Polyhyaluronic acid and steady shear flow

Rotarance theory explains non-Newtonian rheological behavior using the physics of macromolecular orientation, and only this physics. This mathematical physics arrives at expressions for the rheological material functions in terms of, and only in terms of, macromolecular lopsidedness. Our previous work on the complex viscosity of aqueous hyaluronic acid arrives at the universal value for apparent macromolecular lopsidedness of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mn>2</m:mn> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>b</m:mi> </m:mrow> <m:mo>̃</m:mo> </m:mover> </m:mrow> <m:mo>/</m:mo> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mo>̃</m:mo> </m:mover> </m:mrow> <m:mrow> <m:mover accent="true"> <m:mrow> <m:mi>ν</m:mi> </m:mrow> <m:mo>̃</m:mo> </m:mover> </m:mrow> <m:mo>≅</m:mo> <m:mn>2.3493</m:mn> </m:math> 2b̃/ãν ̃ 2.3493 [Pulatsu et al., Phys. Fluids , vol. 37 , no. 3, p. 033116, 2025]. By universal , we mean independent of molecular weight, dispersity, temperature, and concentration. In this Letter, we will test a new and recent analytical expression from rotarance theory for the steady shear viscosity function [Giacomin et al., Phys. Fluids , vol. 35 , no. 8, p. 083111, 2023]. We will rely upon seminal steady shear viscosity measurements to test this new theory against the universal value abstracted from complex viscosity measurements. We find this new theory to be accurate up to Weissenberg number one half.