
The description of multiphase flow as interpenetrating continua incorporates the concept of phasic volume fractions , denoted here by . Volume fractions represent the space occupied by each phase, and the laws of conservation of mass and momentum are satisfied by each phase individually. The derivation of the conservation equations can be done by ensemble averaging the local instantaneous balance for each of the phases [ 10] or by using the mixture theory approach [ 37].
The volume of phase , , is defined by
(23.51) 
where
The effective density of phase is
(23.53) 
where is the physical density of phase .