Thin film flow on spinning disks with finite rate chemical surface reactions

The Kármán–Pohlhausen-type integral boundary layer solution of the thin film approximation (in short TFA-IBL) has been extended to cover species mass transfer with realistic finite rate chemical surface reactions. The extended model is used to investigate centrifugal force driven films on a spinning disk with central vertical jet feed. For the considered chemistry, the effect of varying jet flow rate and spin speed on the etching turned out to be very limited. The concentration field is consistently predicted as very uniform in all cases, with the wall species concentration remaining close to the level of the bulk feed. The observed little impact of the advective–diffusive transport conditions on the etching essentially reflects the low Damköhler numbers parameterizing the chemical mechanism. The predictions of the TFA-IBL model are thoroughly validated against results from highly resolved computational fluid dynamics (CFD) simulations. The introduction of a velocity boundary layer bounded by an inviscid stagnation point solution into the depth-averaged formulation ensures a reliable description of the central impingement region, where the thin film approximation otherwise breaks down. Due to the high Schmidt number of the liquid solution, the occurrence of interfacial waviness only weakly alters the species wall flux, so that the etch rates are predicted well also in the outer wavy region, despite the model's smooth film assumption. The high accuracy of the predictions seen over the whole radial domain for all cases proves the proposed extended TFA-IBL model as computationally low expensive but reliable alternative to the CFD approach.