*2.3. Mass Conservation Equation*

The mass conservation equation of the q phase is

$$\frac{\partial}{\partial t}(\mathbf{a\_{q}}\rho\_{\mathbf{q}}) + \nabla \cdot \left(\mathbf{a\_{q}}\rho\_{\mathbf{q}}\overrightarrow{\boldsymbol{v}}\_{\mathbf{q}}\right) = \sum\_{\mathbf{P}=1}^{n} \left(\dot{m}\_{\mathbf{P}\mathbf{q}} - \dot{m}\_{\mathbf{qp}}\right) + S\_{\mathbf{q}}\tag{3}$$

where <sup>→</sup> *<sup>v</sup>* q, . *m*pq, and *S*<sup>q</sup> are the velocity of the q phase, the mass transfer from the p phase to q phase, and the source phase, respectively.
