The flow of thin liquid films over spinning disks:  Hydrodynamics and mass transfer

We study the hydrodynamics and mass transfer associated with gas absorption into a thin liquid film flowing over a spinning disk. We use the thin-layer approximation in conjunction with the Karman–Polhausen method to derive evolution equations for the film thickness and the volumetric flow rates in the radial and azimuthal directions. We also use the integral balance method to derive evolution equations for the thickness of the diffusion boundary layer as well as the concentration of solute at the disk surface. Numerical solutions of these partial differential equations, which govern the hydrodynamics and the associated mass transfer, reveal the formation of large finite-amplitude waves and elucidate their significant effect on the mass-transfer characteristics. We illustrate this dependence quantitatively by examining the effect of system parameters on the time-averaged and spatially averaged Sherwood numbers. The results are assessed by comparison with computations of the parabolized convective diffusion equation and experimental data.