Continuum Theories for the Viscoelasticity of Flexible Homogeneous Polymeric Liquids

Abstract

Abstract There are two primary reasons for seeking a precise mathematical description of the constitutive equations for viscoelastic fluids, which relate the state of stress to the state of deformation or deformation history. The first reason is that the constitutive equations are needed to predict the rheological behavior of viscoelastic fluids for a given flow field. The second reason is that constitutive equations are needed to solve the equations of motion (momentum balance equations), energy balance equations, and/or mass balance equations in order to describe the velocity, stress, temperature, and/or concentration profiles in a given flow field that is often encountered in polymer processing operations. There are two approaches to developing constitutive equations for viscoelastic fluids: one is a continuum (phenomenological) approach and the other is a molecular approach. Depending upon the chemical structure of a polymer (e.g., flexible homopolymer, rigid rodlike polymer, microphase-separated block copolymer, segmented multicomponent polymers, highly filled polymer, miscible polymer blend, immiscible polymer blend), one may take a different approach to the formulation of the constitutive equation. In this chapter we present some representative constitutive equations for flexible, homogeneous viscoelastic liquids that have been formulated on the basis of the phenomenological approach. In the next chapter we present the molecular approach to the formulation of constitutive equations for flexible, homogeneous viscoelastic fluids. In the formulation of the constitutive equations using a phenomenological approach, emphasis is placed on the relationship between the components of stress and the components of the rate of deformation (or strain) or deformation (or strain) history, such that the responses of a fluid to a specified flow field or stress can adequately be described. The parameters appearing in a constitutive equation are supposed to represent the characteristics of the fluid under consideration. More often than not, the parameters appearing in a phenomenological constitutive equation are determined by curve fitting to experimental results. Thus phenomenological constitutive equations shed little light on the effect of the molecular parameters of the fluid under investigation to the rheological responses of the fluid.