Species A is a dilute solute in a stagnant liquid film of thickness H. The device is at a steady state. Species A is fed on withinside the liquid film with the aid of using a homogeneous, first-order, and irreversible reaction, wherein R(A) = - kC(A). Species A additionally diffuses withinside the liquid film with diffusion coefficient D(A). The interface at y=0 is impermeable and nonreactive. At the liquid-gas interface (y=H), there is external convection consistent with the convective boundary condition with mass transfer coefficient kc. There is likewise a solubility coefficient a (relative to the liquid film), wherein C(A), gas = a*C(A, liquid) at the interface. The concentration of species A withinside the gas phase far from the liquid film is C. The film is very wide in the x and z directions and thus variations in those directions may be neglected.

a) Write the conservation equation for species A and the associated boundary conditions in the liquid film.

b) Solve for the concentration profile CA(y) in the liquid film and use the boundary conditions to find any unknown coefficients.

c) Sketch the concentration profile of species A, CA(y), in the limit that the reaction rate is i) very slow or ii) very fast compared to the rate of diffusion of species A, and the gas phase has very low mass transfer resistance compared to the liquid phase (so that CA,gas (y=H) ~ C).

d) The Biot number is a dimensionless parameter that relates the diffusion and convection fluxes at an interface. Show where the Biot number appears in your solution for CA(y). Biot number = Bi = kc H / DA = convective flux (on gas side) / diffusive flux (on liquid side)