A soluble gaseous reactant (specie A) dissolves into a deep liquid film where it undergoes the following second-order, irreversible reaction:
The rate of disappearance of dissolved gaseous A is:
By making a mass balance for dissolved A across a differential volume element in the film, it can be shown that the resulting differential equation is:
At z = 0 (at the gas-liquid interface), CA = CA* (4a)
As z→∞ (deep into the liquid film), CA →0. (4b)
(a) Solve equation (3) using the boundary conditions (4a) and (4b) and find an expression that relates the concentration of dissolved gaseous A in the film CA(z) to the equilibrium solubility CA*, the liquid – film coordinate z and other system parameters.
(b) Using assumed values for the parameters, evaluate the concentration profile CA (z) derived above as a function of z.
(c) Find an expression for the mass transfer rate at the gas-liquid interface where CA = CA*. Using the parameters assumed in step b, evaluate the mass transfer rate as a function of z.
(d) Suggest dimensionless variables and show the form of the transformed equation and boundary conditions