Increased nitrogen off-gassing 10ft/3m VS 20ft/6m on 100% oxygen

[Jacob BV]

So I am camp it should make zero-negligible difference due to what @inquisit and others have said. Some of @Iowwall's thought experiments are interested though, and potentially relevant. What I beleive it boils down to is the half life of 2 gasses reaching absolute pressure equilibrium when there is a difference (this will be a function of how the 2 gasses are allowed to mix). I suspect this is much quicker than the inert gas half lifes - and hence not a driving or significant factor, especially as we ascend continously rather than instantaneously. Furhermore, our bodies are not like the example of opening a cylinder in a room, biology and perfusion will change this. I believe there are some models out there that model the interchange from perfusing to diffusion but I don't know much about them.

Oh wait I see the flaw in the logic. The example of opening a cylinder of air at pressure in a room at 1atm is a compelling anology. But no this is not a fair analogy, the PPN2 in the cylinder is way above 0.79ATM and that drives the diffusion. If you filled a cylinder to 200 bar absolute but PPN2=0.79 (with the rest say oxygen or anything else) nitrogen would not be driven out of the cylinder it would move back and forth freely and randomly.

Ignoring biology off-gassing at 6m or 3m on O2 will result in the same off-gassing. I say ignoring biology since there could be effects like higher PPO2 causing more vasodilation, promoting more inert gas diffusion. But no studies have showed effects like this yet.

 

[lowwall]

from thermopedia - DIFFUSION

"Three types of diffusion are distinguished, viz., molecular, Brownian, and turbulent. Molecular diffusion occurs in gases, liquids, and solids; both diffusion of molecules of extraneous substances (impurities) and self-diffusion are observed. Molecular diffusion occurs as a result of thermal motion of the molecules. It proceeds at a maximum rate in gases, at a lower rate in liquids, and at a still lower rate in solids—these differences being accounted for by the nature of thermal motion in these media.

In a gaseous phase, molecules possess a certain mean velocity depending on the temperature, but their motion is chaotic and in colliding, they change the direction of this motion. However, on the whole, the molecules of the substance migrate at a velocity much lower than the mean velocity of the molecular free motion. The higher the pressure, the denser is the molecule packing, the less is the free-path length, and the slower is the diffusion. The same occurs as molecule mass and size increase. Conversely, elevation of temperature causes an increase in the free-path length, a decrease in the number of collisions, and growth of free-motion velocity. These factors all lead to a speed-up of diffusion."

In our original situation, we have non-blood tissues at some pressure x and a choice of two pressures for the blood tissues of approximately 1.3atm and 1.6atm. The total pressure of the system is higher at the greater depth (6m), thus according to the above, diffusion will be slower. At the shallower depth (3m), diffusion will be faster.

 

[Jacob BV]

from thermopedia - DIFFUSION

"Three types of diffusion are distinguished, viz., molecular, Brownian, and turbulent. Molecular diffusion occurs in gases, liquids, and solids; both diffusion of molecules of extraneous substances (impurities) and self-diffusion are observed. Molecular diffusion occurs as a result of thermal motion of the molecules. It proceeds at a maximum rate in gases, at a lower rate in liquids, and at a still lower rate in solids—these differences being accounted for by the nature of thermal motion in these media.

In a gaseous phase, molecules possess a certain mean velocity depending on the temperature, but their motion is chaotic and in colliding, they change the direction of this motion. However, on the whole, the molecules of the substance migrate at a velocity much lower than the mean velocity of the molecular free motion. The higher the pressure, the denser is the molecule packing, the less is the free-path length, and the slower is the diffusion. The same occurs as molecule mass and size increase. Conversely, elevation of temperature causes an increase in the free-path length, a decrease in the number of collisions, and growth of free-motion velocity. These factors all lead to a speed-up of diffusion."

In our original situation, we have non-blood tissues at some pressure x and a choice of two pressures for the blood tissues of approximately 1.3atm and 1.6atm. The total pressure of the system is higher at the greater depth (6m), thus according to the above, diffusion will be slower. At the shallower depth (3m), diffusion will be faster.

It's another good point, however, inert gasses in tissues are not gaseous. They are disolved and their diffusion governed by different laws, for example Fick's law. So I still believe the gas physics of off-gassing are the same on oxygen at all depths.

 

[lowwall]

It's another good point, however, inert gasses in tissues are not gaseous. They are disolved and their diffusion governed by different laws, for example Fick's law. So I still believe the gas physics of off-gassing are the same on oxygen at all depths.

Interesting. Anyone have access to Diffusion of Dissolved Gases in Liquids (Himmelblau 1964)? Page 547 "Effect of Pressure on Diffusivity" and "Effect of Concentration on Diffusivity" look useful. Although it may not cover pressure gradients.

I think I'll post this to stackexchange physics and see what happens.

 

[goldfishtornado]

governed by different laws

Both cases are governed by Fick's law. The key assumption that is different is that in the quote where they talk about "higher pressure" they say:

So far, the above discussion has focused on the so-called pure concentration diffusion proceeding under the effect of concentration gradient

(Emphasis mine)

Pressure and partial pressure are only equal for pure substance.

Latter in the article they talk about how to treat mixtures. In the Dalton limit of Fick's law of diffusion the particles are point particles in gaseous phase, and so never collide. Then you can freely treat the species as independent and use pure partial pressures. In real gasses the particles do collide. You then must calculate the interdiffusion coefficient from the chemical potentials or fugacity. Fick's law expressed in terms of potentials is true from thermodynamic first principles, Dalton's (and other ideal gas) laws are an approximation.

When you apply Fick's law to solutions the partial pressure approximation is the same as the Dalton's law limit for the gaseous phase. This is not the reason to believe that in the case of real gases there is no dependence on the partial pressure of oxygen inspired. In the solution case you are still dealing with real gasses. The reason why it is believed to be a negligible difference is apparently because most of the oxygen in the venous system is bound to hemoglobin. This is probably true for the depths people care about for practical purposes, but is not true at all depths. The level of oxygen saturation in blood hemoglobin probably changes with an increase in inspired oxygen pressure, but because the oxygen is so tightly bound to hemoglobin it does not affect the chemical potential or effective radius from the perspective of nitrogen diffusion.

I do tend to believe that the difference is negligible. There must be some difference though, because if there were no change in the chemical potential oxygen would not bind to hemoglobin.

 

[Jacob BV]

Interesting. Anyone have access to Diffusion of Dissolved Gases in Liquids (Himmelblau 1964)? Page 547 "Effect of Pressure on Diffusivity" and "Effect of Concentration on Diffusivity" look useful. Although it may not cover pressure gradients.

I think I'll post this to stackexchange physics and see what happens.

They don't study it, the ranges in the table are the range of measurements as opposed to the range seen at different pressures.

I've done a bit of a literature search and there's no low hanging fruit explaining diffusion of dissolved gases vs pressure. If you find a title or abstract that looks interesting but you don't have access let me know.

 

[inquis]

Three types of diffusion are distinguished,

That describes how things move around when everything is at the same pressure. In our case, the driving mechanism is a (partial) pressure difference.

The higher the pressure, the denser is the molecule packing, the less is the free-path length, and the slower is the diffusion.

Our pressures are substantially lower than where these effects are significant.

 

[lowwall]

I posted this a couple of hours ago: Do pressure gradients affect diffusion speed for gases dissolved in liquids (scuba offgassing question)

This question comes from a scuba forum where we are discussing the technical scuba technique of breathing 100% O2 during stops at shallow depths to speed up the offgassing of nitrogen (N2) from body tissues. What we are trying to determine is whether it makes a difference as far as N2 offgassing speed whether the stop takes places at 3m (1.3 atmospheres) or 6m (1.6atm). These stops are during the ascent at the end of the dive.

From what I understand, this is essentially a question of diffusion of dissolved gases between two liquids surrounded by a permeable membrane where one liquid (body tissues other than blood) contains a given partial pressure of dissolved N2 and the other liquid (blood) contains only dissolved O2 (0% N2) at a partial pressure of either 1.3atm or 1.6atm. Will the N2 diffuse (or otherwise move) more quickly into the liquid at 1.3atm or 1.6atm or does it not make any difference?

FWIW, there are two camps in this debate. Camp 1 says the only thing that matters is the difference in partial pressures of N2 between the two tissues/liquids and since the ppN2 in the second liquid is 0 in both cases, then the diffusion rate will be identical. Camp 2 says the increased pressure gradient between the N2 tissue and the 1.3atm liquid will drive a faster rate than the 1.6atm alternative. So far no one is saying that the deeper stop will result in faster offgassing.

I hope this is an acceptable framing of the question. If there are glaring errors, let me know and I can edit it. Or you can create an account (or use any existing stackexchange or stackoverflow login) and reply.

No answers yet. For some reason there's a lot less activity on physics.stackexchange than stackoverflow

 

[lowwall]

They don't study it, the ranges in the table are the range of measurements as opposed to the range seen at different pressures. View attachment 744977

Thanks.

I had to grin at "The effect of pressure on diffusivities of dissolved gases is a topic which remains virtually untouched by theoretical analysis."

I've learned a lot in the last 48 hours. With the result that I'm far less sure about what's actually going on with offgassing at the tissue level . I can see why those building modern deco models ignore all this in favor of nice clean partial pressure calculations and then cranking in a little conservatism.

 

[inquis]

Seams like a reasonable summary to me. Calling the non-blood a "liquid" is a little weird, but it shouldn't change the answer.