Shock structure and multiple sub-shocks in Grad 10-moment binary mixtures of monoatomic gases

The problem of sub-shock occurrence within a shock structure solution is investigated for an inert binary mixture of monoatomic gases, modelled by a Grad 10-moment approximation of the Boltzmann equations. The main purpose of this paper is to show by numerical simulations the existence of discontinuous shock structure solutions for values of the shock speed below the maximum unperturbed characteristic velocity. Moreover, for suitable concentrations of the two species, and for shock velocities beyond the maximum unperturbed characteristic velocity, each constituent of the mixture generates a jump discontinuity, and the shock structure solution exhibits two sub-shocks.

     

Shock structure for macroscopic multi-temperature model of binary mixtures: comparison with kinetic models

The present study deals with the shock wave profiles in the macroscopic multi-temperature (MT) model of binary gaseous mixtures. For that purpose we have adopted the hyperbolic model developed within the framework of extended thermodynamics [1] in which we include viscosity and thermal conductivity to eliminate restriction on parameters. This allows us to compare our results with more sophisticated kinetic solutions, which were computed for hypothetic mixtures of gases [2]. Numerical implementation of the MT model is considerably simpler than the one for Boltzmann equations for mixtures or the direct simulation Monte Carlo method (DSMC). (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Shock Waves in Dispersive Eulerian Fluids

The long-time behavior of an initial step resulting in a dispersive shock wave (DSW) for the one-dimensional isentropic Euler equations regularized by generic, third-order dispersion is considered by use of Whitham averaging. Under modest assumptions, the jump conditions (DSW locus and speeds) for admissible, weak DSWs are characterized and found to depend only upon the sign of dispersion (convexity or concavity) and a general pressure law. Two mechanisms leading to the breakdown of this simple wave DSW theory for sufficiently large jumps are identified: a change in the sign of dispersion, leading to gradient catastrophe in the modulation equations, and the loss of genuine nonlinearity in the modulation equations. Large amplitude DSWs are constructed for several particular dispersive fluids with differing pressure laws modeled by the generalized nonlinear Schrödinger equation. These include superfluids (Bose–Einstein condensates and ultracold fermions) and “optical fluids.” Estimates of breaking times for smooth initial data and the long-time behavior of the shock tube problem are presented. Detailed numerical simulations compare favorably with the asymptotic results in the weak to moderate amplitude regimes. Deviations in the large amplitude regime are identified with breakdown of the simple wave DSW theory.     

Thermodynamics of binary liquid mixtures

Excess volumes, V^E, of binary liquid mixtures (1) Toluene-Bromo-benzene, (2) Toluene-Nitrobenzene, (3) Toluene-Cyclohexanone, (4) Cyclo-hexane-Nitrobenzene, (5) Cyclohexane-Cyclohexanone were measured at 30° C. The results were analysed in terms of Flory’s theory. It is found that the theory, in general, is applicable to the mixtures studied.     

Viscosities of binary liquid mixtures

Eyring deduced a relationship between viscosity and molar volume of a pure liquid on theoretical considerations. Katti and Chaudhri assumed that the molar free energy of activation of flow of a mixture is an additive property and derived an equation correlating viscosity of an ideal mixture with molar volumes and composition. This expression was further modified for non-ideal mixtures by introducing a work function to represent the deviation from ideal behaviour. The validity of this equation was examined using binary mixtures in which intramolecular and intermolecular interactions are present. It is concluded that this equation is not applicable to binary mixtures of components which exhibit self-association.     

Molecular clustering in binary liquid mixtures

Proceedings - Mathematical Sciences - The earlier investigations on the intensity and depolarisation of the transversely scattered light in liquid mixtures in the neighbourhood of the critical...     

Boundary value problems in the theory of binary mixtures

In this paper, the boundary value problems of steady oscillation (vibration) of the linear theory of thermoelasticity for binary mixtures are investigated by means of the boundary integral equation method (potential method). The uniqueness and existence theorems of solutions of the exterior boundary value problems by means potential method and multidimensional singular integral equations are proved. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On quasi-stationary models of mixtures of compressible fluids

We consider mixtures of compressible viscous fluids consisting of two miscible species. In contrast to the theory of non-homogeneous incompressible fluids where one has only one velocity field, here we have two densities and two velocity fields assigned to each species of the fluid. We obtain global classical solutions for quasi-stationary Stokes-like system with interaction term. This work was supported by SFB 611.     

An oscillating plate in a binary mixture of hemihedral fluids

Summary The sinusoidal oscillations of an infinite plate in a mixture of two incompressible Newtonian hemihedral fluids are investigated. The solution is compared with the previously derived corresponding one for holohedral fluids.

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Zusammenfassung Es werden die sinusförmigen Schwingungen einer unendlichen Platte in einer Mischung von zwei inkompressiblen Newtonschen hemiedrischen Flüssigkeiten untersucht. Die Lösung wird mit der früher erhaltenen entsprechenden Lösung für holoedrische Flüssigkeiten verglichen.

     

Propagation of weak discontinuities in binary mixtures of ideal gases

The propagation of the weak discontinuities in binary non-reacting mixtures of classical ideal monoatomic gases is analyzed. The normal speeds of propagation are determined and compared with those of a single fluid. The differential equation governing the growth and the decay of the acceleration waves is obtained and the solutions for plane, cylindrical and spherical waves are shown. The influence of the different atomic masses of the constituents is also investigated.     

Cahn-Hilliard vs Singular Cahn-Hilliard equations in simulations of immiscible binary fluids

An efficient semi-implicit spectral method is implemented to solve the Cahn-Hilliard equation with a variable mobility in this paper. We compared the kinetics of bulk-diffusion-dominated and interface-diffusion-dominated coarsening in two-phase systems. As expected, the interface-diffusion-controlled coarsening evolves much slower. Also we find that the velocity field will be caused different greatly by using Singular Cahn-Hilliard equation and using Cahn-Hilliard in the simulation of immiscible binary fluids.     

Shock structure in viscoelasticity of relaxation type

We are concerned with the shock structure in viscoelasticity of rate type. The existence of a shock profile, which in the vanishing relaxation limit becomes an elastic shock, is demonstrated by an explicit construction of the solution of viscoelastic equations provided that the equilibrium stress–strain relation is governed by a parabolic law. For a more general stress–strain law which does not differ substantially from a parabolic one, the solution is obtained from a perturbation expansion.