Aerodynamics at the Particle Level
  This paper is intended to clarify some of the rather well-known aerodynamic phenomena. It is also intended to pique the interest of the layman as well as the professional. All aerodynamic forces on a surface are caused by collisions of fluid particles with the surface. While the standard approach to fluid dynamics, which is founded on the fluid approximation, is effective in providing a means of calculating various behavior and properties, it begs the question of causality. The determination of the causes of many of the most important aerodynamic effects requires a microscopic examination of the fluid and of the surface with which it interacts. The Kutta-Joukowski theorem is investigated from first physical principles. It is noted that the circulation does not arise alone as a physical phenomenon, e.g. air doesn't flow forward under a wing, but must be added to the translation flow. The circulation term is necessary to take into account the vertical deflection of the air flow by a wing. Various aerodynamic devices are discussed, e.g. rocket engine exhaust diffuser and the perfume atomizer. The section on slurries discusses pyroclastic flow as occurs in violent volcanic eruptions. 
Charles A. Crummer (University of California, Santa Cruz)