A scaling law in the hydrodynamics of anisotropic viscous liquids

Summary We show that 1) the stationary flow of an isotropic liquid in a given viscosimeter is described by the same equations valid for a wellaligned nematic liquid crystal, having suitable values of the five viscosity coefficients, flowing in a viscosimeter like the previous one, but whose dimensions along the average molecular directionň are contracted; 2) a similar equivalence exists for a nematic flowing in a suitably chosen viscosimeter in two experiments which differ only for the direction ofň. This equivalence allows us to exactly compensate boundary effects in the measurement of the ratio between two of the Miesowicz viscosity coefficients. Furtherly a new particularly simple derivation of the Rayleigh dissipation function for nematics is given. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

A super space-time form of the hydrodynamics of free relativistic fluids

The dynamics of a free, special relativistic, adiabatic fluid results from an odd dynamical system in an space-time.     

A multi-moment vortex method for 2D viscous fluids

In this paper we introduce simplified, exact, combinatorial formulas that arise in the vortex interaction model found in [33]. These combinatorial formulas allow for the efficient implementation and development of a new multi-moment vortex method (MMVM) using a Hermite expansion to simulate 2D vorticity. The method naturally allows the particles to deform and become highly anisotropic as they evolve without the added cost of computing the non-local Biot–Savart integral. We present three examples using MMVM. We first focus our attention on the implementation of a single particle, large number of Hermite moments case, in the context of quadrupole perturbations of the Lamb–Oseen vortex. At smaller perturbation values, we show the method captures the shear diffusion mechanism and the rapid relaxation (on Re^1/3 time scale) to an axisymmetric state. We then present two more examples of the full multi-moment vortex method and discuss the results in the context of classic vortex methods. We perform numerical tests of convergence of the single particle method and show that at least in simple cases the method exhibits the exponential convergence typical of spectral methods. Lastly, we numerically investigate the spatial accuracy improvement from the inclusion of higher Hermite moments in the full MMVM.     

Projection tensor hydrodynamics: Generalized perfect fluids

The geometry of a projection tensor field in curved space-time is expressed in a way that does not restrict the dimensionality of the projection. The thermohydrodynamics of a perfect fluid then takes a compact and symmetrical form which also describes such exotic media as classical string fluids.Work supported in part by the National Science Foundation under grant No. MPS 74-18386-A01 and in part by the Alfred P. Sloan Foundation.     

Integro-differential equation method in the hydrodynamics of an incompressible viscous fluid

An integro-differential equation method is proposed to describe the motion of an incompressible viscous fluid. The method uses an analogy between the hydrodynamic equations for an incompressible viscous fluid and the magnetostatic equations. An analysis is made of the flow of an incompressible viscous fluid round an object as a specific application. The solution automatically satisfies the boundary conditions at the surface of the object and at infinity. Zh. éksp. Teor. Fiz. 112, 1332–1339 (October 1997)     

Equations of fluctuating nonlinear hydrodynamics for normal fluids

The full set of fluctuating nonlinear hydrodynamic equations for normal fluids is derived from the conventional Langevin equations extended to include multiplicative noise. The equations describing the set of conserved variables (the mass density, the momentum densityg, the energy density) agree with those found by Morozov for a case of a driving free energy which is a local function of the hydrodynamic variables. We show here that if the standard form of the hydrodynamic equations is to hold in the absence of noise, then the driving free energy must be a local function ofg and, but it may have to be a nonlocal function of the mass density.     

On wave equations for viscous fluids

This paper deals with wave equations describing small-amplitude disturbances in horizontally stratified, continuously varying, viscous fluids; gradients of the static pressure and of the coefficient of viscosity are neglected. A set of equations in first-order matrix form, which describes coupled longitudinal and transverse disturbances, is treated by the methods ofClemmow andHeading and ofHeading.The work of this paper could be extended in a number of ways; for example, the effect of a gravitational field could be included, and the coefficient of viscosity could be allowed to vary with position.     

Stochastic hard-sphere dynamics for hydrodynamics of nonideal fluids

A novel stochastic fluid model is proposed with a nonideal structure factor consistent with compressibility, and adjustable transport coefficients. This stochastic hard-sphere dynamics (SHSD) algorithm is a modification of the direct simulation Monte Carlo algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nanoparticle suspended in a compressible solvent.     

A velocity decomposition approach for moving interfaces in viscous fluids

We present a second-order accurate method for computing the coupled motion of a viscous fluid and an elastic material interface with zero thickness. The fluid flow is described by the Navier–Stokes equations, with a singular force due to the stretching of the moving interface. We decompose the velocity into a “Stokes” part and a “regular” part. The first part is determined by the Stokes equations and the singular interfacial force. The Stokes solution is obtained using the immersed interface method, which gives second-order accurate values by incorporating known jumps for the solution and its derivatives into a finite difference method. The regular part of the velocity is given by the Navier–Stokes equations with a body force resulting from the Stokes part. The regular velocity is obtained using a time-stepping method that combines the semi-Lagrangian method with the backward difference formula. Because the body force is continuous, jump conditions are not necessary. For problems with stiff boundary forces, the decomposition approach can be combined with fractional time-stepping, using a smaller time step to advance the interface quickly by Stokes flow, with the velocity computed using boundary integrals. The small time steps maintain numerical stability, while the overall solution is updated on a larger time step to reduce computational cost.     

Maxwell's equations and vorticity: A note on the viscosity of magnetic fluids

In magnetic fluid flows, it is generally assumed that the magnetization is kicked out of alignment by viscous forces when the vorticity has a component orthogonal to the magnetic field. Analytical expressions for the rotational viscosity π_r have been derived from this assumption.Here, it is argued that one must not forget the Maxwell equations in this derivation: Even a non-equilibrium magnetization has still to obey the magnetic field laws. Consequences of their inclusion are discussed; the results are supported by available data. An experiment is proposed to test the predicted field dependence of νr in more detail.     

非等温非牛顿黏性流体流动问题的修正光滑粒子动力学方法模拟

为准确、有效地模拟非等温非牛顿黏性流体的流动问题,本文基于一种不含核导数计算的核梯度修正格式和不可压缩条件给出了一种改进光滑粒子动力学(SPH)离散格式,它较传统SPH离散格式具有较高精度和较好稳定性.同时,为准确地描述温度场的演化过程,建立了非牛顿黏性的SPH温度离散模型.通过对等温Poiseuille流、喷射流和非等温Couette流、4:1收缩流进行模拟,并与其他数值结果作对比,分别验证了改进SPH方法模拟非牛顿黏性流动问题的可靠性和提出的SPH温度离散模型求解非等温流动问题的有效性和准确性.随后,运用改进SPH方法结合SPH温度离散模型对环形腔和C形腔内非等温非牛顿黏性流体的充模过程进行了试探性模拟研究,分析了数值模拟的收敛性,讨论了不同位置处热流参数对温度和流动的影响.     

Inertial effects in the response of viscous and viscoelastic fluids

We consider the effect of inertia on the high frequency response of a general linear viscoelastic material to local deformations. We calculate the displacement response and correlation functions for points separated by a distance r. The effects of inertia and incompressibility lead to anticorrelations in the correlation or response functions, which become more pronounced for more elastic materials. Furthermore, the stress propagation in viscoelastic media is no longer diffusive, as for simple liquids.     

Spatiotemporal resonances in mixing of open viscous fluids

In this Letter, we reveal a new dynamical phenomenon, called "spatiotemporal resonance," which is expected to take place in a broad range of viscous, periodically forced, open systems. The observation originates from a numerical and theoretical analysis of a micromixer, and is supported by preliminary experimental observations. The theoretical model nicely matches the numerical results, which again is supported by the experiment. Because of the general nature of the phenomenon, this phenomenon is not limited to microsystems. Because of the resonances, a slight tuning of the control parameters makes the mixer enhance the mixing, or suppress it, enhancing interfacial diffusion instead.     

A note on Hamiltonian structures for compressible,stratified and incompressible fluids

Relationships between Hamiltonian structures for compressible, stratified and incompressible fluids are examined and shown to be closely related, using an approach and perspective different to that adopted by Verosky.     

基于不可压缩光滑粒子动力学的黏性液滴变形过程仿真

应用基于投影算法的不可压缩光滑粒子动力学(incompressible smoothed particle hydrodynamics, ISPH)法对黏性液滴变形过程进行了数值仿真. 对于张力失稳导致的粒子非物理簇集问题, 采用粒子移位技术加以解决. 为了验证本文ISPH 算法的精度和稳定性, 分别模拟了圆形黏性液滴的拉伸变形过程以及方形液滴的旋转变形过程, 得到了不同时刻液滴内部的压力变化特征, 准确地捕捉了液滴自由面演化过程, 并将数值计算结果与文献中的解析解进行了比较.分析结果表明, 基于投影算法的不可压缩光滑粒子动力学方法结合粒子移位技术, 能够有效地模拟黏性液滴变形过程, 可以得到精确和稳定的结果. 关键词： 不可压缩光滑粒子动力学 黏性液滴 自由面流动 数值仿真     

Effects of bulk viscosity on hadron spectra and the Hanbury-Brown Twiss radius by causal viscous hydrodynamics

The particle spectra and Hanbury-Brown Twiss (HBT) radius of Au+Au collisions at RHIC energy are investigated by a hydrodynamical expanding source with both shear and bulk viscosities ($\zeta$). With a large width of the ratio of $\zeta$ to entropy density s, both the particle transverse momentum spectra and the ratio R_\rm out/R_\rm side of HBT radii in the direction of the total transverse momentum of detected two particles (R_\rm out) and perpendicular to both this direction and the beam direction (R_\rm side) become a little steeper.     

A note concerning the gravitational indistinguishability of a neutrino field and stokesian fluids

We show that the source of the Novello-Soares cosmological model may be either a neutrino field or a stokesian fluid. We make some comments on the problem that such an arbitrariness causes for Rainich's already unified program.