An energetic approach of powder mixing by manipulating cohesive interaction in a magnetic field

In a typical powder mixing system, the end homogeneity of the key ingredient and the rate to achieve homogeneity are a function of the cohesive interactions of the key ingredient, its adhesive interactions with the bulk powder and the shear impact as a result of the motion of the bulk powder. While there are numerous offline instruments providing indices of these properties, linking them directly to the performance of mixing is difficult due to dissimilarity between the testing and mixing conditions. The current study presents a novel methodology to directly quantify the shear energy of a rotating powder mixing system and the cohesive energy of the key ingredient in the mixing environment. The principle used in this study is based on the concept of the Arrhenius relationship which is widely used to link the activation energy with the thermal energy of molecules when describing the rate constant of a chemical reaction. By mixing iron powder with the bulk powder under various magnetic fields, the constant shear impact from the bulk powder was determined by using the Arrhenius type equation and manipulating the cohesive energy of iron powder via the strength of a magnetic field. The Arrhenius type relationship was demonstrated to be applicable in connecting the shear energy with the cohesive energy and quantifying either of them when describing the rate constant of powder mixing. This finding unveils a route to quantify the shear impact from the bulk powder, which is affected by the composition of the bulk powder, the geometry, the fill fraction and the speed of the mixing equipment. Furthermore, the Arrhenius type relationship can also be used to quantitatively differentiate materials of various cohesiveness by mixing them with a bulk powder of known shear energy. In summary, the novel understanding of the mathematical relationship between the shear energy and the cohesive energy makes it possible to match mixing requirements of the key ingredient with the composition of mixture, equipment and operational parameters.