The stability of the helical flow of pseudoplastic liquids in a narrow annular gap with a rotating inner cylinder

Abstract

The stability of a laminar helical flow of pseudoplastic liquids in an annular gap with a rotating inner cylinder is investigated theoretically. The analysis is carried out under the assumption of a torroidal form of the secondary flow (torroidal Taylor vortices) for the narrow gap geometry. The power law model has been applied to describe the pseudoplasticity of liquids. The problem of the stability has been formulated with the aid of the method of small disturbances, and solved using the Galerkin method. In order to describe the stability limit the Reynolds and Taylor numbers defined with the aid of the mean viscosity value have been introduced. It has been found that pseudoplasticity has a considerably destabilizing influence on the Couette motion as well as on the helical flow in the initial range of the Reynolds number values (Re 30, the stability limit of the flow of pseudoplastic liquids can be described by a general dependence of the critical valueTa c onRe, which is consistent with results obtained for the case of Newtonian fluids.