Capillary parameter for a falling film ($S=2\gamma /(3\rho g{L}^2\sin \alpha )$)

For downslope length scale $L$, film thickness scale $h_0$ and surface velocity scale $U_0=\rho g{h}_0^2\sin \alpha /(2\mu )$, this normalization makes the capillary part of the Benney equation flux $\epsilon S{h}^3{h}_{xxx}$. The dimensionless capillary pressure is $-3S{h}_{xx}/2$. Keeping $S=O(1)$ specifies a distinguished long-wave approximation in which surface tension remains relevant.