Incompressible Ionized Non-Newtonian Fluid Mixtures

Chemically reacting mixtures represent a framework for modelling of various complicated processes in biology and chemistry. The model proposed in (Rou05a; Rou05b; Rou06; Rou07) uses incompressible framework with the barycentric impulse balance. This “barycentric” approach is called the Eckart-Prigogine’s (Eck40; Pri47) concept, simplifying phenomenologically the description by considering only one temperature and one velocity of the whole mixture and having been awarded in the context of nonequilibrium thermodynamics of dissipative structures by Nobel prize in chemistry in 1977; in the compressible case, see also (ADM82; dGM62; Gio99). For a comparison with less phenomenological Truesdell model (TrTo60) see (Sam07). The incompressibility refers here both to each particular constituent and, through a volumeadditivity hypothesis (i.e. Amagat’s law) also to the overall mixture. To cover biological applications on a cellular or subcellular level where intensity of electric field on cell membranes is very high, the self-induced electrostatic field must be considered, too.