Nonlinear effects in the shear viscosity of fluids near the critical point

We present a microscopic theory for the nonlinear shear viscosity of fluids near the critical point, and find that dependence on shear gradients should be observable in capillary viscometer experiments. We suggest that the leveling off (cusplike behavior) of viscosities that has been observed experimentally may be a result of shear gradient effects. Further experiments to test our theory are suggested.