A semi-empirical model relating flow properties to particle contacts in fine binary powder mixtures

Binary powder mixtures, consisting of large and small diameter particles, are used in electrophotographic (EP) printing devices where control of the relationship between the flow properties and mixing ratio is of great importance. In this study, we have experimentally investigated the bulk flow properties (i.e. bulk cohesion and internal friction) of large-and-small fine binary powder mixtures (size ratio: dl/ds = 9.17) as a function of the volume ratio of the smaller component, xs. Using polymer spheres as the smaller constituents, whose bulk cohesion was controlled by surface additives, we have obtained systematic data on the effect of the smaller constituent. A semi-empirical model was then developed, in which the total bulk cohesion is expressed as a linear superposition of the numbers of the three types of particle–particle contacts (i.e. large–large, small–small, and large–small) involved in the shear motion. The model successfully reproduced the experimental data after fitting appropriate values of a parameter representing the adhesion at large–small particle contacts. The rapid increase of the number of particles involved in the shear motion as a function of xs near xs = 0 was also considered in the model. The model clarifies the contributions of the three types of particle–particle contacts to the total bulk flow properties. The effect of large–small particle contacts on the bulk cohesion was observed for almost all values of xs. The value of xs at which the contribution of large–small particle contacts in the total bulk cohesion becomes a maximum shifted in the direction of larger xs when a less cohesive small powder was used. This also resulted in a shift of xs at which the internal friction reached a minimum.