i've enjoyed this thread and the opposing positions on the best way to increase the DO of your water. it made me go back and go through a number of studies on the best way to oxygenate water and gas transfer. (i won't go into supersaturation of the water with air to the point of killing the fish.)

there are many variables that have an impact on the ability and limitations of gas absorption and exchange. temp, ph, TDS, turbidity, size, depth, and shape of container.

for an aquarium, tank or vat, i will without question stick with small bubbles in a controlled column. large wastewater treatment companies use this type of air diffusing system as the preferred method of gas exchange. the small bubbles do transfer gas very effectively. ask companies such as GE that provide equipment, and engineering for these facilities.

the old formula, when we did not have air diffusers that could produce such small bubbles, the ration was 90% at the surface 10% through the large bubbles. the smaller bubbles rise to the surface much slower than the large bubbles because of the higher impact of gravity on the ascention of the larger bubbles.

i believe the most effective method of transfer, incorporates the affect of water over rocks or waterfalls; is a column of large biomedia suspended over the water as water decends down the column, air is is forced up through the column. this would be very difficult to do in aquaponics. i have done this over large vats containing fish. the drawback is that hanging above the water the water does not have the upheavel of a submersed air diffuser.

i'm not sure if this is worth 2 cents