Final answer:
The brush designed to allow the greatest airflow for quick hair drying while styling is called a vent brush, not to be confused with ink brushes or wind turbine blades.
Step-by-step explanation:
The brush that allows the greatest airflow to the hair for quick drying and directing hair into the lines of the design is known as a vent brush. The design of a vent brush typically features widely spaced bristles and an open back that allows air from a hairdryer to flow through easily, drying the hair faster while styling. While the information on brush and ink is interesting, it does not relate to this specific question about hair styling tools. Similarly, the description of blades functioning like airplane wings is more relevant to wind turbines or similar technologies and does not apply here.