Removal of ammonia as the ammonium ion calls for an ion-exchange process and ion-exchangers can do this effectively in fresh water. Even these exchangers, however, have limited capacity and once the available sites are saturated no further adsorption can take place. Ammonium ions, however, are not strongly held by ion-exchangers and the addition of even relatively small quantities of salts, as is frequently done in fresh-water aquaria, dramatically decreases the ability of ion-exchangers to remove ammonium. Under ideal conditions, the best synthetic ammonia absorber has a capacity of about 60 mg of ammonia per ml of absorber. For a 10 gallon aquarium, this translates into a capacity of 1.5 mg/Liter (ppm) for each ml of absorber. For a 10 gallon aquarium, about 50-200 ml of absorber would generally be used, giving a total capacity of 75-300 ppm of ammonia. This is a cumulative capacity and once attained the absorber will be saturated and no longer function, unless regenerated. The addition of as little salt as 5 teaspoons per gallon will cut capacity by more than 50%. Zeolite absorbers have about 1/4 to 1/5 the capacity of synthetic absorbers. Zeolites are easily recognizable as dusty, white to tan granules, similar to kitty litter. Synthetic absorbers are dustless, tan to brown beads or fibers.

Dynamics Of Aquarium Filtration
The most useful vantage from which to examine aquarium filtration is efficiency, which is defined as percent impurity removal per unit of time. A complex interaction of interdependent factors, depicted in Figure 2, govern the efficiency of aquarium filtration. Any factor which results in an increase in the volume that must pass through the filter decreases efficiency, while any factor that increases throughput increases efficiency. However, since many factors do both. the net result of changing any filtration variable is not usually as obvious as might be supposed.

The most obvious, but also the most overlooked, factor is recirculation, which causes clean or filtered water issuing from the filter to be continuously mixed with the relatively less clean or unfiltered in the aquarium. The mathematics of recirculation are similar to compound interest, except the percent change is
negative. Assuming a filter totally removes all of a given impurity, that is, it retains 100% of an impurity of the water passing through the filter, no mixing at all would require that 100% of the total volume of water pass through the filter to remove all available impurity; a 50% mix would require that 332% of the water pass through to remove all of the impurity; a 90% mix would require 437%; a 99% mix would require 458%; and continuous mixing, the actual situation with aquarium filtration, would require 460%. Put differently, recirculation is a constant that decreases aquarium filtration efficiency by increasing by a factor of 4.6 the cycle frequency, or the number of aquarium volumes, that must pass through the filter to effect 99% impurity removal.

The factor that has the most influence on efficiency is retention, the percentage of impurity concentration retained on the filter medium or removed from the passing water. Figure 3 shows the percentage of total volume, or number of cycles, that must pass through a filter to achieve 99% impurity removal at different % retentions. Since 100% retention is a rare exception. it is clear that the combination of low retention and recirculation requires very large volumes of water pass through a filter for effective removal of impurities.

Four factors directly effect retention: geometry. flow rate, solute-adsorbent effects. and concentration effects. Poor geometry is without a doubt the principle cause of low retention and consequent low filtration efficiency characteristics of too many aquarium filters. The two most common geometry defects are tubing locations that allow leakage around the filter medium, and low filter bed heights. Filtration requires a minimum bed height of about I cm, and the deeper the bed the better. Deeper beds are more retentive because they minimize leakage, they increase contact time, and each progressive layer behaves as a series of separate filters rather than a parallel of separate filters.

There are three basic filter geometries: the box filter, the cartridge filter, and the canister filter. The box filter is characterized by a relatively small surface area with limited flexible bed depth. Disposable "cartridges" for box filters impose, in addition, a fixed and shallow bed depth. Box filters also generally have several locations for by-passing (leakage) the filter medium around flow tubes or cartridges. Cartridge filters are characterized by relatively large surface areas with fixed shallow bed depths, and, therefore, are more retentive as sieve filters than as depth filters. Canister filters have small surface areas, but deep beds. Both cartridge and canister filters have insignificant by-pass or leakage.

Retention of solutes on a filter medium is directly proportional to the volume or quantity of that medium, and, for a given amount of medium, is proportional also to the bed depth. Figure 4 shows the effect of bed depth on the break-through flow rate for representative volumes of filter medium. Break-through flow is the minimum flow, expressed as volumes of the filter medium, at which solutes leak through the medium. It is evident that canister filters, with their deep beds, have remarkably more retention than either box or cartridge filters. The break-through flow can be determined empirically with dye solutions. It can also be approximated by calculation:

Break-through flow (gal/hr) = dcm(0.009)cc where d is the depth of the filter bed in cm and cc is the volume of filter medium. The volume of various filters can be calculated as follows:

box volume: (cc) = lcm x wcm x dcm
cartridge volume: (cc) = [hπr²]e – [hπr²]i
canister volume: (cc) = dπr²

where l is length, w is width, h is height, d is depth, r is radius. For box and canister filters, d = h; for cartridge filters, d is equal to distance between external and internal walls. All dimensions should be in cm. Typically. the break-through flow rate for a small box filter equipped with a disposable cartridge is about 2 gal/hr; for a cartridge filter, about 10-12 gal/hr;
and for a canister filter, about 100-140 gal/hr.
The break-through flow rate is not usually the optimum operating flow rate. As is evident from Figure 3, large volumes of water must pass through the filter for effective removal of impurities. For this to happen in a timely manner, it is usually necessary to sacrifice some absolute retention for overall timely removal. Figure 5 shows the effect on retention of increasing the flow rate beyond the break-through flow rate. Figure 6 re-draws the data from Figure 3 against unit time where unity is defined as the time required to clear 99% impurity at break-through flow rate. This type of plot shows the effect of the interaction of retention and flow rate on filtering efficiency.
For example, the plot shows that filtration at 100% break-through rate is no more effective than filtration at 340% that rate. The overall optimum is about 200% of the break-through flow. The plot shows that flow rate can be increased up to about 400-500% of the break-through rate without seriously sacrificing efficiency. Beyond that, however, increased flow rate begins to have consequential negative effects on filtration efficiency. Typically, this limit to about 10 gal/hr for box filters, 60 gal/hr for cartridge filters, and 700 gal/hr for canister filters. Both box and cartridge filters generally are operated well beyond this maximum, while canister filters are operated well below this maximum. Canister filters, in fact, are operated very closely to their optimum, generally around 150 gal/hr.

Solute-adsorbent effects are relatively complex and have already been discussed, but, in general, hydrophilic solutes are adsorbed at hydrophilic sites and hydrophobic solutes at hydrophobic sites. Carbons and polymeric adsorbents are more hydrophobic than hydrophilic. Synthetic ion-exchangers are more hydrophilic than hydrophobic. Some gel-type adsorbents are more hydrophilic than hydrophobic. Concentration of solutes affects solute adsorption in a manner which is predictable from mass action considerations. The greater the concentration of solute, up to a limit characteristic of the capacity of the adsorbent, the more readily is it adsorbed. As the solute concentration drops, the rate of removal drops proportionately.

These principles of filtration dynamics have been worked out primarily for chemical filtration, but they apply, generally, to any type of aquarium filtration, with the exception of mechanical filtration by sieving action. In that case, the depth of the filter bed is of little importance and external surface area becomes paramount. For mechanical filtration by sieving action, cartridge filters are unexcelled. For all other types of filtration, including mechanical depth filtration, biological filtration. and chemical filtration, the canister filter is clearly superior. Box filters, as they currently exist, with their poorly placed tubing, small volumes, and shallow bed depths, are remarkably inefficient.