A second-order fluid is a fluid where the stress tensor is the sum of all tensors that can be formed from the velocity field with up to two derivatives, much as a Newtonian fluid is formed from derivatives up to first order. This model may be obtained from a retarded motion expansion truncated at the second-order. For an isotropic, incompressible second-order fluid, the total stress tensor is given by

where

is the indeterminate spherical stress due to the constraint of incompressibility,
is the -th Rivlin–Ericksen tensor,
is the zero-shear viscosity,
and are constants related to the zero shear normal stress coefficients.

This article uses material from the Wikipedia article Second-order fluid, which is released under the Creative Commons Attribution-Share-Alike License 3.0.