This third volume describes continuous bodies treated as classical
(Boltzmann) and spin (Cosserat) continua or fluid mixtures of such
bodies. It discusses systems such as Boltzmann continua (with trivial
angular momentum) and Cosserat continua (with nontrivial spin balance)
and formulates the balance law and deformation measures for these
including multiphase complexities. Thermodynamics is treated in the
spirit of Müller-Liu: it is applied to Boltzmann-type fluids in three
dimensions that interact with neighboring fluids on two-dimensional
contact surfaces and/or one-dimensional contact lines. For all these
situations it formulates the balance laws for mass, momenta, energy, and
entropy. Further, it introduces constitutive modeling for 3-, 2-, 3-d
body parts for general processes and materially objective variable sets
and their reduction to equilibrium and non-equilibrium forms.
Typical (reduced) fluid spin continua are liquid crystals. Prominent
nematic examples of these include the Ericksen-Leslie-Parodi (ELP)
formulation, in which material particles are equipped with material unit
vectors (directors). Nematic liquid crystals with tensorial order
parameters of rank 1 to n model substructure behavior better, and for
both classes of these, the book analyzes the thermodynamic conditions of
consistency.
Granular solid-fluid mixtures are generally modeled by complementing the
Boltzmann laws with a balance of fluctuation (kinetic) energy of the
particles. The book closes by presenting a full Reynolds averaging
procedure that accounts for higher correlation terms e.g. a k-epsilon
formulation in classical turbulence. However, because the volume
fraction is an additional variable, the theory also incorporates
'k-epsilon equations' for the volume fraction.
