Modeling Periodic Stratified Segregation in Granular Heap Flows

Significance 

Granular materials, when set in motion, can exhibit a range of complex behaviors not seen in ordinary fluids including segregation, where particles separate based on physical properties like size, density, or shape. Indeed, granular segregation is a common challenge in various industries such as pharmaceuticals, agriculture, and materials processing, and non-uniformity in mixed granular products can lead to quality control issues, which negatively affect the consistency and reliability of the final product. Consequently, there is an urgent need to develop new methods to control segregation by manipulating the flow conditions, thereby enhancing product quality. To this end, in a new study published in Chemical Engineering Science and conducted by Assistant Professor Hongyi Xiao, Dr. Zhekai Deng, Professor Julio Ottino, Professor Paul Umbanhowar, and Professor Richard Lueptow, the researchers investigated the behavior of granular heap flows under conditions of periodically modulated feed rates to better understand how changes in the rate at which granular material is fed onto a heap affect the stratification and segregation patterns of particles of different sizes.

The research team utilized an advection-diffusion-segregation model, which is a modification of the advection-diffusion equation commonly used in fluid dynamics but adapted to include a term that accounts for the segregation of different particle species based on size. The model was calibrated and verified against experimental observations, to ensure relevance and accuracy in predicting real-world phenomena. A quasi-two-dimensional experimental setup was used to consider granular heap flow dynamics under periodically modulated feed rates, which involved a screw feeder to adjust delivery rates of small and large spherical glass particles, aimed to mimic pharmaceuticals and materials processing. The screw feeder was programmed to change its delivery rate at controlled intervals, thereby modulating the feed rate onto the experimental heap setup. High-resolution imaging and advection-diffusion-segregation model simulations tracked the segregation and stratification of the particles to reveal how distinct layers formed, their stability, and their evolution over time. The authors’ findings highlight that periodic modulation of feed rates leads to stratified segregation with greater heap uniformity compared to heaps formed under constant feed rates. This modulation affected layer uniformity and thickness and influenced the dynamic heap segregation behavior as the feed rate transitions from low to high (or vice versa), introducing waves of movement, impacting both erosion and deposition. This suggested to the authors that precise control of feed rates could significantly enhance material consistency and quality in industrial applications involving granular materials, highlighting the importance of feed rate kinematics in the segregation process. Their work also highlighted the ability of their advection-diffusion-segregation model to predict granular segregation and mixing in complex time-dependent flows.

The new study by Professor Richard Lueptow and colleagues has significant scientific and industrial implications. First, it enhances our understanding of granular flow dynamics, especially under unsteady conditions, which is challenging due to the complex behaviors exhibited by granular materials. It also validates a time-dependent continuum model that incorporates the effects of time-varying feed rates on segregation and further develops the theoretical framework that describes these processes. Moreover, industries such as pharmaceuticals, food processing, and mining that handle granular materials often struggle with segregation issues, which can affect product quality and consistency. The new reported method to control and manipulate segregation through the modulation of feed rates, provides a potential tool for these industries to improve the uniformity of mixed granular products. This could lead to better quality control, reduced waste, and optimized processing techniques. Furthermore, understanding how to control the flow and mixing of granular materials can lead to innovative designs for material handling equipment. For instance, the design of hoppers, conveyors, and chutes could be improved to specifically handle the dynamic behaviors of granular materials under varying flow conditions. This could include new types of feed mechanisms that are capable of dynamically adjusting flow rates to manipulate material segregation on the fly. Additionally, the new model could also be applied in environmental engineering, where understanding granular flow could enhance the management of sediment transport in waterways or the handling of waste materials. Indeed, the continuum model developed and validated in the reported study enhances predictive capabilities for granular segregation, which is vital for the planning and optimization of industrial processes and can significantly reduce the trial and error typically associated with these processes.

Aknowledgement: This material is based upon work supported by the National Science Foundation under Grant No. CBET-1511450.

Video caption: In the experiment on the left, a mixture of large 2 mm blue particles and small 0.5 mm red particles are fed onto the top left of a heap, alternating between a fast feed rate and a slow feed rate, resulting in layers of small and large particles. The model results on the right closely match the experiments, demonstrating the effectiveness of the advection-diffusion-segregation approach, even for complicated transient flows.

About the author

Hongyi Xiao is an Assistant Professor of Mechanical Engineering at the University of Michigan. He holds a B.E. degree in Thermal Engineering from Tsinghua University (2014) and a PhD degree in Mechanical Engineering (2018) from Northwestern University. His research focuses on the physics of granular and soft matter and relevant applications in chemical engineering, additive manufacturing, and robotic locomotion. He has published 17 journal papers.

About the author

Zhekai Deng earned his undergraduate degree from the University of Rochester and completed his doctorate at Northwestern University. His research has focused on granular segregation, resulting in the publication of four journal papers on poly/multi-disperse segregation across various granular flow geometries. Currently, he serves as a Project Leader at Boston Consulting Group, where he works closely with biopharmaceutical and industrial goods companies, as well as private investors, on a range of topics, including operation strategy and due diligence.

About the author

Julio M. Ottino is the Distinguished McCormick Institute Professor and Walter P. Murphy Professor of Chemical and Biological Engineering, and professor (by courtesy) of Mechanical Engineering at Northwestern University. He is the former dean of the McCormick School of Engineering at Northwestern and the founder of the Northwestern Institute on Complex Systems. His work on fluid mixing and granular dynamics has impacted a wide range of fields in physical and geophysical sciences, engineering, and nonlinear dynamics. He is member of the National Academy of Engineering, the National Academy of Sciences, and the American Academy of Arts and Sciences, as well as having received many other awards and honors. He recently authored a book with Bruce Mau entitled The Nexus, dealing with creativity and innovation at the intersection of art, technology, and science.

About the author

Paul Umbanhowar is a Research Professor of Mechanical Engineering at Northwestern University.  He received a BA in physics from Carleton College and a PhD in physics from The University of Texas at Austin.  His research interests include granular materials, robotic locomotion, and pattern formation.  He has over 120 journal publications and three patents.

About the author

Richard M. Lueptow is Senior Associate Dean at the McCormick School of Engineering, Co-Founder of the Master of Product Design and Development Program, Professor of Mechanical Engineering and of Chemical & Biological Engineering (by courtesy), and former Charles Deering McCormick Professor of Teaching Excellence at Northwestern University.  His research interests include granular flow physics and molecular simulations of water purification systems. He has published over 180 journal papers and 6 patents.  He has received numerous teaching and research awards and is a Fellow of the American Institute of Chemical Engineers, the American Physical Society, and the American Society of Mechanical Engineers.

Reference

Hongyi Xiao, Zhekai Deng, Julio M. Ottino, Paul B. Umbanhowar, Richard M. Lueptow, Modeling stratified segregation in periodically driven granular heap flow, Chemical Engineering Science, Volume 278, 2023, 118870,

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