Mixture Viscosity Models
The Newtonian viscosities of interpenetrating media are not readily available. Instead empirical and analytical models for the dynamic viscosity mixture have been developed, usually as a function of the dispersed volume fraction.
A simple mixture viscosity model, which is only available when there is one dispersed phase covering the entire range of particle volume fractions sd is the Krieger type model (Ref. 1):
(6-144)
Here ϕd,max is the maximum packing limit, by default 0.62. An extension of Equation 6-62 can be applied for liquid droplets/bubbles:
(6-145)
where μc and μd are the viscosities of the continuous and dispersed phase, respectively.
When there is more than one dispersed phase, the following Krieger type mixture viscosity model (Ref. 3) is used:
(6-146)
where
with di the particle diameter of phase i, and
(6-147)
For fluid-fluid systems, the volume averaged viscosity defined by
(6-148)
is also available.