Falkner-Skan Solution for Gravity-Driven Film Flow

Abstract

It is demonstrated that the development of a viscous film flow down along a vertical wall can be described by the classical Falkner-Skan equation from aerodynamic boundary layer theory for the particular parameter-value m = 1/2. This leads to a well-known exact solution for the velocity field, as long as the viscous boundary layer can be considered not to interact with the free surface of the film. An exact reference solution for developing film flow is thus made available, against which approxiate solutions may be tested for accuracy.