Diffusion and Reaction in a Falling Liquid Film
Diffusion and Reaction in a Falling Liquid Film
This Demonstration considers the adsorption of a gas that undergoes a first-order irreversible chemical reaction in a falling film of liquid in laminar flow.
The equations describing this system for the reaction are:
AB
k
→
v
max
2
x
δ
∂
c
A
∂z
2
∂
c
A
∂
2
x
c
A
v
max
2
x
δ
∂
c
B
∂z
2
∂
c
B
∂
2
x
c
A
with the following boundary conditions:
c
A
c
B
c
A
c
0
c
A
∂(δ,z)
c
A
∂x
∂(δ,z)
c
B
∂x
where and are the concentrations of the adsorbed and product gases, respectively, is the maximum fluid film velocity in the direction, represents the coordinate along the thickness of the fluid film, is the thickness of the film, is the diffusion coefficient, is the reaction constant and is the solubility of as determined by the partial pressure of in the contiguous gas phase.
c
A
c
B
v
max
z
x
δ
k
c
0
A
A
The first boundary condition corresponds to the fact that the film has no gases at the top , the second indicates that at the liquid-gas interface only is present at a concentration determined by its solubility and the third boundary condition states that the gases cannot diffuse through the solid wall.
(z=0)
A
The system of equations is solved using Mathematica's built-in NDSolve. The solution is shown for various values of the rate constant , film depth , axial distance , diffusivity , maximum axial velocity and the solubility of gas , .
k
x
z
v
max
A
c
0