Relationship between Flow Properties and Elastic Stresses of Dilute and Ultra-Dilute Polymer Solutions Passing through Small Apertures

Abstract

The Weissenberg number, defined as the product of relaxation time and strain rate, reflects the ratio of elastic forces to viscous forces in a viscoelastic flow. Thus, at high strain rate based on a small (micrometer-scale) characteristic length, elastic properties are important for understanding the flow properties of dilute (100 ppm and 10 ppm) and ultra-dilute (1 ppm) aqueous polymer solutions. However, the very small elasticity and high strain rate make it difficult to measure the elastic properties precisely. In this study, flow properties and elastic stresses were investigated for dilute and ultra-dilute polymer solutions flowing through small slits with characteristic lengths of between 122 µm and 1.1 mm. The pressure drop (PD) and jet thrust (JT) for polyethylene oxide (PEO) and polyacrylamide (PAA) solutions were measured from their flow properties and elastic stresses, respectively. The pressure difference upon passing through a small slit and the momentum issuing from the slit at a constant flow rate were measured as the PD and JT, respectively. Although the measured PD of water and silicone oil agreed with the numerical predictions of the Navier-Stokes equation, the resultant PDs for all PEO samples were less than those for water and silicone oil. Similar results were obtained for all PAA samples; the PDs for aqueous solutions of 100 ppm, 10 ppm, and 1 ppm PAA were reduced. The JT values were also smaller than those for water and silicone oil. Even though ultra-dilute solutions were used, it is interesting that the PDs and JTs were reduced. Furthermore, to understand the experimental results, elastic stress was determined from the JT. The calculated elastic stress depended on the mean velocity. The relationship between the flow properties and the elastic properties was clarified, and the effect of surface tension was described by estimating the capillary number.