There are reactive sites on the solid in the film, participating in liquid+solid reactions to cause film growth. There are species in the liquid absorbed in the film, participating in both liquid+liquid reactions to cause chain initiation, propagation, and termination and liquid+solid reactions to cause film growth. The gradient in species concentration in the absorbed liquid causes diffusive fluxes. As the film grows, the interface between the bulk liquid and the film is moving and more liquid and liquid-phase species are absorbed into the film. We simulate the one-dimensional film growth using the finite volume method and discretize the film in the axial direction. We refer to the control volume at the boundary near the tray surface as i = 1 and the one near the bulk liquid as i = N , where i is the index of each discretization, and N is the total number of discretizations. For boundary conditions, we assume a no-flux boundary at the tray surface, and we assume the liquid-phase species concentrations in the bulk liquid stay at the steady-state concentrations, as illustrated in Fig. . In order to handle the moving boundary, we define the control volume such that it expands when the solid mass within it increases, and it moves in space when control volumes below it grow and push it toward the bulk liquid. We derive the governing equations starting from the macroscopic conservation equation for moving control volume, 31