As a science experiment to measure the diffusion coefficient this seems a good method. However, considering the limited time that you have I am not sure if this is the best rabbit hole to dive into. Diffusion constants are already known from literature, as well as in the paper that I will attach. Once your invest your time and we would have the diffusion constant established, we will still have the uncertainty what is our assumption on the boundary layer thickness, related to surface agitation and turbulence, and it is not clear to me if this will be the shortest and most efficient route bring us closer to our dream for the planted tank.
Thank you,
@Yugang, for the paper you attached; it uses a very similar approach that I also intend to use, and it employs the correct scientific terms, which adds clarity. I think that we are actually much closer in thinking than it may appear at first glance.
I fully agree that what matters in aquariums is not simply a molecular diffusion in a static system, but gas–liquid mass transfer governed by surface renewal, turbulence, and agitation. That is exactly why I am not trying to determine a molecular diffusion coefficient or assume the physical boundary layer thickness.
The parameter I am aiming to identify is the mass-transfer coefficient (k
La), as they refer to in the paper, which, by definition, already incorporates:
- diffusivity,
- effective boundary layer thickness,
- interfacial area,
- turbulence and surface renewal
In other words, the uncertainty in boundary layer thickness is not an unresolved problem—it is precisely what k
La is meant to absorb. This is the same abstraction used in chemical engineering or medical applications (with which I am more familiar) whenever the microscopic hydrodynamics are inaccessible or irrelevant, which is the case here as well.
I referred to this parameter before as diffusion capacity or conductance. In this paper, they determine the very same parameter (as mass transfer coefficient) for their reactor, which is specific to the system. I would like to determine this parameter in a system that is more similar to an aquarium setup, and then in a real aquarium. With the help of the parameter, we can also determine the CO2 absorption by the plants in a real setup to get the answer to the question whether CO2 mass transport on the air/water surface is on par with the plant usage at the given CO2 concentrations.
I completely agree that k
La is not universal and depends on agitation and setup. That is not a drawback from my perspective; it is the reason to measure it under aquarium-relevant conditions rather than trying to infer it theoretically.
On the specific suggestions:
1. I think that using the indicator dyes is less precise than what I plan to use; I plan to infer dissolved CO2 from changes in headspace CO2 concentration. This could be done more precisely, calculating with the speciation under an aquarium-relevant alkalinity condition (CO2<-->bicarbonate<--> carbonate) or less precisely, using RO water and ignoring the minor effect of the speciation under these conditions. Alkalinity mainly affects the dynamics, not the final equilibrium, so it may not be critical for the questions we are trying to answer. Another issue with bromothymol blue is that it only works under specific conditions: the KH needs to be adjusted to the target CO₂ level (for example, at ~1% CO₂, the KH would need to be around 2 dKH to give the “right” colors). Also, the color would depend on the concentration, lighting, and perception, all of which add uncertainty. Also, matching the surface/volume ratio alone does not guarantee that the effective kL is comparable between a stirred beaker and a real tank.
Instead, I would use a range of water movements in the "model aquarium" (e.g., still water vs strong stirring) to have a feel for the CO2 transfer rate range, and then see where the parameter lies in a real aquarium. This would give us a more realistic approximation of the actual situation.
2. This experiment is more difficult for me to conduct, since I do not have the equipment to keep CO2 constant in the headspace, which I think is required for a meaningful pH drop in the aquarium.
@PeerUnk might be better equipped to perform this experiment. What I
can do, however, is measure how quickly the CO2 disappears from the headspace to determine what level of sealing is realistic for an aquarium. I can also measure pH changes in the dark and during lighting, as you suggested, but with CO2 levels already at around 30 ppm, to estimate what CO₂ transfer rates are required and how those compare to realistic transfer rates.
This setup and level of theory may sound like overkill for a hobby context, but I believe it is the correct approach and one that is achievable with the home-made equipment we have.
