For simple shear flows, some of the differential viscoelastic models require a purely viscous component to be added to the extra-stress tensor for stability reasons. In other words, a purely viscous component is added for guaranteeing a monotonically increasing shear stress curve vs. shear rate. This is true for the PTT model when is nonzero, and for the Giesekus model when α is greater than 0.5. For the PTT model with a nonzero value of , the ratio of the Newtonian viscosity to the total viscosity must be greater than or equal to 1/9 when vanishes, while lower values can be selected when is nonzero. For the Giesekus model, the ratio of the Newtonian viscosity to the total viscosity must be greater than or equal to 1/9 when α equals 1, while lower values can be selected when α decreases.

This is true for the PTT model when is nonzero, and for the Giesekus model when α is greater than 0.5. In these cases, the ratio of the Newtonian viscosity to the total viscosity must be greater than or equal to 1/9.

The inclusion of a purely viscous component can also be considered for other models as well, in order to make the problem more stable numerically. Eventually, a nonvanishing value has to be selected for the additional Newtonian viscosity of the Leonov model. When needed, an evolution scheme can be applied on it.

When a multi-mode viscoelastic model is used, the purely viscous component of the extra-stress tensor is defined through the first mode only; more precisely, for models of the Oldroyd family and for the FENE-P model, the corresponding viscosity will be given by the product . For the DCPP and Leonov models, you will explicitly enter the corresponding.

The addition of a purely viscous component affects both the shear viscosity and the normal-stress difference of the model. Shear thinning is still present, but the viscosity curve also shows a plateau zone at high shear rates, while the normal-stress difference is uniformly reduced.