B. Svendsen, A LOCAL SUPERPOSED-CONSTITUENT VOLUME-FRACTION MIXTURE THEORY-BASED ON RELATIVE MOTION, International journal of non-linear mechanics, 29(6), 1994, pp. 845-860
This work presents a local formulation of kinematics and balance relat
ions for a mixture composed of superposed-constituents as based on the
ir motion relative to a model of the mixture as a moving region, with
the motion of this region being determined by that of all the constitu
ents. The relative motion of each constituent with respect to this mov
ing mixture region can be interpreted as its diffusive motion in the m
ixture. A number of constituent kinematic properties in the mixture, i
n particular the constituent volume density (i.e. the infinitesimal vo
lume-fraction) and constituent diffusion velocity, are determined by t
he constituent diffusive motion, and arise naturally in a formulation
based upon it. In addition, this formulation yields in a natural fashi
on an evolution relation for the constituent volume density relative t
o the moving mixture region. The consequences of this kinematic model
for constituent and mixture local balance relations, as well as the su
m relations, are investigated in the last part of the work.