Considerations of Unconstrained Elastic Recovery in Viscoelastic Fluids

Abstract

Analyses are presented of 3-dimensional unconstrained elastic recovery of viscoelastic fluids following the release of stresses. The influence of the nature, variation, and duration of the deformation history are discussed. The problem of recovery from a stressed state is considered. Primary attention has been given to the character of the viscoelastic constitutive equation, especially the significance of the relaxation function which may be deformation rate-dependent and the strain measures. Calculations of instantaneous unconstrained elastic recovery in viscoelastic fluids following steady flow have been carried out for: (i) uniaxial extension, (ii) biaxial extension, (iii) planar extension (pure shear) and (iv) simple shear. It is shown that for fluids with equivalent maximum relaxation times and (Maxwellian) relaxation functions but different strain measures, the 3-dimensional character of the recovery may vary considerably. For specified Maxwellian relaxation time and deformation and deformation rate, the elastic recovery from uniaxial extension is greater for constitutive equations based upon the Finger deformation tensor than for those based upon a Cauchy deformation tensor. The reverse is true for biaxial extension. Lateral recovery from planar extension (pure shear) even possesses opposite signs for these two fluids. The lateral recovery from simple shear for a constitutive equation containing a Cauchy deformation tensor is the square of that for a Finger deformation tensor. The relationship of these responses to the second normal stress difference is discussed.