Applied Math Talk: Thin liquid film resulting from a distributed source on a vertical wall given by Yadong Ruan (CGU)

In this talk, we will talk about the thin film model derived for liquid film resulting from a distributed source on a vertical wall and some distinct properties about the model. We will discuss the different behavior and properties of the model with and without considering surface tension. When the surface tension is neglected, a critical source strength is found below which the film flows entirely upward due to the airflow, and above which some of the flow is carried downward by gravity. In both cases, a steady state is established over the region where the finite source is located. The presence of surface tension, even when small, causes a dramatic change in the film profiles and the speed and structure of the shock waves. These are studied in more detail by examining the traveling wave solutions away from the source region.