Orthogonal superposition of oscillatory shearing upon steady shear flow from polymer rotarance theory: normal stresses

One of the most intriguing experiments in polymer physics, is the superposition of small shearing oscillations upon steady shear flow. This experiment allows us to explore how the steady shear flow affects the complex viscosity, and the complex components of the first and second normal stress differences. The novelty of this paper is its exploration of the how the direction of this superposition matters to the complex components of the first and second normal stress differences in orthogonal superposition. Whereas, these complex components of the normal stress differences have been measured in parallel superposition, these have not been measured in orthogonal. Previously, we derived material functions from rotarance theory for the (previously measured) normal stress responses to the parallel superposition of small-amplitude oscillatory shear flow upon steady shear flow [ Phys. Fluids , 37 , 033133 (2025)]. The novelty of this work is that we arrive at analytical expressions for the (not previously measured) orthogonal superposition counterparts. We choose rotarance theory for our exploration, for its unique diversity of macromolecular structure. By rotarance theory , we mean accounting for the elasticity of polymeric liquids by considering, and by only considering, the physics of macromolecular orientation. We find that both the first and second normal stress difference responses in orthogonal superposition differ importantly from their parallel superposition counterparts.