MULTISCALE, HYBRID MIXTURE THEORY FOR SWELLING SYSTEMS .1. BALANCE LAWS

A three-scale problem involving swelling media is considered. The stru cture of the system (e.g. day, polymers, etc.) is assumed to be charac terized by particles composed of more than one phase (usually solid an d liquid) which may swell or shrink. The swelling (or shrinkage) is th e result of mass transfer from (to) a multicomponent solution which is in contact with the particles. Mesoscopic equations for the particles themselves have been obtained elsewhere. The macroscopic equations fo r the combination of swelling particles and bulk solution as well as t heir interfaces, considered as a mixture, are obtained here. Constitut ive theory for the system is the subject of a subsequent manuscript.