Interfacial instability of two rotating viscous immiscible fluids in a cylinder

Abstract

A complete original study of the linear temporal instability analysis of two viscous and immiscible fluids enclosed in a rigid cylinder rotating about its axis and separated by a cylindrical interface is performed for the case of higher density fluid located in the annulus. The results of the present contribution fill the lack of an overall assessment of the system behavior due to the increase of both the analytical difficulties and the number of the governing parameters when the several physical effects are all included. The analysis is carried out numerically by discretizing the equations of the evolution of disturbances separately in the two phases formulated in a rotating reference frame. Normal mode analysis leads to a generalized eigenvalue problem which is solved by means of a Chebyshev collocation spectral method. The investigation of the preferred modes of instability is carried out over wide ranges of the parameters space. The behavior of the system is physically discussed and is compared to inviscid asymptotic limits and to viscous approximate solutions of the previous literature.