We discuss free-surface flow motion of viscous liquid
falling down a solid wall,
referred to as falling film flows.
If we take the -axis downward along the wall
and the
-axis perpendicular to it,
denoting the velocity field
by
and the surface location by
,
then the basic equations are written as follows:
It is the convention to introduce the representative film thickness
and thereby define two non-dimensional parameters
(besides the inclination angle
), namely