A significant feature of gravity-driven film flows of Newtonian and rheologically complex fluids down an inclined/vertical substrate is the instability of the free surface which manifests as surface waves having wavelengths much larger than the film thickness. There are a number of applications which can be modeled as thin film flow systems on porous substrates. Pascal  investigated the stability of a falling power-law film on an inclined porous substrate. This model for the fluid predicts a viscosity that goes to infinity as the shear rate approaches zero. There is a need to employ a more appropriate model to examine the effects of non-Newtonian rheology on the dynamics and stability of thin film free surface flows down inclined or vertical rigid/porous substrates. The four-parameter Carreau model predicts a viscosity that remains finite as the shear rate approaches zero and is given by
Weinstein  and Rousset et al.  have considered the Carreau model and have examined the temporal stability of a film flow down an impermeable rigid inclined substrate. The authors show that a shear-thinning Carreau fluid film on a rigid impermeable substrate is more unstable than a Newtonian film. This calls for an analysis that includes both the effects of Carreau non-Newtonian rheology and bottom permeability and the present study reports such an investigation of a Carreau non-Newtonian film on a porous inclined substrate.
Volume Subject Area:3rd Joint US-European Fluids Engineering Summer Meeting
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