Ω liq+solid = S liq+solid,liq R liq+solid (19) where C j,i liq∈film refers to the concentration of liquid-phase species in control volume i, and C j,N +1 liq∈film = C j liq,S.S. . D liq is the diffusion coefficient for liquid-phase species, i ± 1/2 refers to the top/bottom boundary of the control volume i, V j,i liq∈film is the volume of liquid part in control volume i, V j,i liq∈film is the rate of change for the volume of liquid part in control volume i. V j,i liq∈film and V j,i liq∈film are computed using