<< Does increasing water flow automatically increase efficiency, thereby increasing how many times the tank water will cycle through.>>
If this means that you have the same water/air contact time and surface area, and you are mixing the water around the bubble more, I'd say the answer is a definate yes, but the increase may be from big to trivially small. How's that for an answer?
In a sense, the question is asking if the water around a bubble gets depleted in organics such that replacing that local water with new water from the tank will deposit more organics. The answer is somewhat circular, but if you have allowed enough time for the bubble to deplete the local water, then yes, more turnover will help. If you are already mixing things fast enough that local depletion of organics is minimal, then any gains from additional mixing may also be minimal.
Consequently, I don't think that an answer can be given, a priori, about whether in any given situation more turnover will result in a substantial improvement.
<< Or, would decreasing water flow to allow more time for water-bubble contact be a more efficient way of capturing protein?
>>
Ahh, now were getting somewhere.
If you are engineering the device to increase water mixing AT THE EXPENSE of the total surface area, then you are in a vary ambiguous situation. I have no general answer.
OTOH, if you are engineering the device to have the same surface area, but lower contact time due simply to faster creation and destruction of bubbles, then I believe that more new bubbles will easily win out over few bubbles that are around for a long time.
There are two reasons for this. Again, any bubble will deplete the water around it, and even incredible mixing will not completely prevent the fact that once the local area is depleted, the movement of organics onto the surface will be slower than it was when the bubble was new.
Also, as the surface gets more and more covered with organics, there is less and less driving force for new organics to attach (with a few exceptions; see below). So the organics will be attracted to a new surface more effectively than they would be to one that is partially covered with organics already.
Consequently, both of these factors suggest that one wants more, new surface area, rather than longer contact times with the same old bubbles.
The exceptions mentioned above would be those organics that like the "mix" or organics present at air/water interfaces more than they like air/water interfaces alone. For example, some very hydrophobic things (like oil)are more readily dissolved in soap (an organc mix similar to that at an air/water interface) than it is on an air/water interface alone.
IMO, this effect is small in reef tanks because most biological materials are not as completely nonpolar as is oil (fat being the only common exception that I'm aware of).
Anyway, lots or rambling on a rather difficult topic.
