Mixing particle softness in a two-dimensional hopper: Particle rigidity and friction enable variable arch geometry to cause clogging

Understanding the clogging of mixtures of soft and rigid particles flowing through hoppers becomes important as soft particle usage increases in consumer products. We investigate this clogging under varying particle size and rigid fraction by quantifying various properties of arches formed in the neck of a quasi-two-dimensional hopper. As more soft particles are added to the mixture, the arch tends to become both narrower and more curved. This effect arises from the fact that soft particles have less ability to sustain a clog than rigid particles. The clogging probability is seen to have a linear correlation with the span (width) of the arch. The angles between the arch particles are shown to have higher values as rigid fraction increases. The arch occasionally shows a partially convex shape at high rigid fractions when rigid particles are sitting next to each other, while soft particles can form angles of less than 180 degrees only. The relation between the span and aspect ratio (width to height) of the arch is theoretically formulated for three-particle arches and extended to arches of more than three particles, using an asymptotic parameter that represents the width of a flat arch. Finally, it is concluded that clogging probability closely correlates with both the arch span and the variation of other geometric arch properties.

Automated summary

Understanding the clogging behavior of mixtures of soft and rigid particles in hoppers is crucial due to the increasing use of soft particles in consumer products. This study investigates the clogging phenomenon by analyzing the properties of arches formed in the hopper neck. It is found that the addition of soft particles narrows and curves the arch, as soft particles are less likely to cause clogging compared to rigid particles. The clogging probability is linearly correlated with the span of the arch, and the angles between arch particles increase with an increase in the rigid fraction. The study also provides theoretical formulations for the arch span and aspect ratio, showing that clogging probability is closely related to various geometric properties of the arch.