Average temperature and Maxwellian iteration in multitemperature mixtures of fluids

Abstract

This paper treats the nonequilibrium processes in mixtures of fluids under the assumption that each constituent is characterized by its own velocity and temperature field. First we discuss the concept of the average temperature of mixture based upon considerations that the internal energy of the mixture is the same as in the case of a single-temperature mixture. As a consequence, it is shown that the entropy of the mixture reaches a local maximum in equilibrium. An illustrative example of homogeneous mixtures is given to support the theoretical considerations. Through the procedure of Maxwellian iteration a new constitutive equation for nonequilibrium temperatures of constituents is obtained in a classical limit, together with the Fick's law for the diffusion flux. These results obtained for n-species are in perfect agreement with a recent classical approach of thermodynamics of irreversible processes in multitemperature case due to Gouin and Ruggeri and generalize our previous papers concerning the case of a binary mixture.

Multi-temperature fluid-dynamic model equations from kinetic theory in a reactive gas: The steady shock problem

“…On the other hand, a multi-temperature approach is needed in several problems of aerothermodynamics [6] or in plasmas at high temperatures [7]. The subject has been quite intensively investigated by methods from extended thermodynamics [8,9,10]. Work on multi-temperature equations as hydrodynamic limit of kinetic equations is in progress, starting from suitable models for chemical reactions and state transitions [11,12], and introducing different scales for different microscopic interactions, according to the process(es) considered as dominant.…”

Second Law Constraints on the Dynamics of a Mixture of Two Fluids at Different Temperatures

“…In the Eringen [13] aware of that addresses this in a serious fashion is Gouin and Ruggeri [9], Ruggeri and Simić [7,8], and Ruggeri and Lou [6]. Two important ideas have emerged from their studies.…”

“…As noted by Ruggeri and Lou [6], most studies consider a common temperature for both constituents even though there are many examples where this is clearly not the case. In fact the only recent papers we are aware of that address multi-temperature mixtures of fluids are the above citation along with Ruggeri and Simić [7,8] and Gouin and Ruggeri [9]. Ruggeri and Lou [6] note that one motivation for single temperature models is to avoid difficulties in measuring constituent temperatures.…”

Multi-temperature Hydrodynamic Limit from Kinetic Theory in a Mixture of Rarefied Gases

“…The macroscopic theory of homogeneous mixtures has been developed from basic principles on the assumption that each constituent obeys the same balance laws as a single fluid, yielding qualitative expressions for the coefficients in the exchange rates for species momentum and energy, and emphasizing the limiting role of a single temperature approach [19]. Several papers were published along this line, dealing with average temperature, Maxwellian iteration, heat conduction [9,18,20], and leading also to a quantitative application to the problem of flame structure [4]. The interested reader is referred to the review article [17] for more exhaustive information on a matter that seems to attract a broad and intensive attention nowadays.…”