The yield normal stress

Normal stresses in complex fluids lead to new flow phenomena because they can be comparable to, or even larger than, the shear stress. In addition, they are of paramount importance for formulating and testing constitutive equations for predicting nonviscometric flow behavior. Very little attention has thus far been paid to the normal stresses of yield stress fluids, which are difficult to measure. We report the first systematic study of the first and second normal stress differences in both continuous and slow oscillatory shear of three model nonthixotropic yield stress fluids, with N₁ > 0 and N₂ < 0. 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. However, the contribution of the normal stresses to the von Mises yield criterion for these materials is small.