Novel approach to estimate quality of binary random powder mixtures: samples of constant volume. III: Range of validity of equation.

The validity of an equation developed to determine the quality of binary random mixtures (eq 1) was evaluated with tablets prepared from random mixtures of a coarse constituent A (sucrose) and fine constituent B [microcrystalline cellulose (Avicel PH 101)-talc] with the A:B ratios (w/w) varying from 10:90 to 80:20. With all A:B ratios, superior agreement was established between the random content variations determined with eq 1 and the content variations found in the tablets. The 80:20 ratio, however, was just at the boundary, and random quality was achieved with the 50-mg tablets but not with the 200-mg tablets because of segregation. From percolation theory, this result is a consequence of the small proportion by volume (bv) of B that is almost equal to the precolation threshold (Pcb) of B of 0.3. With bv less than Pcb, the fine constituent B does not form a coherent lattice, and eq 1 is no longer valid. To estimate the volume proportions av and bv from the mass proportions a and b, two methods were established. Method 1 assumed the bulk densities of A and B to be representative and was used when av was higher than the percolation threshold (Pca) of A of 0.3 (a, 0.5). Method 2 used the true particle density of A and was valid with av values of less than 0.1 (a, 0.3), in which case the particles of A were dispersed as individuals in the matrix of B.