Absorption with Chemical Reaction in a Semi-Infinite Medium
Consider the unsteady-state absorption with a chemical reaction in a semi-infinite medium. The governing equation is:
where and are the diffusion coefficient and first-order reaction rate constant, respectively.
The initial and boundary conditions are:
where is the saturation concentration and is the position.
This problem admits an analytical solution  given by:
The rate of absorption is given by :
This Demonstration plots the solution , as well as the rate of absorption versus time. The numerical solution obtained using the Chebyshev orthogonal collocation is given by the red dots. The analytical solution is given by the blue curve. The numerical rate of absorption is shown with a red curve. The analytical rate of absorption is given by the blue dashed curve. Excellent agreement between both solutions is observed.
You can vary the values of , , and as well as the number of Chebyshev collocation points, .