(409e) Powder Blending Kinetics Using a Controlled Cohesion Apparatus and Its Application

The current study presents a novel method to characterize the shear energy of a powder blending system by quantitatively manipulating the cohesive interaction of a minor ingredient to be homogeneously mixed. The blending kinetics was studied using the concept of reaction kinetics (Arrhenius equation). The characterized system can be used to quantify the cohesive energy of a minor ingredient following the methodology presented in the current investigation. In a typical low-shear mixing apparatus, such as bin blenders, the maximum homogeneity of powder mixture and the rate to achieve the homogeneity are important factors to determine whether a low shear mechanism will suffice, which depends on the cohesiveness of the ingredient of interest and the adhesive interaction of that ingredient with other components in the mixture. Applying the concept of reversible chemical reactions, the maximum homogeneity is analogous to the concentration of product at the equilibrium status of a reaction, while the rate of mixing is analogous to the rate of the forward reaction. The current investigation focuses on the determination of the rate constant of mixing. During the initial period of blending, the mixing step (forward reaction) is dominant compared to the demixing step (reverse reaction). This period is thus considered irreversible. The Arrhenius equation was used to estimate the kinetic rate constant for mixing, where the resistance (similar to activation energy of a chemical reaction) originates from the cohesive energy of the component of interest and the driving force (similar to the thermal term RT for a chemical reaction) is exerted by the shear energy due to powder movement. In a typical reaction kinetic experiment, the initial reaction rates at various temperatures are measured and fit against temperature and the activation energy is calculated using the Arrhenius equation. In this study, a magnetic field was used to control the cohesive interaction (activation energy) of iron powder (to mimic the active pharmaceutical ingredients) to characterize the shear energy of a typical pharmaceutical blend in a bottle blender. The use of a magnetic field allows changing only the cohesive interaction between iron particles without inducing other changes in the properties of the iron powder, such as particle size and surface area, which could alter the adhesive interaction between iron powder and other non-magnetized components. Since all other ingredients are non-magnetizable and the loading of iron is low, the shear energy is considered constant under various magnetic fields. An exponential decay relationship is assumed for the mixing kinetics, which has been commonly used since it was suggested 50 years ago by Rose H.E. [1]. The relative standard deviation around the expected concentration (RSDE) of iron is used to represent the homogeneity rather than the normally used standard deviation around the observed mean. The following figures show the model predicted blending homogeneity curve vs. the number of revolutions (in lieu of time). A good match of experimental kinetics vs. the model under various magnetic fields is observed. This model demonstrates that an Arrhenius type relationship is valid for the mixing period and the magnetic attraction (Eind) is the dominant source of cohesive energy. The shear energy of the system was further derived from the Arrhenius equation. [1] Rose, H.E., 1959, A suggested equation relating to the mixing of powders and its application to the study of the performance of certain type of machine; Transactions of the Institution of Chemical Engineers