This award supports theoretical research that is motivated by a key question in granular physics: how can one describe the statics and dynamics of dry granular media at large length scales and long time scales? The PI focuses on the nature of stress propagation near jamming. Our ability to predict and control the response of granular materials to external changes hinges on our ability to connect features such as force chains observed at short length scales to the large-scale deformation of granular media. Therefore, a theoretical framework that links the microscopic and collective behavior of grains has the potential of transforming the landscape of granular research. A property of granular materials that is responsible for most of the non trivial phenomenology, and leads to most of the theoretical challenges is the existence of a large number of different microscopic metastable states that are macroscopically equivalent. This feature is also present in a broader class of materials in their jammed states. Jamming, the transition from a fluid state to a disordered solid state is influenced by the presence of metastability, and granular materials exhibit strong fluctuations close to jamming. Experiments and simulations have shown that fluctuations in stresses, flow fields, and density have well defined distributions characterized by only a few external parameters. The existence of well-characterized distributions has led to notion of an underlying statistical description for granular media. Statistical ensembles analogous to those of equilibrium statistical mechanics have been proposed to create the desired link between microscopic and macroscopic, fluctuations and response. The PI will use a recently developed stress ensemble to make predictions about spatial fluctuations in static granular packings. The rheology of granular materials is also strongly affected by the existence of multiple, metastable states for a given set of macroscopic parameters. In recent work, the stress-ensemble, combined with a concept of metastability in a ?stress landscape? has been able to reproduce the logarithmic strengthening of granular materials under shear. A goal of the proposed project is to achieve better understanding of the dynamics of slowly deformed granular media using models that incorporate metastabilty, disorder and stochasticity.
This project will provide valuable educational opportunities for graduate and undergraduate students. The PI has a strong record of including under-represented students and faculty in her research. The PI has also taken leadership roles in the complex fluids and granular community by founding and organizing workshops and conferences.
NON-TECHNICAL SUMMARY This award supports theoretical research and education on granular materials and the phenomenon of jamming. The granular materials encountered in our daily lives, such as sand, salt, or rice, have remarkable properties. The cereal in the box compactifies when shaken, rice makes pyramidal structures only when poured out carefully, and sand flows at a constant rate in an hourglass. Failures of grain silos are caused by unpredictably large stresses exerted on the sidewalls as the flow arrests. Avalanches and earthquakes are examples of the unjamming of grains leading to flow. Yet, our grasp of such behavior of granular matter is limited. The main obstacle that hinders the understanding of granular matter is that it is fundamentally out of thermal equilibrium. Grains are macroscopic objects that interact through dissipative contact. The dissipative nature of the interactions implies that energy has to be constantly supplied to maintain a steady state. The macroscopic size makes thermal fluctuations irrelevant for changing the state of grains, and granular materials are effectively zero-temperature systems that do not equilibrate spontaneously. There is a growing realization that the study of granular media offers unexpected challenges in physics, having behavior unlike that of liquids or solids. The PI aims to develop a theoretical framework which captures the diverse phenomena displayed by granular materials.
From a practical perspective, granular matter and emulsions are widespread, finding applications in the food industry, cosmetics, pharmaceuticals and geomorphology. Often, the handling of granular materials is based on empirical methods due to a lack of understanding of these complex systems. A fundamental basis for these systems would make it possible to develop new procedures and reduce handling costs, thereby having a significant impact on industry and on American competitiveness.
This project will provide valuable educational opportunities for graduate and undergraduate students. The PI has a strong record of including under-represented students and faculty in her research. The PI has also taken leadership roles in the complex fluids and granular community by founding and organizing workshops and conferences.
Version:1.0 StartHTML:0000000200 EndHTML:0000008485 StartFragment:0000003405 EndFragment:0000008449 SourceURL:file://localhost/Users/bulbulchakraborty/Desktop/nsf_publicity/Project_Outcomes.doc A stroll on the beach can mean sinking your toes into smooth sand or walking firm-footed on a surface that appears almost solid. While both properties are commonplace, exactly what is it that makes granular materials change from a flowing state to a "jammed," or solid state? Whether it’s sand on a beach or rice grains in a hopper, being able to predict the behavior of granular matter can help engineers and manufacturers of a wide range of products. This information could also potentially be used to further understand? natural phenomena, such as avalanches, earthquakes and erosion. The project, "Fluctuations and Response in Granular Matter near Jamming" addressed the basic theoretical question of how granular materials can form solids. Solids have the unique property of being able to resist shearing: liquids and gases cannot do that and they flow when sheared. In garden variety solids there are attractive interactions that hold atoms and molecules together and at low temperatures when these are not being agitated too much, the atoms or molecules get organized to form a solid. Dry sand grains in a bucket or grains in a hopper have no attractive forces holding them together. It is the constraints exerted by the container that can lead to solidification. Dapeng Bi, a PhD student working on the project, asked the question: how can this be? In the absence of attractive forces, how does a solid form? A unique opportunity to explore these questions arose from observations made in the laboratory of Bob Behringer at Duke University. Traditionally people have thought of shearing as a mechanism for breaking up materials, but these experiments showed that granular materials could be solidified by just shearing them without changing the density. Dapeng’s analysis of the Duke experiments explained how a granular solid is created by shear. This work appeared in Nature in 2011. What our earlier work did not address is why shearing leads to solidification. For this, we needed to develop a new theoretical framework. This framework is described in Dapeng’s thesis, and provides an intriguing picture of ordering in the space of forces, not positions of the grains. We are in the process of submitting this work for publication. The accompanying image illustrates some of the basic ideas in the theory. In a granular solid, all the forces on a grain have to balance out so that they do not move. This allows us to associate with each grain a polygon defined by the forces acting on it, which we call a force-tile. What is remarkable about shear-induced jamming is that these tiles have anisotropic shapes. Shearing leads to increasing alignment of the long directions of these tiles and that is what creates the solid. The analysis of the experiments focused on how tenuous structures, which bear most of the forces generated by shearing, propagate from one end of the system to another. We developed quantitative tools that are now being used in the Behringer group to analyze new experiments. Grains can solidify through non-conventional routes because they never reach thermal equilibrium. A video created by the National Science Foundation, uses experiments from the Behringer group and our theoretical analysis to highlight the striking features of granular matter that straddles the boundary of fluids and solids (www.livescience.com/21001-mysterious-materials-behave-like-both-solids-and-liquids.html).
