where τ is the extra stress tensor, which is defined as a sum of a viscous and a viscoelastic or elastic contribution as
where μs is the solvent viscosity,
S is the strain-rate tensor, and
Te is the elastic (or viscoelastic) stress tensor. To adequately describe a flow of fluid with a complex rheological behavior, the symmetric stress tensor
Te is represented as a sum of the individual modes:
The theory about boundary conditions is found in the section Theory for the Single-Phase Flow Interfaces. Note that for the viscoelastic models, the extra stress tensor is defined as a sum of a viscous and an elastic contribution:
τ = K + Te. Therefore, an additional term should be added to the expression for the normal extra stress:
Kn = Kn + Ten.