Mixture concepts are nowadays used in a great number of subjects of
the - ological, chemical, engineering, natural and physical sciences (to
name these alphabetically) and the theory of mixtures has attained in
all these dis- plines a high level of expertise and specialisation. The
digression in their development has on occasion led to di?erences in the
denotation of special formulations as 'multi-phase systems' or
'non-classical mixtures', 'structured mixtures', etc., and their
representatives or defenders often emphasise the di?erences of these
rather than their common properties.
Thismonographisanattempttoviewtheoreticalformulationsofprocesses which
take place as interactions among various substances that are spatially
intermixedandcanbeviewedtocontinuously?llthespacewhichtheyoccupy as
mixtures. Moreover, we shall assume that the processes can be regarded
to becharacterisedbyvariableswhichobeyacertaindegreeofcontinuityintheir
evolution, so that the relevant processes can be described
mathematically by balance laws, in global or local form, eventually
leading to di?erential and/or integralequations,
towhichtheusualtechniquesoftheoreticalandnumerical analysis can be
applied. Mixtures are generally called non-classical, if, apart from the
physical laws (e. g. balances of mass, momenta, energy and entropy),
also further laws are postulated, whicharelessfundamental,
butmaydescribesomefeaturesofthe micro-structure on the macroscopic
level. In a mixture of ?uids and solids -
thesearesometimescalledparticleladensystems-thefractionofthevolume that
is occupied by each constituent is a signi?cant characterisation of the
micro-structure that exerts some in?uence on the macro-level at which
the equations governing the processes are formulated. For solid-?uid
mixtures at high solids fraction where particle contact is essential,
friction between the particles gives rise to internal stresses, which
turn out to be best described by an internal symmetric tensor valued
variable.
