vkalia:
Assuming that the controlling tissue doesnt change, a slow ascent should indeed work better. Taken to a hypothetical extreme, if there was a tissue with a superfast half-time, a slow ascent would result in the tissue pressure equalizing more or less in sync wih the divers ascent. Slow tissues are less likely to be affected. So, depending on the function, either there is an optimal range of controlling tissues where the above doesnt hold; or it doesnt hold at all; or the controlling tissue changes which puts the math far beyond my abilities.
The controlling tissue does indeed change. The slower the ascent, the more it will change towards the slower compartments. The whole purpose of the ascent is to balance coming up to reduce loadings in the medium to slower compartments, while giving the faster compartments enough time to offgas.
Go up too fast, and the faster compartments get too high of overpressure. Go up too slow and you continue to load up the slower compartments and will eventually take them to their limits.
To help put this is perspective, below is a table showing compartments of various halftimes, and the fsw (absolute) N2 surfacing pressure limit for each compartment, and the depth on air and on EAN32 at which you have that inspired N2 partial pressure. Shallower than that depth, you can stay indefinitely and never exceed the compartment limit. For example, at 90' on either air or EAN32, you will never exceed the allowable pressure for direct ascent in the 5 minute compartment.
HT ... DSAT M0 (fsw).. AIR DEPTH ..EAN32
60 .......... 51.44 ........ 32' ....... 43'
40 .......... 55.73 ........ 37.5' ..... 49'
30 .......... 59.74 ........ 43' ....... 55'
20 .......... 66.89 ......... 52' ....... 65'
10 .......... 82.63 ....... . 72' ....... 88.5'
5 ........... 99.08 ........ 92' ....... 113