Laminar Flow of a Power-Law Fluid in a Horizontal Pipe

A non-Newtonian fluid has a viscosity that changes with the applied shear force. For a Newtonian fluid (such as water), the viscosity is independent of how fast it is stirred, but for a non-Newtonian fluid the viscosity is dependent. It gets easier or harder to stir faster for different types of non-Newtonian fluids. Different constitutive equations, giving rise to various models of non-Newtonian fluids, have been proposed in order to express the viscosity as a function of the strain rate. In power-law fluids, the following relation is satisfied: , where is the power-law exponent and is the power-law consistency index. Dilatant or shear-thickening fluids correspond to the case where the exponent in this equation is positive, while pseudo-plastic or shear-thinning fluids are obtained when . The viscosity decreases with strain rate for , which is the case for pseudo-plastic fluids (also called shear-thinning fluids). On the other hand, dilatant fluids are shear-thickening. If , the Newtonian fluid behavior can be recovered.