Pressure drop of a Boger fluid in a converging channel

Abstract

• Pressure drop measurements of a viscoelastic fluid in a converging channel match those of Newtonian fluids. • No apparent effect of elasticity in converging flows up to a Deborah number of 4. • Predictions of pressure drop for Newtonian fluids in a slowly converging channel, by analysis and Fluent, agree with experiments. • Die swell at the exit of the converging channel was measured and analyzed. • The Oldroyd model is shown not to be appropriate for N1 data of Boger fluids. The pressure to drive a Boger fluid through a long converging channel was measured as a function of flow rate. The channel geometry and flow rates were designed to avoid an upstream vortex and to maximize extensional effects, specifically, to achieve Deborah numbers up to 3 along with a minimum strain of 3. The first measurements of pressure drop were made with two Newtonian fluids, and predictions were made by analysis and Fluent. The latter two agreed to within 1%, and the measurements deviated from these by 5% at most. Four Boger fluids were prepared – three PIB/PB solutions and a solution of PAA in corn syrup. Only one produced reliable pressure-drop measurements, and the data exactly matched that for an equivalent Newtonian fluid, in contrast to the literature where non-Newtonian pressure drops were up to several times higher. Although elasticity apparently had no effect, significant die swell was observed at the channel exit. The explanation for the matching data appears to lie with the radial presssure distribution, which caused migration of the fluid inward, thus lowering shear rates and shear stresses at the wall. Measurements of die swell were made and used to calculate N 1 , from which the axial stress due to shearing on the exit plane was estimated. The extensional stress at the centreline was also estimated, and found to be only a small fraction of the shearing axial stress.