Laminar Flow of a Power-Law Fluid in a Horizontal Pipe
The velocity profile versus radial position is obtained for the laminar flow of a pseudo-plastic or dilatant fluid (orange curve) and a Newtonian fluid (blue curve) in a pipe under the assumption of equal volumetric flow rate. The pipe radius is and the applied pressure gradient is . The power-law consistency index is chosen to be . If the power-law exponent is 1, then a Newtonian fluid is recovered. For the pseudo-plastic fluid, the velocity profile is flatter near the center, where it resembles plug flow, and is steeper near the wall, where it has a higher velocity than the Newtonian fluid or the dilatant fluid. Thus, convective energy transport is higher for shear-thinning fluids when compared to shear-thickening or Newtonian fluids.
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.