Steady-state rimming flow of the generalized Newtonian fluid

Rimming flow of a liquid polymer on the inner surface of a horizontal rotating cylinder is investigated. Using a scale analysis, a theoretical description for steady-state non-Newtonian flow is obtained. Simple lubrication theory is applied since the Reynolds number is small and the liquid film thin. Since a steady-state viscometric flow is considered, the general constitutive law requires only a single function relating shear stress and shear rate that corresponds to a generalized Newtonian liquid. For this case the existence of a continuous steady-state solution is proved. The properties of the solution for the different flow regimes are discussed. Numerical results are carried out for the Carreau-Yasuda model, which exhibits the Newtonian behavior at low shear rates with transition to power-law shear thinning at moderate shear rates.