Significance of deformation rate softening of memory in viscoelastic fluid mechanics and polymer processing

Abstract

Abstract It is pointed out that in viscoelastic fluid constitutive equations, non‐linear response to deformation rate and strain beyond the second order is usually interpreted in terms of the deformation rate or strain dependence of the memory function. These non‐linearities act to decrease the extent of the memory. The dependence may be characterized by one or more dimensionless material parameters. A new dimensionless group based on the primary material parameters describing the intensity of the deformation rate dependence of the memory function is introduced and its significance is discussed. This is called the Yamamoto number. The solutions of viscoelastic fluid mechanics problems are considered to depend upon both the Weissenberg and Yamamoto numbers. Such problems include topics of interest in polymer melt processing such as uniaxial elouigatioiial flow, fiber spinning and vortex development in extrusion through a die entry.