I don't understand this. You start off talking about ascent rates so it seems to be about reducing ambient pressure but then talk about a rapid increase in ambient (Pamb being ambient pressure I assume) crushing bubbles. Can you explain?
I'll use the term 'tissue dissolved inert gas pressure' rather than P
amb, as this might confuse people. Pamb actually refers to the combination of dissolved gas pressure in the tissues plus pressure existing in body tissues (i.e. blood pressure), across different compartments, at different levels of saturation.
Factors on ascent:
- Think of a bubble as a flexible container.
- Bubble expands on ascent via Boyle's Law
- Bubble radius increase lowers internal bubble pressure
- Bubble radius increase lowers surface tension
- Diffusion between bubble and surrounding tissue is quick (much quicker than diffusion of inert gas in/out of the body)
- Diffusion into a bubble causes growth much quicker than Boyle's Law.
- Oxygen widow effect (metabolism of O2 in tissues) increases diffusion out of the bubble, at a rate determined by the O2 content of the gas breathed.
- At significantly deep depths (~10ata+) it's theorised that bubble surfactant density lowers or prevents diffusion through the bubble surface.
- Diffusion speed of dissolved gas in the tissues is dependant on a tissue-ambient gradient. The higher the gradient, the swifter the diffusion (off gassing speed), up until the M-value.
The Effect of Ascent Speeds:
1. If ascent is too fast, Boyle's law and inert gas diffusion into the bubble increases bubble volume. As a bubble grows its internal pressure reduces, allowing greater diffusion into the bubble from the dissolved inert gas in surrounding tissues. At the same time, the increasing bubble radius also decreases surface tension, further contributing to bubble growth.
In a nutshell, if bubble pressure is less than the combination of tissue dissolved gas inert pressure and bubble surface tension, then the bubble will grow.
This is bubble
growth.
2. If ascent is too slow, a bubble might otherwise diffuse to match surrounding tissue pressure as it decreases, causing the bubble to shrink in line with reducing pressure. However, the bubble surface tension serves to keep bubble pressure just marginally higher than the tissue diffused inert gas pressure. There's little/no diffusion out of the bubble.
In a nutshell, if bubble pressure equals the sum of tissue dissolved inert gas pressure and surface tension, the bubble will maintain volume.
This is bubble
persistence.
3. If ascent rate is optimal, you're keeping bubble pressure greater to
the sum of tissue dissolved inert gas pressure
and bubble surface tension. The ascent speed keeps tissue dissolved inert gas pressure decreasing rapidly enough to 'outpace' the decrease of pressure inside the bubble, even accounting for bubble surface tension. This permits a favorable positive gradient for gas to diffuse out of the bubble into surrounding tissues.
Collapsing bubbles during ascent (not stops) is about a fine balance, dictated by a pressure differential influenced by bubble surface tension.
In a nutshell, if bubble pressure is greater than the combined pressure of tissue dissolved inert gas and surface tension, then the bubble will shrink.
This is bubble
collapse.
It all seems very counter-intuitive right?
We're used to things growing when ambient pressure reduces or shrinking when ambient pressure increases. However, bubble volume is FAR more influenced by gas exchange / diffusion than Boyle's Law.
Summary of Principle:
We ascend quickly to our first stop because bubble-to-tissue diffusion is very quick, but tissue-ambient diffusion is much slower. Boyle's Law is relatively insignificant compared to diffusion.
We need to maximise the tissue-ambient gradient to increase diffusion and get tissue dissolved inert gas pressure lower than bubble pressure. That facilitates bubble collapse.
Context:
On recreational dives, this is important because stops (where bubble collapse can occur easier) are limited...and there's a limited oxygen window effect. There is, however, a more pronounced ambient pressure change on ascent in shallowee water. Nonetheless, you can be too slow.
On technical dives, we're talking about ascent through a depth range where there's less pronounced ambient pressure change. We want to get ourselves moving up so that we can create a positive gradient from the bubble to surrounding tissue. Deep stops can kick in when the bubbles reach 'critical radius' for collapse...or they can be ignored and resolved on shallower stops.. all aided by a substantial oxygen window.
(I think I've got that right... it's early am here and I'm distracted by watching GoT re-runs) LOL