Measuring the properties of a viscoelastic fluid using a tethered swimmer

Chiu, Selena, et al.

Link: https://pubs.aip.org/sor/jor/article/70/4/809/3388422/Measuring-the-properties-of-a-viscoelastic-fluid

DOI: https://doi.org/10.1122/8.0001162

Abstract

Viscoelastic normal stresses can generate propulsion in swirlers—axisymmetric swimmers that break fore-aft symmetry and rotate about their axis of symmetry—even in the absence of propulsion in a Newtonian fluid at low Reynolds numbers. In this study, we demonstrate the first measurements of the zero-shear first normal stress coefficient, ψ1,0⁠, and the longest relaxation times, λ1 and ⁠λ2, of a viscoelastic fluid using a tethered swirler, simply via measurements of its propulsive force. Through the combined application of microhydrodynamic theory and numerical simulations, we establish transfer functions relating a swirler’s propulsive force to the surrounding fluid’s zero-shear normal stress coefficients and linear viscoelastic spectrum, thereby enabling rheological measurements without viscometric flow. The transfer functions are then applied to experimentally measured propulsive forces to give precise measurements of ψ1,0⁠, λ1⁠, λ2 and of a viscoelastic Boger fluid, for which measurements of ψ1,0 are not achievable on standard benchtop rheometers due to limited sensitivity. Furthermore, for a given fluid, the propulsive force is a function of swimmer and confinement geometry, with the geometric dependence quantitatively predicted by analytical theory and Newtonian fluid simulations. Our work provides a proof of concept of a “tethered swimming rheometer” that not only is capable of measuring both steady and dynamic properties of viscoelastic fluids but also implies a large design space where geometry can be optimized to enhance measurement sensitivity and range.