Ok...I'm glad I'm sparking some thought.
Nikki you're welcome. I'm enjoying it. Also, right now, what you are saying is correct. I want to leave the biology completely out of it for now. I am trying to lay down some basic tools we can use to understand the biology as we go forward, which is really the important part. For right now...I just want to look at the chemistry. For the next few discussions, I will assume that the substrate (be it rocks, sand, mud or whatever) is completely sterile and has always been that way and will never grow any creatures. That way, we focus only on the chemical processes. Keep in mind though that biology is really chemistry. Everything in biology works through chemistry and it all centers around equilibrium. Unfortunately for us, the systems are very complicated and interrelated so the equilibriums sometimes take more complex roles than we are discussing now as I'm sure you are aware. As I think we either know now or will see as the discussion progresses, it is the biology that causes the problems, not the chemistry. I have shown that the chemical processes can be caused to equilibrate and manage quite easily by water changes alone. That is not true with the bio-sink. However, let's reserve that for later.
As far as how soon the equilibrium is reached it depends. In the simple example of water in a jar with sand and Pi, it is reached virtually immediately, or within a few seconds anyway. In this case, it simply depends upon the binding constant and how much Pi we put into the water. In a dynamic system like our aquariums (no biologics though. remember we're sterile now), where we have input sources, chemical aequilibrium and export sources, it will depend. It depends upon:
A) How fast we are adding Pi to the system
B) How strong the binding constant is and
C) How fast we are taking Pi out of the system through export.
In the examples in the plots, which are not that accurate as I did not take the time to get real values for the parameters I used, it takes several months. This is probably pretty fair, however, whether it is 2 months or 15 months who knows. If you want, I can send you the spreadsheet and you can put in more accurate variables if you want. However since the model doesn't take biologics into account it is mainly just a conceptual tool.
Reedman...just because you are adding Pi, doesn't mean it HAS to come out. It will only come out if you have an export mechanism. Exactly what that mechanism needs to be can vary and opinions vary. In our clean system now with no biologics, we are just using water changes to remove Pi and Top off Water and Food to add it. The equilibrium point is determined by the variables A, B and C above. Since we don't really know those exactly right now and I don't want to take the time to dig them up, I suggest we just settle for understanding that there is an EQ point and that we can make it less by inputing less or taking it out faster. Remember again...we are only taking it out by water changes now and aren't considering biologics.
Dan..very perceptive of you
Reedman again. Since we aren't considering biologics...if we put Pi in, only Pi will come out. The only way it comes out is if we take it out. Elsewise it will increase forever until it becomes saturated and precipitates out.
Mike...a rock is a sink. Rock is very porous and unless completey has its pores clogged or is sealed with epoxy or something (virutually impossible) it will always be in equilibrium with the water. However, it is a weak sink. Once we start getting to biologics, other factors you mention will begin to dominate the limestone/water equilibrium such that it is negligable. I understand how you are using the word sink. I believe you are thinking of it as something that really traps P hard and long. However, I would like for us to think of the word more generally, as something that equilibrates with its surroundings. In this scenario a rock would be a weak sink (category 2) and a biology population would be a strong sink (category 3). Later I will talk about how biologics are really not even an category 3 sink, but a category 4 sink, but for now it is helpful for us the think of it as a category 3.
Sincerley...Collin