where N j,i fragm is the number of moles of reactive sites in control volume i of swollen film on the surface of tray j, S liq+solid,fragm is the rectangular 8 × 6,606 stoichiometric matrix for reactive sites (the shape is the number of fragments by the number of liquid+solid reactions), R liq+solid are the rates of the liquid+solid reactions, k f,liq+solid and K eq,liq+solid are the rate constants and the equilibrium constants for the liquid+solid reactions (see the SI of our prior work 6 for the estimation of K eq,liq+solid ), and C j,i liq∈film are the concentrations of liquid-phase species absorbed in the film in control volume i of swollen film on tray j.