Fully-Developed Circular-Pipe Flow of a Non-Newtonian Pseudoplastic Fluid

A fully-developed flow of a non-Newtonian pseudoplastic fluid through a circular pipe has been studied using a four-parameter model, as an example, for the shear-rate dependent apparent viscosity. The model used in this investigation is a modification of the two-parameter Ostwald-de Waele power law (1), which correctly represents the lower and upper regions of Newtonian behavior characteristic of pseudoplastic polymer melts and solutions. Since there has only one set complete experimental data available for the shear-rate dependent viscosity, we use them to show that a perfect match can be achieved between the mod- ified power-law viscosity model and the experimental data. Such a perfect match is required for an accurate prediction of the flow behavior in internal flow problems. the non-dimensional parameter, the fluid behaves like a Newtonian fluid with a viscosity equal to the zero-shear- rate viscosity in the central region of the pipe, and like a Newtonian fluid with a viscosity equal to the infinite- shear-rate viscosity in the outer region of the pipe adja- cent to the pipe wall; power-law behavior is seen in the middle region of the pipe, between the central and outer regions. At intermediate values of the non-dimensional parameter, there are two distinct regions of flow: an inner central region where the fluid behaves like a New- tonian fluid with a viscosity equal to the zero-shear-rate viscosity, and an outer region adjacent to the pipe wall where the fluid behaves like a power-law fluid. The re- sults have been compared with those predicted by the Ostwald-de Waele power-law model (1); the superiority and necessity of the modified model is clearly demon- strated. Non-Newtonian fluids may be broadly classified into three categories: viscous time-independent fluids, vis- cous time-dependent fluids and viscoelastic fluids. Flu- ids for which the shear stress at a point is deter-