Constitutive Equations for Viscoelastic Fluids for Short Deformation Periods and for Rapidly Changing Flows: Significance of the Deborah Number

Abstract

Abstract The proper forms and asymptotic characteristics of constitutive equations which may be useful for the description of viscoelastic fluids in flow fields of engineering interest are considered. It is seen that the Deborah number emerges as a natural ordering parameter which determines, on the one hand, whether simple approximations explicit in stress may suffice to describe the fluid properties or, on the other hand, whether implicit or integral equations are required. Methods of scale up are discussed.