Just want to point out you want to size the air stone on the finished size of root system. As the roots grow you need more and more bubbles to do the same job, here is some more info
Injury from low (or no) oxygen in the root zone can take several forms and these will differ in severity between plant types. Often the first sign of inadequate oxygen supply to the roots is wilting of the plant under warm conditions and high light levels. Insufficient oxygen reduces the permeability of the roots to water and there will be an accumulation of toxins, so that both water and minerals are not absorbed in sufficient amounts to support plant growth. This wilting is accompanied by slower rates of photosynthesis and carbohydrate transfer, so that over time, plant growth is reduced and yields are affected. If oxygen starvation continues, mineral deficiencies will begin to show, roots die back and plants will become stunted. If the lack of oxygen continues in the root zone, plants produce a stress hormone - ethylene, which accumulates in the roots and causes collapse of the root cells, at this stage pathogens such as pythium can easily take hold and destroy the plant.
While an air pump tube alone can bubble air into a nutrient solution, oxygenation or the process of getting atmospheric oxygen dissolved into the liquid nutrient, is much more effective where many tiny bubbles of air are created, rather than a slow stream of larger bubbles. The greater the surface contact between the air bubbles and the nutrient, the more oxygen will diffuse into the nutrient solution and smaller bubbles create a far greater surface area than a few larger bubbles will. The further the bubbles have to travel to reach the surface of the nutrient, the more time oxygen has to diffuse into the liquid and the higher the rates of dissolved oxygen than can be obtained from an air pump and stone set up.
Oxygen and Temperature Effects - Effective Aeration
While forcing air bubbles deep down into the nutrient reservoir generally increases the dissolved oxygen levels in the nutrient, there is one other major factor to consider and that's the temperature of the air being pumped into the nutrient. As the temperature of a nutrient solution increases, its ability to hold dissolved oxygen decreases. So a cool nutrient solution may in fact hold twice as much oxygen at 'saturation level' than a warm solution. For example a nutrient solution at 45 F can hold around 12ppm of dissolved oxygen at 'saturation', (meaning it is the most it can hold), but the same nutrient solution at a temperature of 85 F will hold less than 7ppm at saturation. This means at a solution temperature of 85F there is much less dissolved oxygen available for the plants root system to take up. To complicate matters further, the requirement of the plants root system for oxygen at warmer temperatures, is many times greater than at cooler temperatures due to the increased rate of root respiration. So warm nutrients mean a very high oxygen requirement from the plants roots, but the nutrient can only hold very limited amounts of dissolved oxygen at saturation, no matter how much air is being bubbled into the solution. Ideally, nutrient solution temperatures for most plants should be run lower than the overall air temperature - this has many beneficial effects on plant growth and development. However, if overly warm air from the growing environment is pumped into an otherwise cool nutrient solution, the warm air will rapidly increase the temperature of the nutrient to that of the growing environment. If air is being pumped via an air machine with an intake close to lights or other heat sources then rapid heating of the nutrient will occur. On the other hand, cool air has the ability to reduce the temperature of the nutrient if sufficient levels are pumped in and thus result in a much more highly oxygenated solution for the plants roots. If keeping the nutrient solution temperature down seems to be a continual problem, checking the air inlet temperature of an air pump is a good idea. Overly warm nutrient solutions (ideally nutrient solutions should remain below 65 - 75 F) for most warm season, high light plants and well below 69 F for cool season.can have serious effects on the plants root system. Apart from the increased oxygen requirement due to a much higher rate of root respiration which can rapidly result in oxygen starvation, high solution temperatures favour many of the root disease pathogens. Plant roots become highly 'stressed' when experiencing high temperatures, particularly if there is a large mis-match between the air the root temperature. Root stress slows the development of new roots, resulting in reserves inside the root tissue being `burned up during respiration faster than they are accumulated, and stress makes the root system in general more susceptible to disease attack. Keeping a check on nutrient temperature is vital, as is ensuring that air machines are not blasting hot air into the solution and cooking plant roots. Aeration is most effective when cool air is bubbled into a nutrient.
Oxygenation and Nutrient Uptake
Healthy roots supplied with sufficient oxygen are able to absorb nutrient ions selectively from the surrounding solution as required. The metabolic energy which is required to drive this nutrient uptake process is obtained from root respiration using oxygen. In fact there can be a net loss of nutrient ions from a plants root system when suffering from a lack of oxygen (anaerobic conditions). Without sufficient oxygen in the root zone, plants are unable to take up mineral nutrients in the concentrations required for maximum growth and development. Maintain maximum levels of dissolved oxygen boosts nutrient uptake by ensuring healthy roots have the energy required to rapidly take up and transport water and mineral ions. Calcium is one important nutrient ion which has been shown to benefit from high levels of oxygenation in the hydroponic nutrient solution Calcium, unlike the other major nutrients is absorbed mostly by the root growing tips (root apex). The root apex has a large energy requirement for new cell production and growth and is therefore vulnerable to oxygen stress If root tips begin to suffer from a lack of oxygen, a shortage of calcium in the shoot will occur. This shortage of calcium makes the development of calcium disorders such as tip burn and blossom end rot of fruit more likely and severe under oxygen starvation conditions. High levels of oxygenation ensure healthy root tips are able to take the levels of calcium required for new tissue growth and development.
Conclusion
While providing oxygenation with the use of air pumps and stones is an excellent method of increasing the dissolved oxygen (DO) levels in a nutrient solution, the temperature of the air intake and nutrient solution must also be managed to ensure oxygen starvation in the root zone does not occur. Pumping hot air into a nutrient not only creates temperature stress in the root zone, it also results in less oxygen carrying capacity in the solution itself - a recipe for root suffocation that will rapidly affect the top portion of the plant as well. Getting oxygenation right means checking both aeration capacity of the equipment being chosen and temperatures in the nutrient and root zone.