Three regimes of a steady-state rimming flow of the liquid polymers

Rimming flow on the inner surface of a horizontal rotating cylinder is investigated. 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. 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 run-off condition is satisfied, the existence of a steady-state solution is proved. In the bounds implied by this condition film thickness admits a continuous solution, which corresponds to subcritical and critical flow regimes. In the supercritical case when the mass of liquid polymer exceeds a certain value or the speed of rotation is less than an indicated limit, a discontinuous solution is possible and a hydraulic jump may occur. As an example, the location and height of the hydraulic jump is determined numerically for Ellis model.