The normal yield stress

TL;DR

This paper investigates the normal stresses in yield stress fluids, revealing their quadratic relationship with shear stress and introducing the concept of a yield normal stress, which advances understanding of complex fluid flow.

Contribution

It provides the first systematic measurement of normal stress differences in yield stress fluids, highlighting their quadratic dependence on shear stress and introducing the concept of a yield normal stress.

Findings

Normal stress differences are quadratic functions of shear stress.

Existence of a yield normal stress in yield stress fluids.

Normal stresses are significant for modeling non-viscometric flows.

Abstract

Normal stresses in complex fluids lead to new flow phenomena because they can be comparable to or even larger than the shear stress itself. In addition, they are of paramount importance for formulating and testing constitutive equations for predicting non-viscometric flow behavior. Very little attention has so far been paid to the normal stresses of yield stress fluids, mainly because they are very difficult to measure. We report the first systematic study of the first and second normal stress differences, N1 (>0) and N2 (<0), in both continuous and oscillatory shear of three model yield stress fluids. We show that both normal stress differences are quadratic functions of the shear stress both above and below the shear yield stress, leading to the existence of a yield normal stress.