Experimental investigations of the stability limit of the helical flow of pseudoplastic liquids

The stability of the laminar helical flow of pseudoplastic liquids has been investigated with an indirect method consisting in the measurement of the rate of mass transfer at the surface of the inner rotating cylinder. The experiments have been carried out for different values of the geometric parameter = R₁/R₂ (the radius ratio) in the range of small values of the Reynolds number,Re < 200. Water solutions of CMC and MC have been used as pseudoplastic liquids obeying the power law model. The results have been correlated with the Taylor and Reynolds numbers defined with the aid of the mean viscosity value. The stability limit of the Couette flow is described by a functional dependence of the modified critical Taylor number (including geometric factor) on the flow indexn. This dependence, general for pseudoplastic liquids obeying the power law model, is close to the previous theoretical predictions and displays destabilizing influence of pseudoplasticity on the rotational motion. Beyond the initial range of the Reynolds numbers values (Re>20), the stability of the helical flow is not affected considerably by the pseudoplastic properties of liquids. In the range of the monotonic stabilization of the helical flow the stability limit is described by a general dependence of the modified Taylor number on the Reynolds number. The dependence is general for pseudoplastic as well as Newtonian liquids.Nomenclature C_i concentration of reaction ions, kmol/m³ - d = R₂ –R₁ gap width, m - F_M() Meksyn's geometric factor (Eq. (1)) - F₀ Faraday constant, C/kmol - i_l density of limit current, A/m³ - k_c mass transfer coefficient, m/s - n flow index - R₁,R₂ inner, outer radius of the gap, m - Re = V_m·2d·/µ_m Reynolds number - Ta_c = _c·d^3/2·R₁^1/2·/µ_m Taylor number - Z_i number of electrons involved in electrochemical reaction - = R₁/R₂ radius ratio - µ apparent viscosity (local), Ns/m² - µ_m mean apparent viscosity value (Eq. (3)), Ns/m² - µ_i apparent viscosity value at a surface of the inner cylinder, Ns/m² - density, kg/m³ - _c angular velocity of the inner cylinder (critical value), 1/s