Suppose the fluid consists of a mixture of i = 1,…,N immiscible phases. The following mass conservation equation describes the transport for an individual phase:

where ρi denotes the density (SI unit: kg/m3), si denotes the volume fraction (dimensionless), and ui denotes the velocity vector (SI unit: m/s) of phase i. In addition, the term Qi denotes a mass source for phase i (SI unit: kg/(m3·s)). It is assumed that the sum of the volume fractions of the phases equals 1:

This means that N − 1 phase volume fractions are independent and are possible to solve for using Equation 6-112. The volume constraint Equation 6-113 is used to reduce the number of dependent variables: one volume fraction, let us say of phase ic (to be specified in the main node of the Phase Transport interface), is expressed using the other volume fractions: