A **cross fluid** is a type of generalized Newtonian fluid whose viscosity depends upon shear rate according to the following equation:

μ
e
f
f
(
γ
˙
)
=
μ
0
1
+
(
μ
0
γ
˙
τ
∗
)
1
−
n
where

μ
e
f
f
(
γ
˙
)
is viscosity as a function of shear rate,

μ
0
,

τ
∗
and

*n* are coefficients.

At low shear rate (
μ
0
γ
˙
≪
τ
∗
), cross fluids behave as Newtonian fluids and at high shear rate (
μ
0
γ
˙
≫
τ
∗
) as power-law fluids.