for the excited atoms, while the boundary condition for the photons corresponds to free photon escape from the system. Our numerical procedure for solving the two coupled kinetic equations for the excited atoms and the photons is an iterative method using variable Eddington factors, and is described in detail. We present a simple model that considers the gas of excited atoms and the radiation field as two interacting fluids, which yields a straightforward interpretation of the various scale lengths encountered in the numerical results for the hydrodynamic properties (density, flux density, mean velocity) of the gas of excited atoms.     

Theoretical evidence for a dense fluid precursor to crystallization

We present classical density functional theory calculations of the free-energy landscape for fluids below their triple point as a function of density and crystallinity. We find that, both for a model globular protein and for a simple atomic fluid modeled with a Lennard-Jones interaction, it is free-energetically easier to crystallize by passing through a metastable dense fluid in accord with the Ostwald rule of stages but in contrast to the alternative of ordering and densifying at once as assumed in the classical picture of crystallization.     

Effects of vibrational anharmonicity on 19F nuclear resonance in SF6

A Barker-Henderson like perturbation theory for polyatomic fluids is developed. The molecular interaction forces are assumed to be described by an interaction site model potential and the reference system is a fluid of hard interaction site model molecules.

The theory is used to study the equation of state of nitrogen, the theoretical results being compared with experimental data and with those coming from other theories. The agreement between theory and experiment is as good as that shown by Barker and Henderson theory for monoatomic systems.     

Back-reaction equations for isotropic cosmologies when nonconformal particles are created

A model proposed some years ago by Hartle to study the back reaction in a cosmological model due to the creation of massless non-conformally coupled particles is reexamined. The model consists of a spatially flat FRW spacetime with a classical source made of two perfect fluids one a radiative fluid and the other a baryonic fluid with the equation of state of dust, and it is assumed that the ratio of baryons to photons is small. The back-reaction equations for the cosmological scale factor are derived using a CTP (closed time path) effective action method. Making use of the connection, in the semiclassical context, between the CTP effective action and the influence functional in quantum statistical mechanics, improved back-reaction equations are derived which take into account the fluctuations of the stress-energy tensor of the quantum field. These new dynamical equations are real and causal and predict stochastic fluctuations for the cosmological scale factor.     

New methods for calculating the dew/bubble curves of classical model fluids

We describe two new methods for locating the dew/bubble curves of fluids. One is a numerical method and the other an analytical method based on the use of series expansions. The utility of these two methods is illustrated by application to a simple one-component fluid model and to several model polydisperse fluids. The numerical method is based on a new geometric representation of the equilibrium conditions-similar in spirit to the geometric representations often used for solving the equilibrium conditions of pure fluids. Our calculations show that the series-expansion technique can be quite effective at producing accurate representations of the phase boundaries.     

A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows

We propose a new model and a solution method for two-phase compressible flows. The model involves six equations obtained from conservation principles applied to each phase, completed by a seventh equation for the evolution of the volume fraction. This equation is necessary to close the overall system. The model is valid for fluid mixtures, as well as for pure fluids. The system of partial differential equations is hyperbolic. Hyperbolicity is obtained because each phase is considered to be compressible. Two difficulties arise for the solution: one of the equations is written in non-conservative form; non-conservative terms exist in the momentum and energy equations. We propose robust and accurate discretisation of these terms. The method solves the same system at each mesh point with the same algorithm. It allows the simulation of interface problems between pure fluids as well as multiphase mixtures. Several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible. The method provides reliable results, is able to compute strong shock waves, and deals with complex equations of state.     

The excitation function of Au + Au in the framework of the (2+1)-fluid model

We present the excitation function of the reaction Au+Au in the frame work of the recently developed (2+1)-fluid model. In the (2+1)-fluid model, it is assumed that two baryonic fluids formed by the projectile and target nucleons produce a third hadronic fluid via inelastic nucleon-nucleon collisions. For this third fluid we use the equation of state of an interacting hadron gas obtained within the relativistic mean field model, including a first order phase transition. The dependence of the pion mean transverse momentum is investigated to observe the predicted plateau in the region of the phase transition of the hadronic matter to the quark-gluon plasma.     

反应流体的移动网格动理学格式

在移动网格上构造一种反应流的动理学格式.首先利用BGK模型推导含化学反应的流体力学方程组,并利用其积分形式构造移动网格上离散格式,再利用自适应移动网格方法得到网格速度,最后利用时间精确的动理学数值方法构造数值通量,得到移动网格单元上新的物理量.一维与二维的数值实验表明这种格式同时具有高精度、高分辨率的特点.     

Solution of the Ornstein-Zernike equation for a soft-core Yukawa fluid

A model for simple fluids is proposed in which the radial distribution function has a parametric form appropriate to a soft-core fluid for interparticle separationr R, whereR is some range parameter. Forr > R, the direct correlation function is assumed to be of Yukawa form. The Ornstein-Zernike equation is solved for this system, yielding the radial distribution and the total correlation function for the entire range of interparticle separation. Methods of relating the model fluid to a real fluid by assigning values to the parameters are discussed.Supported by ARGC grant No. B7715646R.     

A Maximum Principle for the Muskat Problem for Fluids with Different Densities

We study the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy’s law. This scenario is known as the Muskat problem for fluids with the same viscosities, being in two dimensions mathematically analogous to the two-phase Hele-Shaw cell. We prove in the stable case (the denser fluid is below) a maximum principle for the L ^∞ norm of the free boundary.     

High-speed cylindrical collapse of two perfect fluids

In this paper, the study of the gravitational collapse of cylindrically distributed two perfect fluid system has been carried out. It is assumed that the collapsing speeds of the two fluids are very large. We explore this condition by using the high-speed approximation scheme. There arise two cases, i.e., bounded and vanishing of the ratios of the pressures with densities of two fluids given by c _s , d _s . It is shown that the high-speed approximation scheme breaks down by non-zero pressures p ₁, p ₂ when c _s , d _s are bounded below by some positive constants. The failure of the high-speed approximation scheme at some particular time of the gravitational collapse suggests the uncertainty on the evolution at and after this time. In the bounded case, the naked singularity formation seems to be impossible for the cylindrical two perfect fluids. For the vanishing case, if a linear equation of state is used, the high-speed collapse does not break down by the effects of the pressures and consequently a naked singularity forms. This work provides the generalisation of the results already given by Nakao and Morisawa (Prog Theor Phys 113:73, 2005) for the perfect fluid.     

Luminescence quenching kinetics upon diffusion-accelerated dipole-dipole energy transfer for a realistic condensed-matter model

The hard-sphere model is considered as a more realistic condensed-matter model. In this model, the radial distribution function of molecules in a medium, used for calculations of luminescence decay kinetics, takes into account the short-range order in fluids and has the shape of damped oscillations. It is assumed that the motion of donor and acceptor molecules in a solution for the lifetime of the excited state of the donor is described by the diffusion equation, while the luminescence quenching occurs due to the long-range dipole-dipole energy transfer. It is shown that, if diffusion coefficients are small, the kinetics determined in this study hardly differs at all from the traditional kinetics. At intermediate and large diffusion coefficients, this difference becomes significant and should be taken into account in estimating the Förster energy transfer radius and diffusion coefficients from experimental luminescence decay curves.     

Effective potential method for active particles

ABSTRACT

We investigate the steady-state properties of an active fluid modelled as an assembly of soft repulsive spheres subjected to Gaussian coloured noise. Such a noise captures one of the salient aspects of active particles, namely the persistence of their motion and determines a variety of novel features with respect to familiar passive fluids. We show that within the so-called multidimensional unified coloured noise approximation, recently introduced in the field of active matter, the model can be treated by methods similar to those employed in the study of standard molecular fluids. The system shows a tendency of the particles to aggregate even in the presence of purely repulsive forces because the combined action of coloured noise and interactions enhances the effective friction between nearby particles. We also discuss whether an effective two-body potential approach, which would allow to employ methods similar to those of density functional theory, is appropriate. The limits of such an approximation are discussed.     

Surface instability on thin fluid layers of a binary mixture

A long-wave model for thin layers consisting of two miscible fluids is presented. The model is a development of a simplified 2D model variant which considers the temperature and the concentration fields as linear functions on the vertical coordinate and neglect the convective terms from the corresponding equations. Now, the 2D thin film equation is coupled to complete 3D energy and mass conservations equation. We discuss the extended system in the linear approximation and in the initial nonlinear stage.     

Prethermalization in one-dimensional Bose gases: Description by a stochastic Ornstein-Uhlenbeck process

In magnetohydrodynamics, model experiments are commonly conducted to investigate the interaction between magnetic fields and electrically conductive fluids. The available flow instrumentation for opaque fluids usually lacks the ability to capture and visualize a velocity field in one shot. We present a multidimensional ultrasound array Doppler velocimeter that employs multiple line arrays of transducers and allows the resolution of small scale structures in complex flows. The system achieves a lateral resolution up to 3 mm, an axial resolution of approx. 1.4 mm and frame rates up to 30 Hz in metal melts at room temperature. A flexible sensor arrangement allows for various measurement configurations, e.g. four planes can be measured simultaneously with one velocity component, two planes with two components or two lines with three components. We present an experiment in a square-shaped container driven by a rotating magnetic field and results of a model experiment for continuous steel casting. The measurement system has proven to be a powerful tool for research in magnetohydrodynamics.     

Spontaneous processes and stable structures in some three-phase cellular fluids

Cellular fluids are systems consisting of a collection of fluid cells surrounded by thin liquid films. In this study, systems composed of two different kinds of cells (i.e., filled with fluids A and B) immersed in a third fluid phase (a liquid C) have been examined. The object of the study is a collection of polyhedra of fluid B separated by a thin film of liquid C (a host B/C network), modified by the insertion of small droplets/bubbles of fluid A. Interfacial tensions acting along the A-C and B-C interfaces are assumed to be the only driving forces determining the structure of the resulting mixed system. Different configurations of mixed A/B/C systems, formed by the insertion of A singlets or doublets into the nodes, edges, films and interior parts of cells of the B/C network have been analyzed in terms of the interfacial energy of the system. The possibility of spontaneous migration of cells A through the B/C network and the possible final cell arrangements have been examined.     

Numerical solution of an extended White–Metzner model for eccentric Taylor–Couette flow

In this study, we have developed a new numerical approach to solve differential-type viscoelastic fluid models for a commonly used benchmark problem, namely, the steady Taylor—Couette flow between eccentric cylinders. The proposed numerical approach is special in that the nonlinear system of discretized algebraic flow equations is solved iteratively using a Newton–Krylov method along with an inverse-based incomplete lower-upper preconditioner. The numerical approach has been validated by solving the benchmark problem for the upper-convected Maxwell model at a large Deborah number. Excellent agreement with the numerical data reported in the literature has been found. In addition, a parameter study was performed for an extended White–Metzner model. A large eccentricity ratio was chosen for the cylinder system in order to allow flow recirculation to occur. We detected several interesting phenomena caused by the large eccentricity ratio of the cylinder system and by the viscoelastic nature of the fluid. Encouraged by the results of this study, we intend to investigate other polymeric fluids having a more complex microstructure in an eccentric annular flow field.     

Effect of the direction of the electric field on the interfacial instability between a passive fluid and a viscoelastic polymer

In this paper, we study the linear stability of the interface between an Upper Convective Maxwell fluid and a hydrodynamically passive fluid subject to an electric field applied either parallel or normal to the flat interface between the two fluids. The fluids are leaky-dielectric and we apply surface-coupled model. We solve the model equations analytically and study the dispersion and neutral curves for various parameters representing the applied potential, the fluid’s elasticity, the physical and the electrical properties of the fluids, and the heights of the fluids in the presence of both normal and parallel electric fields. It is found that the critical wavenumber is independent of the Weissenberg number. However, increasing the Weissenberg number increases the maximum growth rate for both the normal and the parallel fields. The critical wavenumber increases with the dimensionless applied voltage for the normal field. Lastly for the normal field, for some values of the dimensionless parameters, the growth rate reached very large values representing some type of singularity as has been observed in the literature. However, for the same values of the parameters no singularity is observed for the parallel field.     

Observationally homogeneous shear-free perfect fluids

It has been conjectured that, in general relativity, shear-free perfect fluids which obey any reasonable barotropic equation of state are necessarily either non-expanding or nonrotating. We prove that this is valid in the restricted case when the fluid's expansion and energy density are assumed to be functionally dependent. In a cosmological context, this condition of functional dependence is of interest, because it is closely related to a recently proposed criterion of observational (spatial) homogeneity, which has been enunciated in the Postulate of Uniform Thermal Histories (indeed, the two are equivalent when the fluid's expansion is nonzero). Our result on shear-free fluids may be readily specialized to the case of hypersurface-homogeneous spacetimes, and in particular to that of spatially homogeneous cosmological models. We briefly examine all subcases in which the fluid's expansion is nonzero and focus attention on the one-parameter family of solutions which are not hypersurface-homogeneous.