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Just a 5 gallon bucket ATM with 4 stones going in it. I use 4 gallons every 4-5 days currently in veg. Would just like to keep 2-3 buckets around and ready to go. ( just a small 4x8 hobby grow, and only using half of it at the moment) I top dress so it'll just be water sitting bubbling. I will brew a tea occasionally but I don't plan on storing that.
I would not bubble air through it. The only outcome of that is that the CO2 in the air will drop pH—you can't super saturate O2 in a nutrient solution by bubbling.
Other than that, there shouldn't be an issue. Nutrients are designed to go into solution easily and most do so quite well. You should adhere to the "mixing order" - silica first, cal mag (if it's part of your nutrient mix), Part A, Part B or whatever they're called.
My res management "nutrient add pack" process is to fill my res (it holds 28 gallons) and to mix a 4 gallon bucket of ferts at double strength. As EC drops, I add enough of the concentrated batch to bring EC up to the desired level. I don't recall there ever being any precipitate in the 4 gallon batch. I don't actually pickup the bucket, I just dip a 2 liter container into it so the bucket will remain motionless for a few weeks at a time.
I've been doing this for a few years and have no reason to think that there's any issues with approach.
BTW, I've been back and forth on how often to change out a res and can't make the argument to replace a res every X days. I looked into this because the conventional wisdom is to swap a res every week. That makes sense if you're selling nutrients. It may not be much of an issue to a grower if it's one or two buckets and it's an enjoyable part of a hobby.
Another approach is to "add back" either ferts or RO water to the res and swap the res when certain evens occur. If you're doing fert add backs, a res should be replaced when pH starts to go out of range. If you're topping off with RO, the advise there is to swap the res when you've added back the amount of RO equal to the capacity of the res.
Again, if it's "just another thing to do", swapping every week is part of the hobby. On the other hand, you can cut down on the amount of labor by actively managing the res.
I've attached a couple of papers that might be of interest.
Note - I mixup (no pun intended) "add back" and "top off". Apparently there is a distinction and there's a 50/50 chance I've described is bassackwards.