In the world of aquaculture, mechanical filtration and biofiltration are very distinct and separate entities, and they must be treated as such. Filtration is the removal of solid waste, whereas biofiltration is the biological process that converts toxic nitrogenous wastes to non-toxic nitrate.
Solid waste is typically categorized by its size and specific gravity. Settleable solids are those solids which have a relatively high specific gravity compared to the water in which they exist. They will settle to the bottom. Suspended solids are those in a category that have a specific gravity the same as, or slightly higher than, the water. They tend to stay in suspension and will only "drop-out" over a long period of time. Dissolved solids are those which actually become a part of the water. The dissolved solids are eliminated by reverse osmosis, anion and cation resins, activated carbon, etc.
One method of removing solid waste from a round fish tank is to use a double drain. It will direct the settled solids to a separate area from the main flow. The settled solids can be directed into a small clarifier, much smaller than one sized to handle the entire flow of recirculating water. The other drain takes the suspended solids along with the nitrogenous waste.
Suspended solids can be removed by several methods. One is the bead filter, which incorporates the use of small polyethylene beads that have a positive electrostatic charge. These beads have an affinity for the negatively charged suspended solids. As the particles pass these beads, they are "statically" drawn to them. When the beads are loaded with solids, it is time to backwash them.
Suspended solids can also be removed by mechanical means such as bag filters, drum filters and vegetative filters.
Biofiltration is the aerobic (with oxygen) breakdown of dissolved nitrogenous fish waste. The process is accomplished by two or more strains of autotrophic bacteria. These bacteria are naturally occurring and will ultimately colonize the bio-media in the biofilter as well as the tank and pipe walls. The speed of this process is dependent on temperature, pH, salinity, surface area, flow rate, etc.
The autotrophic bacteria use oxygen in a two-step process to first convert the toxic ammonia (NH3 or NH4+) to nitrite (NO2-). Another strain of bacteria converts nitrite (NO2-) to nitrate (NO3-). Nitrate is much less toxic and typically tolerated by most cultured species until it reaches very high levels. Controlling nitrate is accomplished by diluting with clean water or by using a denitrification chamber that converts nitrate into nitrogen gas (this is an anaerobic process that uses a group of heterotrophic bacteria). A third method to keep nitrate levels in check is the use of plants. You can have a green water system (using algae), a vegetative filter or even use a hydroponic plant system to remove nitrate.
Regardless of which type of filtering equipment you decide to use, the one thing to keep in mind is to stage the filtration. It is a common mistake to design a system that relies too heavily on a single filtering device to provide all of the filtering requirements of a recirculating system. By staging filtration components, the system will perform at or near its peak.