Sliding drops on an inclined plane

An evolution equation for the film thickness was derived recently combining diffuse interface theory and long-wave approximation (Phys. Rev. E 62 (2000) 2480). Based on results for the structure formation in a thin liquid film on a horizontal plane, we study one-dimensional periodic drop profiles sliding down an inclined plane. The analysis of the dependence of their amplitude, velocity, advancing and receding dynamic contact angles on period and the interaction parameters reveals an universal regime of flat drops. The main properties of the flat drops do not depend on their volume. Both types of drops—the universal flat drops and the non-universal drops—are analyzed in detail, especially the dependence of their properties on inclination angle. Finally, an outlook is given on two-dimensional drops and front instabilities.