Instability of a rotating liquid film with a free surface

Abstract

The centripetal acceleration of a rotating liquid film is tantamount to a centrifugal force, which tends to cause the liquid film to form rings around the circular cylinder to which it is attached. The stabilizing factors are surface tension and, presumably, viscosity. But it is shown in this paper that instability occurs even for large values of the surface-tension para­meter and at small Reynolds numbers. The critical wave number is shown to depend pre­dominantly on the surface tension. Its dependence on the Reynolds number, R , is slight if R is small, and nil if R is large. The effect of viscosity is therefore essentially to slow down the rate of amplification of the unstable disturbances. The analysis is carried out for both large and small Reynolds numbers, for various ratios of film thickness to cylinder radius, and for various surface tension parameters. (The calcula­tion for intermediate Reynolds numbers turns out to be unnecessary for the purpose of com­parison with the experiments obtained. Enough information is provided by the calculations performed for practical applications.) Numerical results are given. Comparison of results obtained from 65 experiments with pure glycerine, water+glycerine mixture, and water with the analytical results shows satisfactory agreement.