Collaborative Research: Analysis of dense suspension properties and dynamics by network methods

NON-TECHNICAL SUMMARYThis project seeks to develop an improved understanding of the basic causes of flow properties of dense suspensions, which are materials containing large amounts of solid particles immersed in a liquid. Examples include cements and ceramics in the building industry, mud in nature, and chocolate in the processing phase, where sugar and chocolate particles are suspended in cocoa butter. Understanding the flow properties improves our ability to control flows in industrial processes as well as predict those related to natural disasters such as mudslides. For dense suspensions, the resistance to flow often undergoes “discontinuous shear thickening” (DST) in which the viscosity increases abruptly due to an increase in the flow rate, as when the mixing rate is increased for cement. Recent research has shown that DST is partially explained by flow driving particles into contact. This breaks the film of liquid between particle surfaces, and then they exert friction and cannot easily slide past one another. This is much like the fact that friction of tires on a dry road surfaces can stop sliding, while a film of oil between the surface and the tire does not. What is not known, and is the key subject of this research, is how the contacts between particles generate networks within the material, or “contact networks.” A contact network, in this case, refers to the connected set of pathways through the particles, which in two dimensions may look like a spider web or a road map. One benefit of understanding what controls network formation is the ability to increase or decrease flow resistance as desired in applications. The project’s primary goal is to characterize the contact networks created by suspensions undergoing DST under various flows and different amounts of solid and liquid. In addition, the project will consider the influence of mixing different size particles. To achieve these objectives, the project will use the tools developed within the project team for computational simulation of the flow. The new aspect of the research is its focus on the networks formed at each time instance. This will use two mathematical methods, one known as k-core analysis (KCA), which uses the contacts between particles, and one called persistent homology (PH), which is based on the strength of the forces between particles that are carried by the contacts. The project will enhance our understanding of how the network structure formed allows the flowing material to influence the flow itself. Small regions of connected particles within the flowing suspension appear to behave as if they were rigid solids, and one goal of the project is to find ways to relate the contact networks to this solid behavior. The project will further seek to use PH and KCA for data reduction, allowing for developing models of the flow behavior that can be tested in applications. The broader impacts of the project include relevance to both fundamental non-equilibrium statistical physics and materials applications from traditional cement to new developments in advanced ceramics and additive manufacturing. The project’s approach has great promise to provide an understanding of the essential features of the networks developed by these amorphous materials, considering, for example, how local rigidity that is exposed by KCA is related to rigidity percolation and the closeness to jamming, with clear metrics from PH correlated to these behaviors. Such understanding will point the way to efficient mechanical or chemical modifications to improve material design and performance. The project includes a strong multi-level educational component, involving undergraduates, PhD candidates, and PIs working jointly in an interdisciplinary environment involving two minority-serving institutions.TECHNICAL SUMMARYThis project focuses on developing fundamental new directions in dynamic material science through a study of the network topology in flowing dense suspensions. The specific aim is to develop and place on a robust mathematical foundation the physical relationship of these properties to the underlying networks of contacts and forces between particles. The suspensions will be described via simulations which have the potential to generate vast amounts of data due to large particle numbers in time-dependent ensemble calculations. These data will be analyzed using tools based on persistent homology (PH) and k-core analysis (KCA). These methods allow for enormous data reduction and also for significant enhancement of physical understanding based on the elucidation of essential structural measures by the two network theoretical approaches. From a mathematical perspective, a coupled study of PH and KCA, one based upon physical cluster classification by connectivity and one based on well-defined metrics of the overall network structure, will deepen our understanding of both methods. This award is jointly supported by the Division of Materials Research and the Division of Mathematical Sciences.STATEMENT OF MERIT REVIEWThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.