Basics of Fluid Mechanics, 2014a

1.5. VISCOSITYVISCOSITY 19
In very low pressure, in theory, the viscosity is only a function of the temperature
with a “simple” molecular structure. For gases with very long molecular structure or
complexity structure these formulas cannot be applied. For some mixtures of two liquids
it was observed that at a low shear stress, the viscosity is dominated by a liquid with
high viscosity and at high shear stress to be dominated by a liquid with the low viscosity
liquid. The higher viscosity is more dominate at low shear stress. Reiner and Phillippoff
suggested the following formula
⎛
⎞
1
dU x
dy
= μ
⎜ ∞ +
μ 0 − μ ∞
( ) 2 τ xy
τxy ⎟
(1.23)
⎝ 1+ ⎠
τ s
Where the term μ ∞ is the experimental value at high shear stress. The term μ 0
is the experimental viscosity at shear stress approaching zero. The term τ s is the
characteristic shear stress of the mixture. An example for values for this formula, for
Molten Sulfur at temperature 120 ◦ C are μ ∞ =0.0215 ( )
N sec
m , 2 μ0 =0.00105 ( )
N sec
m , 2
and τ s =0.0000073 ( )
kN
m . This equation (1.23) provides reasonable value only up to
2
τ =0.001 ( )
kN
m . 2
Figure 1.12 can be used for a crude estimate of dense gases mixture. To estimate
the viscosity of the mixture with n component Hougen and Watson’s method for
pseudocritial properties is adapted. In this method the following are defined as mixed
critical pressure as
the mixed critical temperature is
and the mixed critical viscosity is
Example 1.6:
P cmix =
T cmix =
μ cmix =
n∑
x i P ci (1.24)
i=1
n∑
x i T ci (1.25)
i=1
n∑
x i μ ci (1.26)
i=1