Improved Equation of the Continuous Particle Size Distribution for Dense Packing

The Furnas model describes the discrete particle size distribution for densest packing. Using a model that considers a continuous particle size distribution for the densest packing to be a mixture of infinite Furnas discrete particle size groups, an equation for the cumulative particle size distribution providing the densest packing was derived. Monosize particles with different shapes have a different packing pore fraction. One parameter in the equation is the pore fraction of packed monosize particles; the particle size distribution for achieving densest packing is a function of this pore fraction. A reduced form of this equation is also presented as a working equation. The equation derived here is compared to the modified Andreasen equation for dense packing. An equation and the correlated graph for calculating theoretically the geometric mean particle size and an equation for calculating the specific surface area of the particle size distribution of the improved equation are also derived.