Similarly, we can integrate Eq. 13 for the liquid part to obtain the governing equations for liquid-phase species absorbed in control volume i of swollen film on the surface of tray j (Eq. 16). As illustrated in Fig. ), the number of moles of liquid-phase species in control volume i of tray j (N j,i liq∈film ) can change due to the diffusive flux entering/leaving the control volume i at the top and bottom boundaries (AF liq ), liquid+liquid reactions (Ω liq ), liquid+solid reactions (Ω liq+solid ), translation of the control volume i due to the expansion of control volumes below it, and expansion of the control volume i due to mass accumulation.