Effect of couple stresses on the rheology and dynamics of linear Maxwell viscoelastic fluids

The constitutive analog of the linear Maxwell viscoelastic fluid model with the explicit addition of couple stresses is derived from thermodynamic first principles. Furthermore, the concepts of the recently proposed “Consistent Couple Stress theory” are considered to fully determine the rheological description of the fluid model. Finally, the resulting linear momentum equations are used to investigate the couple stress modulated flow dynamics of a few simple flow configurations. The plots of the variations in the elastic behavior of the fluid due to the presence of couple stresses show that the couple stress acts in addition to the conventional force-stress to increase the diffusion of momentum and thereby enhance the dampening of the elastic deformations in the equivalent spring-dashpot interpretation of the linear Maxwell viscoelastic fluid.