The steady elongation of elasto-viscous liquids

Solutions of the problem of the extension of a cylinder of elasto-viscous liquid have frequently been obtained by assuming specific constitutive equations for the liquid. The assumption of a specific constitutive equation can be avoided, however, by using the Coleman and Noll theory of simple fluids with fading memory: a theory with very general application to isotropic elasto-viscous liquids. Under certain restrictive conditions (including the condition that the influence function of the liquid h ( s ) shall decrease exponentially fast as s -> ∞ ) this theory gives the tension in slow steady elongation as a series of powers of the strain rate. The coefficients of the first, second and third powers of the strain rate can be calculated from measurements made in very slow steady simple shear and in small oscillatory motion of very low frequency by means of a rheogoniometer. This result may have some application in such processes as fibre spinning.