As this is a thought experiment, and assuming the RELATIVE rate of change of absolute pressure is the important part (R = Pdot/P)
I wanted to circle back and acknowledge this assumption is incorrect. Since V is inversely related to P under the ideal gas law, the critical ratio to maintain in order to
maintain the same rate of bubble expansion is actually R = Pdot / P^2. Working through things from there, we arrive at a depth-dependent ascent rate (imperial units) of:
- Ascent Rate = Reference Rate * ( (Depth + 33) / (Reference Depth + 33) )^2
This clearly backs up the overwhelming consensus that one should slow WAY down during the final ascent. With a reference rate of 30 ft/min and reference depth of 30 ft, the rate when nearing the surface should be about 8 ft/min to maintain the reference rate of bubble expansion. The flip side to this, however, backs up the comments by
@Superlyte27 that you can basically ascend as fast as your scooter can take you when very deep. (The calculation evaluates to more than 1000 ft/min when passing through 333 ft, so anything slower than that results in SLOWER bubble growth than you have at 30 ft!)
(Metric folks should use 10 instead of 33 in the bulleted expression. The ascent rate when nearing the surface is 2.5 m/min assuming a reference depth of 10 m and reference rate of 10 m/min.)
To be clear, I'm not recommending that anyone depart from their training, and the choices you make on your own dive are your own. Again, this is merely a thought experiment, and like the OP, I find the question interesting. (The validity of the above assumes the rest of the ideal gas law terms -- particularly the number of gas molecules -- does not significantly increase over the timescales in question. I have no evidence that is true.)