The Prandtl-Frank Equation

The Prandtl-Frank equation describes how the shape of a surface affects the flow of a thin liquid film moving over it, particularly considering surface tension effects. It accounts for how variations in surface tension, often caused by temperature or concentration differences, influence the film's motion and shape. This equation helps in understanding phenomena like droplet formation or coating processes, where the balance between gravitational, viscous, and surface tension forces determines the behavior of the liquid layer. Essentially, it provides a mathematical framework to predict how a thin liquid film will behave on different surfaces under various conditions.