  The rimming flow of a viscoelastic thin film inside a rotating horizontal
cylinder is studied theoretically. Attention is given to the onset of
non-Newtonian free-surface instability in creeping flow. This non-inertial
instability has been observed in experiments, but current theoretical models of
Newtonian fluids can neither describe its origin nor explain its onset. This
study examines two models of non Newtonian fluids to see if the experimentally
observed instability can be predicted analytically. The non-Newtonian viscosity
and elastic properties of the fluid are described by the Generalized Newtonian
Fluid (GNF) and Second Order Viscoelastic Fluid (SOVF) constitutive models,
respectively. With linear stability analysis, it is found that, analogously to
the Newtonian fluid, rimming flow of viscous non-Newtonian fluids (modeled by
GNF) is neutrally stable. However, the viscoelastic properties of the fluid
(modeled by SOVF) are found to contribute to the flow destabilization. The
instability is shown to increase as the cylinder rotation rate is lowered, from
which the fluid accumulates in a pool on the rising wall. Viscoelastic effects
coupled with this pooling cause the fluid's angular stretching, which is
suggested to be responsible for this onset of instability.
