A generalized model to predict the viscosity of solutions with suspended particles. IV. Determination of optimum particle‐by‐particle volume fractions

A new approach has been introduced to establish the optimum composition for all particles within a mixture or suspension to achieve the optimum packing fraction, φn, and/or the minimum viscosity, η. The derivation to obtain the optimum particle volume fraction assumed that a previously developed optimum composition for binary particles applied to any two particle volumes Vi and Vj in the mixture. The composition of the maximum packing fraction for a mixture of more than two particles was then assumed to be calculable from the optimized relationship of each separate binary pair of particle volumes Vi and Vi in the mixture. This derived equation was successfully shown to predict the optimum particle‐to‐particle composition of McGeary's experimentally measured binary, tertiary, and quaternary mixtures. The difference between the calculated and measured volume fractions was no greater than 3.85% and, in most instances, was significantly less than 3.85%. The maximum packing fractions, φn, determined experimentally by McGeary, were also successfully predicted to better than 3.26%. Theoretical particle‐to‐particle volume fractions evaluated for an example pressure‐agglomerated latex appeared to predict the particle‐size distribution only within a narrow range of particle sizes. However, when the theoretical and experimental results were evaluated as a function of the number of particles for each particle diameter, it was apparent that the agglomerated distribution closely approximated the theoretical optimum distribution above 600 Å. Agreement with theory below 600 Å was unsatisfactory. The decrease in viscosity of the example agglomerated latex appeared to have been enhanced as the optimum theoretical particle‐size distribution was approached.