Azimuthal and streamwise disturbances in a fluid layer flowing down a rotating cylinder

Abstract

In this paper an extensive investigation is done of the linear stability of a film falling down a vertical rotating cylinder. Two cases are considered: flow in the outside and flow in the inside of the cylinder. To this end, a system of differential equations which describe the instability is solved numerically with the Runge–Kutta fourth and sixth order methods. We show that in different circumstances the azimuthal disturbances become the most unstable when the rotation is taken into account. Moreover, a splitting of the azimuthal modes appears due to the Coriolis force. In the case of flow in the inside there is a threshold in the centrifugal force above which the flow is linearly stable. Besides, new results for the nonrotating case are also obtained.

Azimuthal instability modes in a viscoelastic liquid layer flowing down a heated cylinder

“…It is found that in the linear and non linear problems, mainly axial mode stability is investigated. For three dimensional flows see [22,[25][26][27]29]. The physical reason for the appearance of azimuthal modes of instability are the azimuthal shear stresses created by thermocapillarity, as will be seen presently in the discussion of the first and second tangential shear stresses of the free surface boundary conditions.…”

“…Therefore, for any radius, the axial mode is the most unstable one inside the cylinder. When a film is flowing down the outside of a rotating cylinder, it has been shown [25][26][27] that the first azimuthal mode may be the most unstable one under different circumstances. Nevertheless, for flow inside the cylinder (as in [28]) the most unstable mode is the axial one.…”