Continuity is solved for each phase: $ \frac{\partial(r_q\rho_q)}{\partial t}+\nabla\cdot (r_q\rho_q\boldsymbol{U}_q)=\sum_{p=1}^N(\dot{m}_{pq}-\dot{m}_{qp}) $ Where: $ \begin{align} p&:\text{primary phase} \\ q&:\text{secondary phase} \\ r&:\text{phase volume fraction} \\ \end{align} $ Mass transfer between phases [[Interface Capturing]] [[Eulerian multiphase model]] Momentum and energy equation solved for each phase Phases share common pressure field $ \frac{\partial(r_q\rho_q\boldsymbol{U}_q)}{\partial t}+\nabla\cdot(r_q\rho_q\boldsymbol{U}_q\boldsymbol{U}_q)=-r_q\nabla p+\nabla\cdot\boldsymbol{\tau}_q+\overbrace{\sum_{p=1}^N(\boldsymbol{D_pq+\dot{m}_{pq}\boldsymbol{U}_{pq}-\dot{m}_{qp}\boldsymbol{U}_{qp}})}^\text{Momentum transfer between phases} $ Each cell centroid will have N velocity fields for each phase Interphase momentum transfer will be dominated by [[Interphase Drag]]