The Effect of Gas Diffusion on Life

Let's say world is completely flat (infinite flat world, think minecraft flatworlds) for the purposes of the question. The gasses of the world started out in a grid pattern, with each square being 1013 miles squared, and the atmospheres being as thick as the Earth's. Each gas starts out in its own square but slowly diffuses with the nearby squares. If life formed at the center of a square consisting of Carbon Dioxide (simulating the early Earth), and another square consisting of Methane, would the diffusion of the two gasses kill the creatures originating from the carbon dioxide square, or would the diffusion be slow enough that the creatures would be able to adapt?

• the gasses would diffuse to fast for any kind of evolution to occur towards the local conditions. the gasses would have long since mixed by the time life evolved to even have a metabolism to worry about. – John Aug 5 '19 at 5:14
• What is gravity like? Are you applying external sources of gravity, or is the only source of gravity the gas itself? Also, when you say "As thick as the Earth's atmosphere, I assume that you mean STP (Standard Temperature and Pressure), the approximate pressure of Earth's surface and 0C, but I'd like to double check. – Arcanist Lupus Aug 5 '19 at 5:32
• @ArcanistLupus The gravity replicates the earth, the reason isn't important though, and I do mean STP. – Nepthys X Aug 5 '19 at 6:08
• Why require an infinite flat plain? Any large spheroidal planet's surface could be gridded this way, tho' you would need an army of Maxwell's Daemons to make the gases start out this way. – Carl Witthoft Aug 5 '19 at 18:48
• An infinite flat plane can't exist, for obvious reasons, in our galaxy. Even if you reduce to maybe 1e10 km-square, with some arbitrary thickness, there is no material or mineral which can hold that shape. It would very rapidly flow into a sphere, and shortly thereafter fusion would almost certainly initiate. – Carl Witthoft Aug 5 '19 at 18:51

Supposing each gas is at one ATM, their diffusion coefficients should be in the 0.1 ~ 0.3 cm2/s range.

We can plug that into Flick's second law to find out how fast they diffuse. It can be simplified to this form:

$$t = \frac{x^2}{2D}$$

Where $$T$$ is time, $$D$$ is the diffusion coefficient, and $$x$$ is distance.

Assuming a general value of 0.2 for all gases, just for a thought exercise. Every second, they should diffuse to a range of:

$$1 = \frac{x^2}{0.4} → x^2 = 0.4 → x = \sqrt{0.4} → x = 0.632456...$$

So every second each gas might diffuse 63 cm into the surrounding squares.

Life as we know on Earth started one billion years after Earth formed. In one billion years, we have approximately 3.15 x 1016 seconds. Taking into account 63 cm/s, that gives us a diffusion of almost 2 x 1018 cm in all directions. Let's adjust that to 2 x 1013 km. Remember, 1 km is approximately 0.62 miles.

So, by the time life is starting to form, each gas has diffused past their immediate neighbors and a fifth of the way through the next, in the orthogonal directions.

Once the planet is four billions and a half old, the diffusion will have gone much 4.5x times further.

Supposing you have a rule that any square cannot be neighbor to another square with the same gas, the distributions should be pretty mixed. And in any case, life will have had billions of years to adapt. Any creature should be able to thrive well and safe in the square it is from, and at the very least in its eight neighboring squares, and the neighbors of those as well.

• Physics in the service of fantasy. I love it. ++ – Willk Aug 5 '19 at 22:10
• Thank you! This should make my world much more interesting... – Nepthys X Aug 6 '19 at 0:49

I guess your main concern is not diffusion. The gases have different densities (CH4 0,656 kg/m³, CO2 1.977 kg/m³). So as soon as the barrier is removed between the squares, CO2 starts to flow to the bottom and spread, CH4 goes to the top and spreads. Of course there will be some diffusion and turbulances, but it does not change the fact, that your lifeforms in the methane square are going to die quickly in a CO2 windstorm.

• I dare not even think about the radon and uranium-hexaflourite gas cubes. – TheDyingOfLight Aug 5 '19 at 10:44
• @TheDyingOfLight if you spend a few weeks thinking about the uranium fluorides, the problem of the radon will go away. – Starfish Prime Aug 5 '19 at 11:09
• I don't think that would happen. In our own atmosphere we find oxygen, carbon dioxide and nitrogen in the same layer. Each has its own density as well. – Renan Aug 5 '19 at 23:01
• @TheDyingOfLight lol it would probably be very rare but a scary thought nonetheless... – Nepthys X Aug 6 '19 at 0:56