Calculating CO2 diffusion rate - The Planted Tank Forum
 
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post #1 of 9 (permalink) Old 10-12-2011, 07:02 AM Thread Starter
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Calculating CO2 diffusion rate

As much as I've been enjoying tinkering with different in-tank reactor schemes, I decided to do some math on it to find out if what I'm trying to do is reasonable. There are two things I want to calculate.
1) Response time for a drop checker.
2) Surface area/flow required to diffuse a set amount of CO2.

This brought me to Fick's Laws of diffusion.
Per Wikipedia: http://en.wikipedia.org/wiki/Fick%27s_law_of_diffusion
flux=-P*A*(c2-c1)
A = transfer area, I can calculate that.
c2-c1 = the concentration difference. In the case of pure CO2 it is 1, for the aquarium water or drop checker it will be ~0.000030 (30PPM).
Unfortunately, I don't know P. I'll worry about reactor bubbles later, but for now I'd like to figure it out for the drop checker. I'm assuming this has something to do with surface velocity, and seems like it should be a known property for CO2/water. Can anyone point me to tables (or anything else) for this?
Also, any advice on calculating the CO2 concentration within the air of the drop checker? Is it the same as the aquarium, or higher? My first guess was the same, but if you think of your aquarium as a giant drop checker then that would imply %CO2 in the aquarium == %CO2 in the air, which is not true.

Always curious.
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post #2 of 9 (permalink) Old 10-12-2011, 08:24 PM
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well there is 350 ppm of c02 in the air on average. its all related to partial pressure which im sure if ur going this far, u are familiar with

what's in the drop checker is what gasses into the DC.. whether it be oxygen, c02, or nitrogen gas
they eventually overfill and dump some out so its constantly changing. what's in when u put it in for the first time only stays there for so long..


IT equilizes to what's in the aquarium.. HOWEVER it takes forever to do that

if the reaction chamber was bigger in a DC it would change faster.... most people don't want a huge DC in their tank

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post #3 of 9 (permalink) Old 10-12-2011, 08:50 PM Thread Starter
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Would the drop checker change faster if it were bigger? I'm assuming the increase in volume would offset the increase in area, assuming the same fluid depth. Given that 350 PPM in air only causes 3ppm in water, I'm assuming the air in the drop checker would have to be >350PPM to cause 30ppm in the water. If this were all gasses or all liquids I'd be ok, but the boundary I don't know how to handle. It's also been a while since I've taken much chem, so it's probably time to brush up on that.

Always curious.
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post #4 of 9 (permalink) Old 10-12-2011, 09:31 PM
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not true.. 350ppm in air translates to 3ppm in water due to pressure.. there's a poop ton more oxygen in the air than i nwater but water reaches saturation at around 11ppm

but c02 diffuses into water more readily which is why we can put more into it

a wide surface area of a drop checker with low depth would be key. just hard to read.

there would be a point where this becomes a useless cause but having a wider bulb would decrease the amount of time it takse for a DC to adjust..

another thing to consider is shake ur DC out of the tank after its changed color.. i bet it changes blue FAST because agitation is key for fluids to absorb gases in air.. ur increasing surface area..
so try putting something that vibrates on it while its in the tank and time how fast it changes

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post #5 of 9 (permalink) Old 10-12-2011, 10:35 PM
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Quote:
Originally Posted by HD Blazingwolf View Post
well there is 350 ppm of c02 in the air on average. its all related to partial pressure which im sure if ur going this far, u are familiar with

what's in the drop checker is what gasses into the DC.. whether it be oxygen, c02, or nitrogen gas
they eventually overfill and dump some out so its constantly changing. what's in when u put it in for the first time only stays there for so long..


IT equilizes to what's in the aquarium.. HOWEVER it takes forever to do that

if the reaction chamber was bigger in a DC it would change faster.... most people don't want a huge DC in their tank

you said theres 350ppm of CO2 in the air we breath alone. So howcome using "airpump" to air the water wont bring the water co2 level up?

or is it because 350ppm is not saturated enough ?


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post #6 of 9 (permalink) Old 10-13-2011, 10:44 PM
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because the nitrogen-oxygen bubble it's riding on is rising too fast to dissolve any siginificant amount of c02

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post #7 of 9 (permalink) Old 10-13-2011, 10:53 PM
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If airstones were a reasonable method of diffusion, we wouldn't need diffusers. Simply put, they just don't make bubbles small enough.
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post #8 of 9 (permalink) Old 10-14-2011, 05:12 AM
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The ppm of CO2 in air and the ppm of CO2 in water are two entirely different things. The ppm is a ratio of masses - miligrams per kilogram, for example. Put a container of water in air, which has some CO2 in it, and the ppm of CO2 in the air will be far different from the ppm of CO2 in the water at equilibrium (where the rate of CO2 leaving the water equals the rate of CO2 entering solution in the water.)

A drop checker's response time is a function of the area of the interface between the air in the DC and the fluid in the DC, the area of the interface between the air in the DC and the water in the tank, one divided by the volume or mass of the fluid in the DC and one divided by the volume of the air in the DC, and one divided by the length of the air path between the tank water and the DC fluid. Knowing that you can figure out the equation relating all of those variables if you have enough different examples of different drop checkers and can measure the response time for all of them. That is work! But, it can also be fun. But, first you need to define what you mean by "response time".

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post #9 of 9 (permalink) Old 10-14-2011, 06:13 AM Thread Starter
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Here I was thinking it was by molecules, not by mass. Either way, this should be a calculable value. Experimentation could confirm it, but I feel that a symbolic solution should exist. For response time I actually should have said time constant, from a system controls perspective.

Always curious.
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