Investigation on laminar pipe flow of a non-Newtonian Carreau-Extended fluid

Many fluids used in petroleum and chemical industries are generally described as complex systems that exhibit time-independent non-Newtonian behavior. To adequately represent the rheological behavior of an oil-tolerant and salt-resistant aqueous foam system, a Carreau-Extended (Carreau-E) rheological model, which includes a yield stress, a shear-thinning parameter and a time constant, has been established based on Carreau and Herschel-Bulkley models. In the present study, generalized Reynolds number definitions are proposed for laminar and fully developed pipe flow of non-Newtonian fluids (Carreau-E, Carreau, Herschel-Bulkley and Bingham fluids). Perturbation solutions for pipe flow of a Carreau-E fluid are obtained and their ranges of validity in the problem parameter space are identified. The quantitative effects of rheological parameters (e.g., yield stress, time constant, shear-thinning parameter) and flow parameters, (e.g., pressure gradient, pipe radius) on the velocity profile and flow rate in pipe flow of a Carreau-E fluid are explored. The results obtained for the flow characteristics can be applied or extended for other types of non-Newtonian fluid flow encountered in practical applications.