Dimensional Problem of the Power Law in Rheology

Abstract

THE power law equation, between shear stress, τ, and strain rate, ɣ̇, may be written ɣ̇=kτ^α: it has often been shown^1,2 to be in accordance with experimental data obtained for many non-Newtonian fluids. The equation is open to the logical objection that it is dimensionally inconsistent unless the constant of proportionality, k, is not a true constant at all but has variable dimensions which depend on the properties of the sample under observation. Nedonchelle and Schutz³ have shown experimentally that for one particular non-Newtonian system there is a relationship between the constant of proportionality, k, and the exponent, α, such that the equation may be reduced to a dimensionless form containing three dimensionally stable constants which are independent properties characterizing the material in its environment.