Use of coupled birefringence and LDV studies of flow through a planar contraction to test constitutive equations for concentrated polymer solutions

Abstract

Laser Doppler velocimetry and flow-induced birefringence are used to measure the rate of deformation and the principal components of the refractive index tensor in a 5% polyisobutylene (PIB) solution in tetradecane (C14) flowing along the centerplane of an abrupt 3.97:1 planar contraction. The stress optical law is used to interpret the birefringence data in terms of the normal stress difference, which is used to calculate a transient elongational viscosity defined along the centerplane. These measurements are compared directly to predictions of six multimode, differential constitutive models (Oldroyd-B, White–Metzner, Acierno et al., Giesekus, Bird–DeAguiar, and Phan-Thien–Tanner) that are fit to steady and small amplitude oscillatory shear flow data for the PIB/C14 solution. The fluid exhibits slight elongational thickening followed by apparent extensional thinning at higher elongation rates. We believe that this ‘‘thinning’’ behavior is due to the decreased residence time of the polymer molecules in the high-strain-rate region as the flow rate (and maximum elongation rate) is increased. The nonlinear constitutive equations, except for the White–Metzner model, are virtually indistinguishable in their description of the dynamical response of the fluid in this experiment; however, the Phan-Thien–Tanner model gives the best quantitative fit to the data. These results point to the need for experiments in which the fluid flowing along the centerline is subjected to a greater total elongational strain.

Alternative derivation of differential constitutive equations of the Oldroyd-B type

“…Based on network theory of rubber-like fluids, Phan Thien and Tanner [20,21] developed in 1977 the PTT model which is one of the most widespread non-linear models in use (cf. critical appraisal by Quinzani et al [22]) and, when the lower convected term in the generalised Jaumann derivative is not considered, by setting the parameter = 0 to avoid non-affine deformations, that constitutive equation is usually written as (PTT model):…”

Mixed finite element methods for viscoelastic flow analysis: a review

“…In a sequence of papers Quinzani et al [132], [133] and [134] have subsequently investigated the rheological properties of a 5 wt % polyisobutylene in tetradecane (PIB/C14) solution in relation to a number of existing constitutive models and have measured velocity and stress distributions for the flow through a planar contraction. In [133] velocity and normal stresses at a number of cross sections are measured and compared with predictions of Newtonian and power-law fluids.…”

“…The order of the singularity near the reentrant corner is demonstrated to (nearly) obey a similarity form that holds for power-law fluids. Measured axial velocity profiles along the symmetry line in a planar four-to-one contraction are used in [134] to access the capabilities of a number of constitutive model to predict the transient elongational stresses. Of the models investigated the multi-mode PTT model performed best.…”

Analytical solution for fully developed channel and pipe flow of Phan-Thien–Tanner fluids

“…Indeed, it has been found (Quinzani, Armstrong & Brown 1995) to be the best simple differential model to represent the elongational properties of polymer solutions in entry flows. For example, both Baaijens (1993) and Azaiez Guénette & Aït-Kadi (1996) have used the linearized form to predict the entry flow through the 4 : 1 planar contraction measured by Quinzani et al (1995); Baloch, Townsend & Webster (1996) have also used it to simulate both expansion and contraction flows. The exponential form of the PTT model gives a maximum of the elongational viscosity at a given level of strain rate in simple stretching flows, as is typical of some polymer melts; it was used, for example, by White & Baird (1988a, b) to simulate their own measurements.…”