The Pigford Problem
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
Many mass transfer operations involve diffusion in fluids in laminar flow—for example, absorption without chemical reaction of a gaseous compound in a thin liquid film of a nonvolatile compound flowing vertically. Another example is laminar flow of compound through the membrane walls of the channel. The first case has applications in chemical engineering and environmental science; the second, in medicine and biomedical engineering. Both cases can be treated by the same equations, based on the solution given by Pigford in 1941.
Contributed by: Jorge Gamaliel Frade Chávez (November 2009)
Open content licensed under CC BY-NC-SA
This Demonstration shows a solution of Pigford's problem using an orthogonal collocation method; the dimensionless equation is
with the initial and boundary conditions
Here is the concentration of compound , is the equilibrium constant, and and are the positions, all expressed in dimensionless units.
 J. V. Villadsen and W. E. Stewart, "Solution of Boundary-Value Problems by Orthogonal Collocation," Chemical Engineering Science, 22, 1967 pp. 3981–3996.
 R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd ed., New York: John Wiley and Sons.