Math question.

[unfathomable]

Let's assume you are diving at sea level. If at 5 ATMs you develop a microbubble with a volume of 10 cubic units, what would it's volume and diameter be at 3 ATMs? Assume no time for offgassing. What about at 1 ATM? or at 8,000 ft. elevation? How do you work this out?

 

[johnny_bravo]

Boyle's law is your friend: p1 V1 = p2 V2

Easiest way is to take the volume to the surface. So 10 cubic units at 5atm will be 50 units at the surface. Then take it back down to 3 atm for a volume of 16.7 units.

Cheers.

-J.-

 

[shakeybrainsurgeon]

The Universal Gas law PV = nRT

Assuming the temo T is the same, for two different volumes v1 and v2 at 2 different pressures p1 and p2

p1v1 = p2v2

v1/v2 = p2/p1

if v1 is 10 and p1 is 5, when p2 is 3

10/v2 = 3/5
v2 = 50/3 = 16.7 units

at 1 atm

10/v2 = 1/5

v2 = 50

the diameter would simply vary by the cube root of the volume since we don't know what your units are, we can't calculate the precise diameter

I don't know what atm is at 8000 ft, but say it's 0.9

10/v2 = 0.9/5

v2 = 50/0.9

 

[rawls]

I could be wrong about this, but I would think that a microbubble will react based on Boyle's law which basically tells you that the volume of a gas is inversely proportional to absolute pressure. So you have a microbubble that is 10 cubic units at 5 ata. That means it is 1/5th the size it would be at sea level. So take the bubble to the surface and it will be 50 cubic units, assuming you are talking 5 atm absolute and not gauge. Then bring it down to 3 ata and you will have 16.7 cubic units. I don't think there would be enough of a difference in the volume of the bubble between the surface and 8,000 feet to make much of a difference because you have to go to about 20,000 ft to decrease the pressure by 1/2 atmosphere. So maybe about 50.5 cubic units thereabouts.

 

[shakeybrainsurgeon]

I looked it up... at 8000 ft, pressure is 0.75 atm, so the bubble would be 66.7, This is the pressure inside a commercial jet cabin

 

[WesTexDiver]

Lets say a tank has 80 cubic feet of air on the surface this shows the amount it will deliver at depth using P1V1 = P2V2


Depth.....ATA.....volume.....fraction.....% change

0......1.....80.....1/1.....0
33.....2.....40.....1/2.....50
66.....3.....27.....1/3.....33
99.....4.....20.....1/4.....25
132.....5.....16.....1/5.....20

 

[unfathomable]

ok. so far so good, these are the answers i got too. but now for the meat of the question....how does the diameter of the bubble change with the volume change? i presume it is the diameter of the bubble that matters most in terms of it's embolism causing capacity? so does the diameter change steadily throughout the pressure change? or does it change more rapidly during one portion? how does a volume change of 10 to 12.5 (5 atms to 4 atms) effect the diameter vs. a volume change of 25 to 50 (2 atms to 1atm)?

 

[ianr33]

But do microbubbles actually follow Boyles Law with respect to the ambient pressure?

Or does the surface tension of the skin throw a cog in the works?

The pressure inside an inflated balloon at sea level will be more than 1 ATA ,even though the ambient pressure is 1ATA.

 

[ianr33]

how does a volume change of 10 to 12.5 (5 atms to 4 atms) effect the diameter vs. a volume change of 25 to 50 (2 atms to 1atm)?

Diameter increase from 10 to 12.5 will be the cube root of 1.25 (12.5/10)

Diameter increase from 25 to 50 will be cube root of 2 (50/25)

 

[WesTexDiver]

Page 109 in the NAUI "Mastering Advanced Diving" book.

According to Haldane, bubbles will not form in a super saturated solution unless the pressure is halved.Ultrasonic doppler detectors have identified the pressence of non-symptom producing bubble. These bubbles may be present even if the no-decompression limits have not been exceeded.These inreavascular bubbles have been termed silent bubble. Silent bubbles are microscopic in size and are believed to originate from tiny gas pockets in the walls of tissue. Excess nitrogen during decompression dissolves into microscopic pockets,causing them to enlarge and extend into the circulatory path untill they finally break free and become tiny bubbles, which by themselves cause no harm. These bubbles can join together, however, to form larger bubbles that can produce symptoms of DCS.During ascent, the volume of the bubbles increases due to boyles law. This lowers the pressure inside the bubble which attracts more gas into the bubble. Therefore, the bubbles grow not only due to the laws of physics, but also because of the inward diffusion of gas.