2 Mechanism of How Air Bubbles Are Generated

Now, let's confirm how air bubbles are formed.Air bubbles form when the amount of dissolved air in a solution exceeds the saturated solubility. Saturated solubility is the amount of air that eventually dissolves in a solution when it is left exposed to air and the air entering and leaving the solution are balanced (in equilibrium state). However, this quantity varies depending on the type of solution, type of gas, temperature, and pressure.

Therefore, scientifically speaking, this is expressed in terms such as "given the partial pressure of oxygen in contact with water at 25 °C is 0.2 atmospheres, the saturated solubility of oxygen with respect to 1 mL of water is 0.006 mL, converted at 25 °C and one atmosphere." 
If more than the saturated solubility is dissolved, then it is referred to as supersaturated, which can generate air bubbles easily when vibrated or stirred.  In contrast, below the saturated solubility level, air can readily dissolve into the solution, but this dissolution rate is not very fast.

Note: 1 atmosphere (1 atm) = 1.033 kgf/cm² = 1.013 × 10⁵ Pa