Analysis of the wall mass transfer on spinning disks using an integral boundary layer method

Spinning disk devices are widely used for wet surface processing to produce thin liquid films offering very intense heat and mass transfer rates. The present work computationally investigates in particular the liquid-to-wall reactive species mass transfer to describe wet surface etching in the limit of diffusion-controlled fast chemistry at very high Schmidt number (Sc=1200). The computations are carried out using a specially adapted Integral Boundary Layer (IBL) method, which accounts explicitly for the development of the velocity and species concentration boundary layers inside the liquid film. The presently used IBL method is proven to capture the radial variation of the wall mass flux and the directly related etching abrasion very well. It particularly provides a reliable description of the momentum and mass transfer in the central region of impingement, which had to be excluded in the most previous IBL based approaches. An Ekman number based criterion is deduced from the validation against CFD results and experiments, which allows to demarcate the outer radial region, where the typically emerging waviness of the liquid surface becomes significant for the wall mass flux. It is shown that the steady-state smooth film predictions of the IBL method generally start to deviate notably from the CFD and experimental data, as the local Ekman number exceeds a certain critical limit.