SYNOPSISSeveral suspension equations available in the literature have been found to have a common derivative form. This common derivative was found to be equivalent to a ratio of the intrinsic viscosity, [ q ] , and a quantity, VInt, defined as the "relative suspension interaction volume" available for particle flow. V,,, was, in general, found to be a relatively simple function of the suspension particle volume fraction, cp, the maximum particle packing fraction, cpn, and a new variable, 6, defined as the particle interaction coefficient. Different forms of this common derivative were obtained by modifying VJnt with a simple adjustment for the value for the interaction coefficient, u. Integration of this generalized derivative yielded a generalized suspension viscosity equation that was found to predict the form of many suspension equations that have previously appeared in the literature. For example, by varying the interaction coefficient, u, the Arrhenius equation resulted when u = 0, the Kreiger-Dougherty equation resulted when u = 1, and when u = 2, the Mooney equation resulted. Fractional values for the particle interaction coefficient were also found to be useful when optimizing the empirical fit of the literature data of Vand and Eiler. Additional insight from such a data fit can also be obtained from the magnitude of both the particle interaction coefficient, u, and the packing fraction, cpn. 0 1993 John Wiley & Sons, Inc.

A new analysis technique has been developed in this paper to evaluate the upper limit of the packing fraction, qn , utilized in the prediction of suspension viscosities. The semiempirical equation developed for the upper limit of the packing fraction, qn, was generated initially from McGeary's binary particle packing fraction data. All possible D,/ D, ratios of particles size averages were evaluated and analyzed in this formulation development. Only the D 5 / D 1 and D 4 / D z ratios of particle diameter averages were found to accurately predict the proper particle volume fraction location obtained in McGeary's data for the correct upper limit packing fraction qn. After developing methodology to calculate qn, for binary particle distributions, an extension was made to include distributions with any number n of different particle size diameters. One of the more general of the suspended particle viscosity equations, as developed in a previous paper by this author, was used to demonstrate the application of this new (P, , methodology to the evaluation of suspension viscosity properties. The blended binary suspension viscosity results of Johnson and Kelsey for near monodisperse latexes were shown to be satisfactorily predicted as a function of the binary volume composition.

SYNOPSISThe generalized suspension viscosity equation utilized in this study was evaluated with both a packing fraction, (P", and a particle interaction coefficient, u, as a function of suspension blend composition, f Z T . The estimation of the packing fraction, ( P, , , in turn, required the further elucidation of the D 5 / D 1 ratio of particle diameter averages. Blend constants developed in this study allowed evaluation of both the D J D , ratio of particle diameter averages as well as the number-average particle diameter, D 1 , as a function of the fraction of one suspension in a blend, fZT. These blend constants were shown to be easily evaluated from each individual suspension prior to blending. The viscosity data of Johnson and Kelsey were shown to be generally predicted as a function of the volume composition when a constant particle interaction coefficient, u, was assumed. However, a better prediction of the results of Johnson and Kelsey was obtained by assuming that the particle interaction coefficient, u, was a function of the number-average particle diameter, D 1 , of the suspension mixture composition. Consequently, a new approach was identified to evaluate the simultaneous effects of small particles to both increase viscosity as a result of increasing particle interaction as well as to decrease viscosity as a result of improving the particle-size distribution. 0 1993 John Wiley & Sons, Inc.

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, p,,, and/or the minimum viscosity, 7. 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 V, 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, pn , 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 A. Agreement with theory below 600 A 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.

ABSTRACT:The objective of this study was to develop some new concepts of importance when trying to optimize the viscosity/modulus and impact relative to the particle-size distribution in suspensions and particulate composites. The results of this study appear to indicate that, conceptually, it is possible to significantly improve the viscosity versus the impact balance for material formulations by optimizing the particle-size distribution. For binary particle-size distributions, the influence of the preferred particle-size distribution, as determined using a square-root distribution, did not yield the most desirable particle-size distribution if the particle-to-particle component of the interaction coefficient was high. However, if three or more particles were utilized in the distribution, then the optimum particle-size distribution utilized can apparently be characterized using the square-root distribution even when the particle-particle component, pc , of the interaction coefficient, , was found to be quite high . In addition, this same square-root particle-size distribution can also satisfactorily predict a probability of impact that can remain consistently high as long as the particles utilized are well chosen and not too close in size. Thus, this preferred particle-size distribution can be utilized to predict at least one of the preferred distributions to optimize the balance of properties between impact and the viscosity/modulus.