The Pigford Problem

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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


Snapshots


Details

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.

References

[1] J. V. Villadsen and W. E. Stewart, "Solution of Boundary-Value Problems by Orthogonal Collocation," Chemical Engineering Science, 22, 1967 pp. 3981–3996.

[2] R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd ed., New York: John Wiley and Sons.



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