Mixture theory is used to model
multiphase systems using the principles of
continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a ''continuous medium'' (also called a ''continuum'') rather than as discrete particles.
Continuum mec ...
generalised to several interpenetrable continua.
The basic assumption is that, at any instant of time, all phases are present at every material point, and
momentum
In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. ...
and
mass balance
In physics, a mass balance, also called a material balance, is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have ...
equations are postulated. Like other models, mixture theory requires
constitutive relations
In physics and engineering, a constitutive equation or constitutive relation is a relation between two or more physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance or ...
to close the system of equations.
Krzysztof Wilmanski extended the model by introducing a balance equation of porosity.
References
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Rheology
Scientific modelling