Viscometric functions (${\sigma }_{xy}=\mu (\dot{\gamma })\dot{\gamma },N_i={\psi }_i(\dot{\gamma }){\dot{\gamma }}^2$)

The three viscometric functions describe steady homogeneous simple shear flow: its shear viscosity and the first and second normal-stress differences per squared shear rate. Take x as the flow direction, y as the gradient direction and z as the vorticity direction, so $N_1={\sigma }_{xx}-{\sigma }_{yy}$ and $N_2={\sigma }_{yy}-{\sigma }_{zz}$. Isotropic pressure drops out of these differences.