This article is from the Aquaria: Filters FAQ, by Bruce Hallman.
For decades, hobbyists have successfully kept fish healthy and happy
through the use of the $2.49 corner filter. Typically, they are clear
plastic boxes, which sit inside the tank. An air stone bubbles air
through an air lift tube, which forces water through a bed of filter
floss or other media. mechanically filtering the water. Colonies of
bacteria build up on the media, providing excellent biological
filtration. (It is important to change only some of the media at any
given time! This way the bacteria does not get wiped out.) Nowadays
people don't use corner filters as much because they're ugly, take up
space in the tank, and require a bit more frequent maintenance than
other filters. But you can't beat the price.
Another use of the corner filter, that is not really matched by other
filter types, is as an impromptu quarantine tank filter. If you have
the need to set up a second tank on the quick, you can take some
gravel from an established tank and put it in a corner filter, and
immediately, you will have a functioning biological filter. This way
you can turn a five gallon bucket into a quick and cheap
hospital/quarantine tank on a moment's notice.
 
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