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 /

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.

= /

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^" /

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.

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.

kinematic viscosity, The ratio of the viscosity of a fluid to its density.

= _s /

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^' /

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.

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.