Stationary spiral waves in film flow over a spinning disk

Stationary spiral waves in liquid film flowing over a spinning disk have been observed in earlier experiments [H. Espig and R. Hoyle, "Waves in a thin liquid layer on a rotating disk," J. Fluid Mech. 22, 671 (1965); A. F. Charwat , "The flow and stability of thin liquid films on a rotating disk," ibid. 53, 227 (1972); G. Leneweit , "Surface instabilities of thin liquid film flow on a rotating disk," Exp. Fluids 26, 75 (1999)]. In the framework of a mathematical model derived by the integral method, it is shown that the waves develop due to nonaxisymmetric liquid feeding onto the spinning disk, and the wave shapes are approximated by the Archimedean spirals, whose coefficients depend on the Eckman number. The dependence has been confirmed by experimental data from recorded videos. (C) 2010 American Institute of Physics. [doi:10.1063/1.3429601]