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3. Functional Forms of Viscosity
Refer to Section 11 for a complete list of symbols used in the following
definitions. Some viscosity terms relating to oscillatory measurements are
defined both here and more explicitly in section 8.
apparent viscosity,
app The value of viscosity evaluated at
some nominal average value of the
shear rate. The apparent viscosity applies, for instance, in the
capillary method, where a range of shear rates are employed.
coefficient of fluidity [fluidity]
,
Reciprocal of the
coefficient of viscosity.
=
1 / ![](eta.gif)
coefficient of viscosity
[viscosity]
,
The ratio of
shear stress to
shear rate under simple
steady shear. The abbreviated form 'viscosity' is used most often in practice, and is frequently employed without discriminating between Newtonian and non-Newtonian behavior. When the quotient is independent of shear rate (i.e., follows the
Newtonian model), it is considered a material constant. When the quotient is dependent on shear rate (i.e.,
non-Newtonian), it should be referred to as the non-Newtonian viscosity.
=
/ ![](Image59.gif)
complex viscosity
,
* The frequency-dependent viscosity function
determined during
forced harmonic oscillation of shear stress; contains both real and imaginary parts.
differential viscosity
,
diff The derivative of shear stress with respect to shear rate.
diff
=
/
dynamic viscosity
,
'
The ratio of the
loss modulus to the angular frequency, determined during
forced harmonic oscillation (dynamic) measurements. The real part of the
complex viscosity.
'
= G" / ![](omega.gif)
infinite shear viscosity
,
The high
shear rate limiting value of viscosity. Often associated with the
second Newtonian region in
pseudoplastic fluids.
inherent viscosity [logarithmic viscosity]
,
inh
A natural logarithmic function of the
relative viscosity reduced by the solute concentration.
![](inh.gif)
intrinsic viscosity [limiting viscosity
number]
, [
] The zero
concentration
limiting value of the
reduced specific viscosity. A characteristic
function for the single molecule in solution. [
] is equivalent to the effective hydrodynamic specific volume for the solute.
![](lim.gif)
kinematic viscosity
,
The ratio of the viscosity of a fluid to its density.
=
s / ![](rho.gif)
out-of-phase viscosity,
''
The ratio of the
storage modulus to the angular frequency, determined during
forced harmonic oscillation (dynamic) measurements. The imaginary
part of the
complex viscosity.
'' = G'
/
![](omega.gif)
plastic viscosity
,
pl
For a
Bingham model, the excess of the
shear stress over the
yield stress divided by the
shear rate, and equal to the
differential viscosity. For
non-ideal Bingham materials, the differential viscosity determined
in the high-shear limiting, linear portion of the flow curve; associated with
viscoplastic fluids.
![](lim2.gif)
reduced viscosity [viscosity number]
,
red
The ratio of any viscosity function to the concentration, c, of the solute or particulate phase. By normalizing viscosity in this way, concentration effects become more apparent. For instance, the reduced
specific viscosity is:
red
=
sp / c
relative viscosity [viscosity ratio]
,
r
Ratio of the viscosity in a suspension or solution to the viscosity of the suspending medium or solvent.
r =
/
s
specific viscosity
,
sp
The
relative viscosity minus unity.
sp =
r - 1
zero shear viscosity
,
0
The low
shear rate limiting value of viscosity. Associated with the first Newtonian region in many
pseudoplastic fluids.
![](lim3.gif)
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