Measure of Synergism for Binary Particle Mixtures

Measure of Synergism for Binary Particle Mixtures 

A mathematical model has been proposed to account for the mutual synergistic action of either particle component on the other in increasing the value of the dimensionless time 0 as shown in Fig. 9b. Thus, the dimensionless time 0X for the coarse particles could be assumed to exert a mass-fraction-based influence on the fine particles, proportional to 0 1 — x2), which is affected by certain interaction by the fines, inclusive of their ability to adhere to the surface of the coarse and form clusters among themselves, lumped in certain appropriate form, for instance, [1 + /(x2)], where the function /(x2) may again be assumed to possess certain appropriate form, for instance, exponential, x2, where n1 may be called the interactive exponent. This results in an overall contribution by the coarse particles, suitably corrected for the interaction of the fine particles, 0 1 — x2Xl + x2l). This function has the property of accommodating the following boundary conditions  

Similarly, the mass-fraction-based contribution of the fine particles would be proportional to 02x2, and the interaction of the coarse particles, for instance, in breaking up lumps and opening up channels of the otherwise 

the overall dimensionless time 0 for the binary system will consist of the algebraic sum of the contributions from the component particles  

At the maximum value of 0 = 0m, x2 = xm, and the first derivative of 0 with respect to x2, d0jdx2 = 0, giving 

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Figure 54. Measure of synergism for binary particle mixtures. (Kwauk, 1984, 1986.)...

VIII. Measure of Synergism for Binary Particle Mixtures 260... 

Mutual synergism of binary mixtures containing fine particles can be quantified in terms of the departure of the 0-x2 curve from a linear tie line, which signifies absence of synergism, joining 7 and 2 for the respective components, as shown in Fig. 54. A convenient measure of this departure is the shaded area lying between the -x2-curve and the linear tie line. This can be derived analytically in terms of what will be called the Synergism number Sy, normalized with respect to 07+0, of both the coarse and the fine particles ... 

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