Finally Bernoulli's law is applyed to the different flow velocities at the upper and lower side of the wing resulting in a lower pressure at the upper surface and a higher pressure at the lower surface. These pressure differences produce a force on the airfoil - the lift. This explanation, however, is not complete. If different flow velocities are to cause different pressures a physical reason for the fact that the air flows faster at the upper side given too. Three types of reasons can be found.
Air flow around an airfoil.
Air which is adjacent before the separation by the airfoil has to meet again behind the airfoil. Adjacent air before the separation indeed does not meet behind airfoil. Figure 2 shows experimental evidence of air streaming along an airfoil. Smoke tracer mark the streamlines. The figure shows at the leading edge adjacent air before the separation.