Non-equilibrium flow

No flashing (non-equilibrium flow) until choke point... 

Two-phase flow in which no flashing of the liquid phase occurs. This may be due to the liquid being non-volatile or due to insufficient time for flashing to occur (non-equilibrium flow). 

In developing this rate kernel [eqn. (303)]. Kapral noted that one term could be ignored because it was small. This is a factor which allows for non-equilibrium flow of A and B towards each other. 

When the second order approximations to the pressure tensor and the heat flux vector are inserted into the general conservation equation, one obtains the set of PDEs for the density, velocity and temperature which are called the Burnett equations. In principle, these equations are regarded as valid for non-equilibrium flows. However, the use of these equations never led to any noticeable success (e.g., [28], pp. 150-151) [39], p. 464), merely due to the severe problem of providing additional boundary conditions for the higher order derivatives of the gas properties. Thus the second order approximation will not be considered in further details in this book. 

Figure 1.4. An example of the volume-fraction field for a highly non-equilibrium flow with Knp = oo. Left the hydrodynamic model predicts that particle clouds cannot cross and all particles end up with zero y momentum. Right the mesoscale model predicts that particle clouds will cross in the absence of collisions. Adapted from Freret et al. (2008).

In summary, we have demonstrated in this section how quadrature-based moment methods can be used to evaluate the terms in the moment-transport equations arising from collisions. The principal observation is that it suffices to know the functional forms for the terms which are derived and tabulated in Section 6.1. We also observed that, unlike traditional moment closures, the closures developed in this section are applicable to highly non-equilibrium flows. 

IcARDi, M., Asinari, R, Marchisio, D. L., IzQuiERDO, S. Fox, R. O. 2012 Quadrature-based moment closures for non-equilibrium flows hard-sphere collisions and approach to equilibrium. Journal of Computational Physics 231, 7431-7449. 

In this Chapter, the theoretical models for non-equilibrium chemical kinetics in multi-component reacting gas flows are proposed on the basis of three approaches of the kinetic theory. In the frame of the one-temperature approximation the chemical kinetics in thermal equilibrium flows or deviating weakly from thermal equilibrium is studied. The coupling of chemical kinetics and fluid dynamics equations is considered in the Euler and Navier-Stokes approximations. Chemical kinetics in vibrationaUy non-equilibrium flows is considered on the basis of the state-to-state and multi-temperature approaches. Different models for vibrational-chemical coupling in the flows of multi-component mixtures are derived. The influence of non-equilibrium distributions on reaction rates in the flows behind shock waves and in nozzle expansion is demonstrated. 

Kustova, E. (2009). On the role of bulk viscosity and relaxation pressure in non-equilibrium flows, in T. Abe (ed.). Rarefied Gas Dynamics 26th International Symposium, Vol. 1084 of AIP Conference Proceedings, pp. 807-812. 

This quantity is a measure of the ratio of adsorption rate to rate of fluid convection through the system. The use of combinations of equations similar to Equations 7.30 and 7.34 to describe non-equilibrium flow behaviour is quite common whether its origin is in dead-end pore mass transfer (Coates and Smith, 1964) or in unsteady-state adsorption (Ramirez et a/., 1980 Van Geneuchten, 1981). Ramirez et al. (1980) have described non-equilibrium adsorption of surfactants in laboratory cores using this approach. 

On the other hand, we may look at thermal feeling of our planetary ecosystems, which, in general, is influenced by positioning in interstellar space [9,191]. No planet is a closed system neither is it in contact with two or more thermal baths. Each planet is in contact with a hot radiator (sun 5800 K) and cold radiation sinks (outer space 2.75 K). Each planet therefore realizes a kind of a specific cosmological engine. Being a sphere is crucial because of its rotation and revolution modes with an inclined axis, which are responsible for the richness and complexity in the behavior induced by the solar influx. The atmospheric fluid motion adds the spice of chaos so that the thermodynamic events, which take place within a planet, are sustained by non-equilibrium flows, which must obey the fundamental laws of non-equilibrium thermodynamics. 

This procedure models a no-slip boundary condition at the surface of the colloid, and also thermostats the fluid at the boundaries. For many non-equilibrium flow conditions, this may not be sufficient, and it may also be necessary to thermostat the bulk fluid also (compare Sect. 2.3). It should also be noted that (74) will be a good approximation only if the radius of the embedded objects is much larger than the mean free path A. For smaller particles, corrections are needed. 

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