Extension of a cylinder of viscoelastic liquid

Abstract

The basic rheological relations for the motion of viscoelastic media and a thixotropic viscoelastic medium in a constant longitudinal velocity gradient field were developed in [1] for the case of plane flow with a stagnation point. The results of that study showed that, in contrast with simple shear deformation, in the case of uniaxial extension steady-state flow of the liquid is not possible after reaching a deformation rate exceeding some critical value, and the liquid will undergo quasibrittle failure. In this case the approximation of the rheological relations by the Maxwell equation gives good qualitative agreement with the behavior of media of a more complex rheological structure. Below we investigate the kinematic and dynamic characteristics of liquid motion in a longitudinal velocity gradient field which is not constant in time, and we study some particular cases using as an example a Maxwellian liquid. The results of the study may be used to analyze the technological processes of forming and drawing fibers, and also for determining the rheological parameters of polymers by the extension method proposed by Kargin and Sogolova [2].