Viscoelastic flow past a confined cylinder of a polyisobutylene solution

Abstract

Viscoelastic constitutive equations are evaluated using the benchmark problem of the planar flow past a confined cylinder for a well-characterized solution of 5%(w/w) polyisobutylene in tetradecane. The ratio of channel height to cylinder diameter is equal to two. We compare finite element simulations with point-wise measured velocities and stresses obtained by means of laser Doppler anemometry and a flow-induced birefringence technique, respectively. The Deborah number (De) ranges from 0.25 to 2.32. In the case of the geometry with a symmetrically confined cylinder, computations were made with a generalized Newtonian model and with both a single- and a four-mode Phan-Thien and Tanner (PTT) model. All model parameters were determined in simple shear flow. A similar analysis is presented in case of an asymmetrically confined cylinder (with De=1.87). Impressively good agreement was found between the predictions of the four-mode PTT model and the measured velocities and stresses. The agreement was even excellent in the geometry with the asymmetrically confined cylinder.