A biofilm with a thickness Lf (cm) grows on the surface of a solid. After traversing a diffusion layer of thickness

L (cm), a chemical compound A diffuses into the biofilm where it is subject to an irreversible first-order reaction that converts it to a product B.

Steady-state mass balances can be used to derive the following ordinary differential equations for compound A:

Where D = the diffusion coefficient in the diffusion layer = 0.8 cm²/d, D_f = the diffusion coefficient in the biofilm = 0.64 cm²/d, and k = the first-order rate for the conversion of A to B = 0.1/d. The following boundary conditions hold:

Where c_a0 = the concentration of A in the bulk liquid = 100 mol/L. Use the finite-difference method to compute the steady-state distribution of A from x = 0 to L + Lf, where L = 0.008 cm and Lf = 0.004 cm. Employ centered finite differences with ∆x = 0.001 cm.

Transcribed Image Text:

Bulk Diffusion layer Solid surface liquid Biofilm 0 dra dx2 d2c Ca=Ca at x = 0 At: C. dx