The science says that higher flow increases a filter's ability to nitrify. practically, you also need contact time otherwise nitrite may come out of the filter due to the second stage in the nitrification process not being completed. This is why trickle filters for instance are better if they are taller. This does not mean that slower flow through a trickle filter improves nitrification, quite the opposite in fact, but rather that there needs to be enough filter media so that the nitrite can also be converted in one pass through the filter. These principles are important in an intensive aquaculture setting but rarely cause a problem in most aquariums/private ponds as the stocking density is rarely that high ie 15 kg fish and upwards/1000L.
In most aquariums/ponds it doesn't matter if a minimal ammount of nitrite is in the water due to low filter retention time as it will quickly be converted to nitrate with the next pass through the filter (all filter types). This is because most aquarium/pond filters have a high turnover rate. If you are running a filter with a low turnover rate of say 4 x per day or less, then contact time becomes more important when considering nitrification.
Heterotrophic bacterial balance in a filter is improved with longer retention time but is only really important if the filter is supposed to eat the mulm like with a Hamburg mat filter. Heterotrophic bacteria populations in filters that are regularly cleaned usually find a state of balance pretty quickly regardless of retention time/turnover.
Generally, the finer the mechanical filter material is, the cleaner the water will be.
Mechanical filtration does however improve for a given filter cross sectional surface area with slower flow rates due to improved adsorbtion. Adsorbtion in this case is the process by which mulm particles are attracted to a filter surface through weak electrical charge. This means that a more coarse mechanical filter material with slower flow rates can sometimes out perform a finer filter material using faster flow rates. So the optimal balance for mechanical filtration retention time versus turnover is filter material specific. A minimum optimal turnover does need to be maintained but this figure is usually much lower that most people assume and is reliant on the individual variables of each aquarium /pond system.
So what does all this mean?
In an aquarium/private pond setting you are unlikely to have a problem around nitrification rates or heterotrophic bacterial growth with 99% of diy or shop bought filters regardless of differences in retention time or turnover rate if the turnover rate is at least once per hour. The mechanical filtration is really the defining factor. To achieve optimal water quality choose a filter with an oversized fine mechanical filter and pump the water through at a moderate rate for that filter but at a rate that still allows the turnover to be multiple times per hour. This may not be economical in a pond setting so usually a balance must be struck.
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