Kreiger-Dougherty equation

At very high concentrations, however, these equations fail to account for the overgrowing, and one should use the empirical Kreiger-Dougherty equation (Kreiger and Dougherty, 1959)... 

Eq. (39) indicates that viscosity of a suspension is dependent on how the particle pack in a liquid medium and the particle volume fraction. When the particle volume fraction approaches to zero, the viscosity of the suspension almost reduces to the viscosity of the liquid medium. Suppose that particles will form a dense random packing in the suspension, thus < )m-0.63 [22], the calculated ris/q, against the particle volume fraction is depicted in Figure 8. For the comparison reason, two widely used viscosity equations, the Kreiger-Dougherty equation (23] expressed in F.q. (40), and Frankel-Acrivos equation [24] expressed in Eq. (41), are also plotted in the same graph. 

Figure 9. The calculated relative viscosity is plotted against particle volume fraction using Eq. (52-54). A dense random packing structure is assumed and ( >m=0.63. K-D represents for the Kreiger-Dougherty equation, and F-A stands for die Frankel-Acrivos equation.

Using functional analysis similar to Mooney, Kreiger and Dougherty (53) derived the following equation ... 

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