THE RUN-OFF CONDITION FOR THE NON-NEWTONIAN RIMMING FLOW

摘要

Rimming flow on the inner surface of a horizontal rotating cylinder is investigated. Using a scale analysis, a theoretical description is obtained for steady-state non-Newtonian flow. Simple lubrication theory is applied since the Reynolds number is small and liquid film thin. Since the Deborah number is very small the flow is viscometric. The Weissenberg number, which characterizes the shear-thinning effect, may be small or large. A general constitutive law for this kind of flow requires only a single function relating shear stress and shear rate that corresponds to a generalized Newtonian liquid. For this case the run-off condition for rimming flow is derived. Provided the runoff condition is satisfied, the existence of a continuous steady-state solution is proved. The rheological models, which show Newtonian behaviour at low shear rates with transition to power-law shear thinning at moderate shear rates, are considered. Numerical results are carried out for the Carreau and Ellis models, which exhibit the Newtonian behaviour near the free surface and power-law behaviour near the wall of the rotating cylinder.