Surface instabilities of thin liquid film flow on a rotating disk

 Steady flow of a liquid jet from a nozzle onto the centre of a rotating disk is studied with a streak line method to determine the superficial velocity of the spreading liquid film. Good agreement is found with an asymptotic analysis of the unperturbed flow field. Experimentally, the liquid surface is always perturbed by surface waves which appear as regular spirals, steady in the laboratory system in the low Reynolds number range. It could be shown that wave formation is very sensitive to entrance conditions. Therefore, it is assumed that wave generation is an entrance effect which acts as periodic forcing on the forming liquid film. Wave velocities outside the entrance region are measured and proved to be in good agreement with the prediction of a linear stability theory, as long as the flow rate and entrance perturbations are small. At higher flow rates or stronger disturbances, the radial development of the wave velocities takes on the characteristics predicted by nonlinear stability theories and is in qualitative agreement with experiments performed on an inclined plane.