Evaluatin of the higashitani and pritchard analysis of the hole pressure using flow birefingence

TLDR: In this article, the authors used flow birefringence data to determine the stress field (i.e. σ and the normal stress difference, σ11 − σ22) in the region of a slot placed perpendicular to the flow direction for a polystyrene melt.

Abstract: Higashitani and Pritchard (H-P) carried out an analysis of the hole pressure (PH) for viscoelastic fluids which leads to expressions relating PH to the shear stress (σ), the wall shear stress (σw), and the normal stress differneces (N1 and N2). Although very good agreement their theory and experimental results has been obtained for several polymer solutions and three polymer melts, it is known that at least two of the key assumptions in the theory are violated. In this study flow birefingence has been used to determine the stress field (i.e. σ and the normal stress difference, σ11 — σ22) in the region of a slot placed perpendicular to the flow direction for a polystyrene melt. Values of σ and σ11 — σ22 were then used to evaluate the integrand in the expression relating Pe1 where Pe1 is the hole pressure measured at the base of the rectangular slot, σ and N1. Values of Pe1 evaluated using flow birefringence data agreed well with those obtained using the same integral expression and cone-and-plate values of N1 and σ, and with directly measured values of Pe1. This agreement occurred even though the stress field was found to be asymmetric around the centerline of the slot and with secondary flow in the slot. A detailed evaluation of the values of N1/2σ, which constitute the integral in the H-P theory, along the centerline of the slot revealed most of the contributions to the integral canceled in integrating from the base of the slot where σ is zero at the centerline of the slit-die. The main contributions to the integral occurred from the integration taken from the centerline of the slit-die to the upperdie