Power-law fluid

NOTOC In continuum mechanics, a power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid (time-independent non-Newtonian fluid) for which the shear stress, τ, is given by where: K is the flow consistency index (SI units Pa sn), ∂u/∂y is the shear rate or the velocity gradient perpendicular to the plane of shear (SI unit s−1), and n is the flow behavior index (dimensionless). The quantity represents an apparent or effective viscosity as a function of the shear rate (SI unit Pa s). The value of K and n can be obtained from the graph of and . The slope line gives the value of n – 1, from which n can be calculated. The intercept at gives the value of K. Also known as the Ostwald–de Waele power law this mathematical relationship is useful because of its simplicity, but only approximately describes the behaviour of a real non-Newtonian fluid. For example, if n were less than one, the power law predicts that the effective viscosity would decrease with increasing shear rate indefinitely, requiring a fluid with infinite viscosity at rest and zero viscosity as the shear rate approaches infinity, but a real fluid has both a minimum and a maximum effective viscosity that depend on the physical chemistry at the molecular level. Therefore, the power law is only a good description of fluid behaviour across the range of shear rates to which the coefficients were fitted. There are a number of other models that better describe the entire flow behaviour of shear-dependent fluids, but they do so at the expense of simplicity, so the power law is still used to describe fluid behaviour, permit mathematical predictions, and correlate experimental data. Power-law fluids can be subdivided into three different types of fluids based on the value of their flow behaviour index: Pseudoplastic, or shear-thinning are those fluids whose behaviour is time independent and which have a lower apparent viscosity at higher shear rates, and are usually solutions of large, polymeric molecules in a solvent with smaller molecules.