Frankel-Acrivos equation

See also the Eilers equation and Frankel-Acrivos equation. 

Frankel-Acrivos equation n. An equation, derived wholly from theoretical considerations, giving the relative viscosity of suspensions of monodisperse spheres in... 

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. 

Eqs. (39-41) predict a similar viscosity behavior, though Eq. (39) gives a relatively larger viscosity in comparison with the Kreiger-Doughty and Frankel-Acrivos equations. Note that both Eq.(39) and (41) cannot be reduced to Einstein s viscosity equation when the particle volume fraction approaches zero. 

Figure 8. The calculated relative viscosity is plotted against particle volume fraction using Eq. (39). A dense random packing structure is assumed and ( )n,=0.63. K-D represents Kreiger-Dougherty, and F-A the Frankel-Acrivos equation.

Landel et al. s equation appears to be reasonably good with less viscous suspensions, whereas the Frankel and Acrivos equation seems to fit the data with more viscous slurries and at higher particle concentrations. It is assumed that all of Nolte s data are taken at room temperature. 

Metzner (1985) pointed out that at high solids concentration levels, the theoretical equation (Equation 2.25) of Frankel and Acrivos appears to do a good job of portraying experimental data of rigid solids dispersed in polymer melts. 

In the region of high concentration levels, that is, near maximum packing concentration, Frankel and Acrivos (54) derived the following theoretical equation on the basis of lubrication theory ... 

Frankel Neil, and Acrivos Andreas. The constitutive equation for a dilute emulsion. J. Fluid. Mech. 44 (1970) 65-78. 

Frankel and Acrivos [100] did away with all empiricisms and artificial boundaries and provided an expression for highly concentrated suspensions of uniform solid spheres intending to complement the classical Einstein s equation (4.1) valid only for very dilute suspensions. 

Frankel and Acrivos [31] have presented a more general constitutive equation based on a first-order deformation of droplets where the viscosity is found to be... 

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