 Inverted falling film

An inverted falling film flows on the underside of an inclined solid surface. Taking the normal coordinate from the solid into the liquid reverses the normal component of gravity relative to an upper-surface film. In the Benney equation, the hydrostatic contribution to the volume flux per unit width therefore changes from $-2\epsilon h^3{h}_x\cot \alpha /3$ to its negative. Normal gravity then amplifies disturbances of long wavelengths, while surface tension resists short wavelengths.