| Abstract: | A numerical method has been developed for simulating fully developed multilayer shear flows of non-Newtonian fluids with arbitrary viscosity functions. Poiseuille and combined Poiseuille/Couette flows in both slits arid annuli may be modeled. The method employs a finite difference system where grid points lie on streamlines and move to their correct positions as the solution procedure converges. Interfaces are easily handled as particular stream lines with the equation of motion replaced by a boundary condition. The method is stable for high interface viscosity ratios and readily handles a large number of layers. Many authors have employed power law models to model multi-layer non-Newtonian flows. We find that the power law is sufficient to predict pressure gradients and interface positions in most cases, but gives unrealistically flat velocity profiles, even when truncated at finite viscosity. Results are presented for the Carreau fluid and for the rubber-like liquid with shear thinning via Wagner's strain functional. |
