TWO-LAYER FLOW OF IMMISCIBLE NON-NEWTONIAN FLUIDS: LINEAR STABILITY ANALYSIS

摘要

Thin-film flow of two layers of non-Newtonian fluids are modeled in this paper. The model accounts for the weak inertial effects. The fluids are assumed to be immiscible i.e. an interfacial tension has been included in the momentum equations. Following a weighted residual approach, the momentum equations are reduced to a single equation relating the buoyancy parameter and interface height. The model is then closed by introducing the kinematic condition at the interface. A linear stability analysis is carried out for a two-layer parallel flow finding perfect agreement with the Orr-Sommerfeld results. The effect of fluids immiscibility (quantified through a Weber number) on the stability neutral curves is studied for a range of flow parameters. For the parameter range studied, it is generally found that the interfacial tension has a stabilizing effect on the flow. The model developed can be used for analyzing both displacement and co-extrusion flows.