Stability of Couette flow of liquids with power law viscosity

The stability of the Couette flow of the liquid with the power law viscosity in a wide annular gap has been investigated theoretically in this work with the aid of the method of small disturbances. The Taylor number, being a criterion of the stability, has been defined using the mean apparent viscosity value in the main flow. In the whole range of the radius ratio, R_i/R_o and the flow index, n, considered (R_i/R_o 0.5, n = 0.25–1.75 ), the critical value of the Taylor number Ta_c is an increasing function of the flow index, i.e., shear thinning has destabilizing influence on the rotational flow, and dilatancy exhibits an opposite tendency.In the wide ranges of the flow index, n > 0.5, and the radius ratio, R_i/R_o > 0.5, the wide-gap effect on the stability limit is predicted to be almost the same for non-Newtonian fluids as for Newtonian ones. The ratio on the critical Taylor numbers for non-Newtonian and Newtonian fluids: Ta_c(n) and Ta_c(n = 1) obey a generalized functional dependence: Ta_c(n)/Ta_c(n = 1) = g(n), where g(n) is a function corresponding to the solution for the narrow gap approximation.Theoretical predictions have been compared with experimental results for pseudoplastic liquids. In the range of the radius ratio R_i/R_o > 0.6 the theoretical stability limit is in good agreement with the experiments, however, for R_i/R_o < 0.6, the critical Taylor number is considerably lower than predicted by theory.