If you grow mangroves without any substrate the root system will continue to grow, stealing energy from the rest of the plant above water. Mangroves, like any plant, need to be potted in a suitable sized pot so root growth can be limited so more leaves and branches can develop. The size of the plant is dictated by the size of the root system. If you restrict the roots growing room too much the plant will be stunted.
Mangroves should be grown with 6500K metal halide lighting. This will provide the intensity and coverage they need. 175 watts will suffice, unless you are growing a lot of them with a higher wattage (250 or 400 watt) metal halide fixture mounted higher above the trees.
Mangroves don't require salt to grow and will actually do better in soil with freshwater. I like to grow them in soil outdoors in the summer. Mangroves cannot compete with terrestrial plants surrounding the estuaries (mangrove swamps) they are found in possibly due to their slow growth rate. They have evolved to be tolerant to saltwater so they can live in marine environments where there is no competition.
Mangroves excrete salt through their leaves so they need to be sprayed with freshwater daily and perhaps wiped. Nature takes care of this job with morning dew and rain. A daily spray will also humidify the air, as they come from a humid environment. Dry air, particularly in our homes during winter, dries out the leaves. Mangrove leaves are shiny due to a protective coating that seals in humidity. A dry room will cause the mangrove to loose some of the water that it works so hard to extract from saltwater.
Mangroves grown in saltwater use magnesium to force/pump sodium salts out through their leaves. If grown in freshwater or soil, they do not require magnesium. Bioavailable magnesium can be supplied via dolomite gravel which is calcium magnesium carbonate. As the chemical name would suggest, it adds the three main elements that reefs require supplementing - calcium magnesium and carbonates (KH). Localized acidity caused by bacteria in the dolomite will slowly dissolve it and make it bioavailable to the tree. Otherwise having a magnesium level of 1300-1500 in the system water is sufficient. If they don't get enough magnesium they experience yellow or shriveled leaves. Growth of the plant and subsequent nutrient uptake will be limited if the magnesium level drops significantly.
If you want to experiment you could add pelletized sulfur to the dolomite for a passive sulfur denitrification filter. Sulfur filters/reactors encourage an acidic environment by feeding denitrifying bacteria. This would create a passive calcium reactor, slightly raise carbonate hardness (KH/alkalinity), and moderately raise magnesium. The added bonus is denitrification (lowering nitrate). You can read up on sulfur denitrification here
http://reefcentral.com/forums/showthread.php?t=1288082 I'm suggesting a scaled down version of the reactors discussed in the thread so dissolution rates will be only marginal in comparison. The Ph will be nowhere near as low as with a calcium reactor (7.7 vs. 6.5 PH). You need to use a 99.9% pure sulfur pellet and not the 90% pure sulfur pellets used in agriculture that are designed to dissolve quickly. The agriculture pellets turn to mush quickly. The effluent (out going) water from the mangrove tank should pass through a granular ferric oxide (GFO) reactor as the iron will react with any residual hydrogen sulfide that forms, converting it to a less toxic form of sulfur.
The amount of nitrogen and phosphorus in reef aquariums is more than enough to supply the mangrove with what it requires for growth. One of the chief limiting factors that you will experience with mangroves grown in a reef system is carbon dioxide (Co2). If you really wanted to encourage growth, you could add a second line from your Co2 tank (for your calcium reactor) and put it on a timer and solenoid to dose Co2 every few hours during the day. Mangroves have pores on the undersides of the leaves called stomata that breath in Co2 and breath out o2 during photosynthesis. Aiming a circulation fan at the mangroves will also provide more Co2 to the leaves. A classroom full of kids is more than enough Co2. Even urban (high) vs. suburban (moderate) vs. rural (low) ambient Co2 levels will effect how well the plant can grow.
Most plants require well oxygenated soil or substrate, but mangroves have evolved in oxygen-poor (anaerobic) soil so they don't need water movement through the root zone. Black mangroves in particular have snorkel roots that are spongy so they can draw oxygen from the surface and deliver it to the root mass. A flow-through substrate with more oxygen (aeroponics) will not provide any benefit to mangroves.
The bark surface above the water is rough and brown, while below the surface it is shiny and bright green. You can lower the water level or raise the tree/pod to simulate a dry season or low tide. By doing this, you encourage the tree to send out prop roots (air roots) as the roots stretch down for more water. Red mangroves have the nicest prop roots. If you leave the mangroves in one static position, they will not develop the prop roots and character they are famous for.
You can trim mangrove trees like bonsai and even bend them with wire to shape them. By pinching off the top leaves occasionally you send growth hormones down to the lower levels of the pod/tree so new branches and leaves start. Bending the top of the plant down a few inches also transfers growth hormones from the top to the lower parts of the plant. This adds new growth to lower areas without compromising (cutting) the top.
Mangroves are slow growers even in the best conditions. You can expect one or two leaves a month growth per plant which will yield a modest dry weight in nutrient uptake. mangroves do not add oxygen to the water as their photosynthesis is independent of what goes on underwater.
You could add some anableps, archer fish, mudskippers, cardinals or fiddler crabs to complete a mangrove estuary theme. An ebb and flow system that raises and lowers the water level in a cycle would also be interesting. If you were short on space you could grow a vertical wall of mangroves but you would have to use a slow flow system to minimize salt creep.