Surfactants will never decrease the viscosity of liquids. Depending on the structure of the surfactant phase, the viscosifying effect may be small or large:
- On the small side, spherical micelles act roughly like hard spheres, so you can use the theory for colloid dispersions (Einstein, Bachelor, Quemada....)
- On the large side, giant micelles act like polymer molecules so you need to start from the theories for the viscosity of polymer solution.
However, the area is complex and vast and the theories that I cited are not always sufficient. Personally, I do not know an overall review.
Viscosity, transfers shear stress to upper layers of fluid and velocity gradient, makes shear stress. So for a stationary fluid shear stress is zero. Also I have some references that I think it could be useful.