Wave propagation in the flow of shear‐thinning fluids down an incline

The effect of shear‐thinning rheology on the spatial growth of waves in multilayered flow down an inclined plane is modeled, utilizing the Carreau viscosity constitutive equation. It is shown that waves associated with the free surface propagate as if they were in a Newtonian system, where the viscosity is some average of the varying viscosities in the shear‐thinning layer. This averaging is due to the global effects of shear thinning, such as changes in velocity profile and film thicknesses. In contrast, waves that are associated with the interfaces between adjacent fluid layers are largely affected by the local interfacial viscosities; wave propagation is not governed by some average Newtonian viscosity across the layer. It is found that shear‐thinning rheology can either increase or decrease the growth of waves associated with a fluid‐fluid interface, compared with a purely Newtonian case.