An experimental and statistical study of 2D hopper flow of binary mixtures
Granular mixing has many applications in the pharmaceutical and food industries. Understanding the quality of the mixture is critical for end-use applications. There are many methods used to define mixing quality, with the Lacey Index being the most prevalent. However, these mixing definitions or indices do not convey if clusters of one material have formed at a scale above the scale of scrutiny, or if some regions of the mixture can be considered well-mixed while other regions may have clustering. In this study, alternative methods will be investigated to identify a better tool (or tools) than the Lacey Index to characterize mixing quality. A transparent 2D hopper and silo are used to mix and hold a binary particulate mixture with varying material density, diameter, and color. Checkerboard, vertically segregated, or horizontally segregated mixtures are initially held in the hopper. Mixing is gravity driven as the particles fall from the hopper into the silo. MATLAB image analysis tools are utilized to extract spatial data from the resulting mixture. Extracted spatial data are analyzed using statistical methods such as point pattern analysis that include quadrat analysis, clustering, and nearest neighbors. The different analysis methods are then compared with established mixing indices to confirm method viability. Results show that using point pattern analysis provides a better characterization tool than the Lacey Index. While more complex than an index that provides a single mixing number between 0 and 1, the point pattern analysis conveys more information about the mixture that is lost in single value mixing indices.