Extensional rheometry of mobile fluids. Part II: Comparison between the uniaxial, planar, and biaxial extensional rheology of dilute polymer solutions using numerically optimized stagnation point microfluidic devices

Author:

Haward Simon J.1ORCID,Varchanis Stylianos1,McKinley Gareth H.2ORCID,Alves Manuel A.3ORCID,Shen Amy Q.1ORCID

Affiliation:

1. Okinawa Institute of Science and Technology 1 , Onna, Okinawa 904-0495, Japan

2. Hatsopoulos Microfluids Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology 2 , 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

3. Departamento de Engenharia Química, ALiCE, CEFT, Faculdade de Engenharia da Universidade do Porto 3 , Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

Abstract

Part I of this paper [Haward et al., J. Rheol. 67, 995–1009 (2023)] presents a three-dimensional microfluidic device (the optimized uniaxial and biaxial extensional rheometer, OUBER) for generating near-homogeneous uniaxial and biaxial elongational flows. Here, in Part II, the OUBER device is employed to examine the uniaxial and biaxial extensional rheology of model dilute polymer solutions, compared with measurements made under planar extension in the optimized-shape cross-slot extensional rheometer [OSCER, Haward et al. Phys. Rev. Lett. 109, 128301 (2012)]. In each case, micro-particle image velocimetry is used to measure the extension rate as a function of the imposed flow conditions, and excess pressure drop measurements enable estimation of the tensile stress difference generated in the fluid via a new analysis based on the macroscopic power balance for flow through each device. Based on this analysis, for the most dilute polymer sample tested, which is “ultradilute”, the extensional viscosity is well described by Peterlin’s finitely extensible nonlinear elastic dumbbell model. In this limit, the biaxial extensional viscosity at high Weissenberg numbers (Wi) is half that of the uniaxial and planar extensional viscosities. At higher polymer concentrations, although the fluids remain dilute, the experimental measurements deviate from the model predictions, which is attributed to the onset of intermolecular interactions as the polymer chains unravel in the extensional flows. Of practical significance (and fundamental interest), elastic instability occurs at a significantly lower Wi in uniaxial extensional flow than in either biaxial or planar extensional flow, thereby limiting the utility of this flow type for extensional viscosity measurement.

Funder

Japan Society for the Promotion of Science

Fundação para a Ciência e a Tecnologia

Publisher

Society of Rheology

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,General Materials Science

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