Tom,
I don't think the are that many facts and they aren't terribly arcane. I'll attempt to summarize and get back on the track :
Terminology:
Advection: predominantly horizontal current and the wave action it produces as it encounters(an) obstruction(s)in it's path as well as the resulting "endo upwelling" under the obstruction. The upwelling occurs directly under the obstruction in a mirror image of it's footprint and height. At a horizontal flow rate of 10cm per second the endo upwelling will occur at a rate of 1cm per hour in the model presented by Sprung and Delbeek. The upwelling also results in water being pulled down .
Sprung and Delbbek use the term advection to describe this phenomenon as do Heutel and Rausch in their research(2). . Esoteric interpretations of discipline specific claims to specific terminology wether they be from engineering, meteorology ,chemistry etc . notwithstanding, I'll stick with them since they represent fields more closely related to reef keeping.
Diffusion: for the purposes of this discussion is the movement of molecules in water toward equilibrium. Some might call this convection but again , I'll use the terminology most commonly used in reef keeping literature.
Nitrification: the aerobic activity of autotrophic bacteria(those that can use inorganic carbon such as bi carbonate and CO2/carbonic acid)in oxic and hypoxic areas to convert decaying material to ammonia and nitrite and coenzymes such as adenosine triphosphate which they uses for energy transfer to enable life functions including cell division.
Denitrification: the anerobic activity of of heterotrphic bacteria(those that need organic carbon for energy) in hypoxic and near anoxic areas to convert nitrate to free nitrogen gas and coenzymes.
Faculative bacteria (those that can use either organic or non organic carbon for energy ) likely also play a role in both nitrification and denitrification.
Applications:
Trickle filters or towers : support high oxygen ,oxic areas and thus produce nitrate as an end product since they do not support heterotrophic bacteria which perish in the presence of oxygen.
Deep sand beds,generally over 4 inches deep as well as live rock can include : oxic , hypoxic and anoxic areas. Both autotrophic and heterotrophic bacteria can flourish in and on them. However, the heterotrophs need a source of organic carbon for energy and coenzme production. The autotrophs do fine with non organic carbon sources. So the deep sand bed needs a supply of organic material(dissolved or undisolved ) to keep the heterotrophs that use the nitrate viable. Obviously, it also needs a supply of nitrate. The bed (or rock) is fed by the water that moves through it via advection and/or the channeling and transport activity of benthic fuana. Diffusion supports the equilibriation of organic carbon molecules and nitrates throughout the water.
A deep sand bed without the proper amount of water movement to bring in the needed organic carbon and nitrate will not function well as a denitrifier. On the other hand too much fluidization will bring in too much oxygen. On the third hand, too much carbon and too little nitrate will set the stage for the bacteria to turn to SO4 for the oxygen they need with the potential for hydrogen sulfide formation as a by product. After that they will move on to metals and other nasty by products.Hence, the caveat on dosing organic carbon when deep sand beds are in play . Although some have suggested seeding a deep bed with sulfur or vodka et al. as a means of sourcing an energy source in a deep bed. I think it's dangerous.
Again a functional deep sand bed needs a force to insure the movement of oxygen depleted water( stripped by autorphic and faculative bacteria)laden with nitrate and a source of organic carbon for the heterotrophic bacteria to thrive and reduce the nitrate .
A bed that is allowed to clog or pack down or is just too deep for things to pass down just wont do very much.Benthic fauna in a live bed can help to maintain viability through channeling activities and assist in transport of organic materials..
Diffusion is a relatively weak force and will not in my opinion provide enough material to promote denitrification.
Advection, can enhance the process multifold( as many as 50 fold see reference (2) putting more water in play in which diffusion can occur.
The study by Tonnen and Wee from the Advanced Aquarist Magazine:
http://www.advancedaquarist.com/2008/8/aafeature3
concludes:
Each sediment-based aquarium design appeared capable of handling nutrient inputs up to 0.5 mg / L / day of NH4+ - which is equivalent to a well-stocked reef aquarium. At this input level, final concentrations of ammonia, nitrite and nitrate did not differ significantly among aquaria 1) with or without plenums, 2) containing deep (9.0 cm) or shallow (2.5cm) sediments, or 3) containing coarse (2.0mm) or fine (0.2mm) mean particle sizes."
So for my money ,deep (9inches or more of sand ) buckets with limited surface area, brisk flow to avoid detritus accumulation and no wave action except perhaps at the perimeter will not denitrify to any significant degree beyond the first few inches if that.
Live deep beds within a display with live rock will do better if the sand is kept live which may require periodic replenishment with fresh live sand..
These beds may also benefit from the effects of advection as the upwelling water passes upward under and through live rock. It seems ensuring sand is under the rock will enhance the process. Issues with the stability of the stack could be handled with pylon pvc structures under the rock backfilled with sand. I have these on my 7 year old in tank deep sand bed.
A remote deep sand bed (ie not in the display) can be more productive in denitrification with a larger surface area since even the small sand grains cause advective wave action and upwelling. Placing live rock on a bed can enhance it's effectivenes as a denitrifier since the effects of advection will enhance water movement under the rock to a depth equal to the height of the submerged rock per the model presented by Sprung and Delbeek.It will also enhance movement of water through the rock.
Nitrate removal can be accomplished by a number of means other than the substratum or rock such as: coil denitrifiers, carbon fed denitriers, sulfur denitrifiers,macroalgae refugia,carbon dosing , the use of granular activated carbon to remove organic material before it turns to nitrate as well as strong skimming and perhaps to some extent ozone in conjunction with granulated activated carbon.
Refernces:
(1)Sprung and Delbeek, The Reef Aquarium Vol 3.
(2)
http://aslo.org/lo/toc/vol_48/issue_4/1674.pdf
(3)
http://www2.hawaii.edu/~toonen/files/Toonen-Wee-05.pdf
If you'd like to tune this up some feel free , Tom. Your input is always appreciated.