A generalized fluidity power law and laws of extrusion

Abstract

Raw rubbers are assumed to obey the fluidity power law, ϕ = f; τ n−1 , ϕ = fluidity, τ = shearing stress, n > 1. For three-dimensional flow the generalized law is assumed to be ϕ = gW (n−1) (n+1) , where W = rate of energy dissipation. It is shown that this law is equivalent to Nadai's three-dimensional law of steady creep, expressed in terms of the octahedral shearing stress and octahedral rate of shear. On the basis of the fluidity power law, laws of extrusion are derived for circular and slit tubes and orifices, surface slip also being included in the analysis. By dimensional analysis a general theorem is established concerning the effects of stress (or pressure) and apparatus dimension on deformation and flow rates. Experimental data, obtained with circular tubes of various lengths and diameters and covering a 100-fold range in extrusion rates, agree roughly with the power form of the derived extrusion laws, but do not give the expected values of the exponent n in some cases. Surface slip was too small to measure in the present experiments.