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Optimal Design of Two-Chamber, Gas Diffusion Cells

Dep. of Mathematics

D. E. Rolston^*

Dep. of Land, Air and Water Resources, Univ. of California, Davis, CA 95616

*Corresponding author.

ABSTRACT

Two-chamber diffusion cells have been used for measuring the gas diffusivity of packed or undisturbed soil cores. Gas diffusivity is calculated from gas concentrations measured initially and at later times in an inlet chamber. The published analytical solution to diffusion in such diffusion cells for the general case of unequal air chamber size was arranged to solve for the soil-gas diffusivity explicitly and error analyses conducted in order to provide guidance in designing diffusion cells. An equation to calculate the first root of the resulting equation was derived. The optimum apparatus design was determined from error analysis to minimize experimental error in measuring the soil-gas diffusivity. The error analysis showed that the inlet and outlet chambers should not necessarily be of equal size, but that the chamber not being sampled should be larger than the sampled chamber. Total measurement error is greatest for very small soil-air contents and small times between initial and successive measurements of gas concentration. The optimum size of both the exit chamber and the soil core increases with measurement time. Thus, an optimum design of diffusion cells should be selected based upon range of soil-air contents expected, desired measurement times, and soil core length. Diagrams of total relative error and optimum soil core and chamber lengths with time for several soil-air contents and total relative error as a function of soil core and sampled chamber lengths provide guidance in designing diffusion cells with minimum experimental error. These estimates of optimum design can be easily changed for additional chamber characteristics or improved precision for measuring gas concentration.

Contribution from the Dep. of Mathematics, the Dep. of Land, Air and Water Resources, and the CA Agric. Exp. Stn., Univ. of California.

Received for publication August 29, 1988.

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