### Functions derived from diffusion-based decompression theory. UHM 2005: VOL 32, ISSUE #6

Relationship between two different functions derived from diffusion-based decompression theory.

H. Ashida, T. Ikeda, P. Tikuisis, R.Y..Nishi

Abstract:

Hempleman's diffusion-based decompression theory yields two different functions;one is expressed by a simple root function and the other by a complex series function. Although both functions predict the same rate of gas uptake for relatively short exposure times, no clear mathematical explanation has been published that describes the relationship between the two functions.We clariﬁed that

(1)the root function is the solution of the one-dimensional diffusion equation for a semi-inﬁnite slab,

(2)the series function is an applicable solution for a ﬁnite slab thickness,

(3)the parameter values of the root function can be used to determine the parameter values of the series function,and

(4)the predictions of gas kinetics from both functions agree until an adequate amount of diffusing inert gas reaches the boundary at the opposite end of the ﬁnite slab. The last point allows the use of the simpler root function for predicting short no-stop decompression limits. Experience dictates that the inert gas accumulation for a 22 min at 100 feet of seawater (fsw)dive is considered safe for no-stop decompression.

Although the constraint,Depth X the square root of bottom time = 100 X the square root of 22 has been applied as an index to determine either the safe depth or bottom time (given the other)for no-stop decompression,it should not be applied more broadly to dives requiring decompression stops.

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