Exact solutions for laminar stratified flows of Newtonian/non-Newtonian
shear-thinning fluids in horizontal and inclined channels are presented. An
iterative algorithm is proposed to compute the laminar solution for the general
case of a Carreau non-Newtonian fluid. The exact solution is used to study the
effect of the rheology of the shear-thinning liquid on two-phase flow
characteristics considering both gas/liquid and liquid/liquid systems.
Concurrent and counter-current inclined systems are investigated, including the
mapping of multiple solution boundaries. Aspects relevant to practical
applications are discussed, such as the insitu hold-up, or lubrication effects
achieved by adding a less viscous phase. A characteristic of this family of
systems is that, even if the liquid has a complex rheology (Carreau fluid), the
two-phase stratified flow can behave like the liquid is Newtonian for a wide
range of operational conditions. The capability of the two-fluid model to yield
satisfactory predictions in the presence of shear-thinning liquids is tested,
and an algorithm is proposed to a priori predict if the Newtonian (zero shear
rate viscosity) behaviour arises for a given operational conditions in order to
avoid large errors in the predictions of flow characteristics when the
power-law is considered for modelling the shear-thinning behaviour. Two-fluid
model closures implied by the exact solution and the effect of a turbulent gas
layer are also addressed.Comment: 36 pages, 27 Figure
