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/m
3),
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/(m
3·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 6-120. The volume constraint
Equation 6-121 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: