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.

Balance Laws of Continuous System.- Kinematics of Classical and Cosserat Continua.- Thermodynamics of Class I and Class II Classical Mixtures.- Thermodynamics of Binary Solid-Fluid Cosserat Mixtures.- A Continuum Approach to Liquid Crystals-The Ericksen-Leslie-Parody Formulation.- Nematic Liquid Crystals with Tensorial Order Parameters.- Multiphase Flows with Moving Interfaces and Contact Line-Balance Laws.