Interesting theory.
My rudimentary understanding is that the fan increases evaporation by increasing the kinetic energy in the water molecules at the surface. ie their speed. The faster they are moving, the more energy they have to break the surface tension. As the faster-moving molecules escape, the remaining molecules have lower average kinetic energy, and the temperature of the liquid thus decreases. You can speed up molecules a number of ways but the obvious ones are increasing their temperature or increasing the air movement at the surface and this is what the fan does. Moving air ie wind feels colder than still air through the same process on your skin as the skin moisture molecules average speed is increased. (The air itself is NOT colder) Humidity also affects the rate of evaporation as the surrounding air nears its saturation point, it is unable to pickup anymore water molecules.
I sure that someone will correct me if I have any of this wrong