Thin film flow over spinning discs: The effect of surface topography and flow rate modulation

We examine the effect of disc topography and time modulation of the liquid flow rate at the inlet on the dynamics of a thin film flowing over a spinning disc. We use a combination of boundary-layer theory and the Kármán-Polhausen approximation to derive coupled equations for the film thickness, and radial and azimuthal flow rates. Substrate patterning is taken into account in the limit of small-amplitude topography. Our numerical results indicate that the combined effects of flow rate modulation at the inlet and disc patterning can lead to a significant increase in interfacial waviness, which greatly exceeds that associated with the constant flow rate, smooth disc case.