Soft matter physics and granular materials

The highly interdisciplinary field of soft matter (involving physicists, chemists, geoscientists, and engineers) seeks to characterize and often design or control materials that are far less stiff than the molecular solids that are studied in traditional condensed matter physics [1]. Important examples of soft materials include colloidal suspensions, emulsions, polymers, and the subfield of my dissertation work, granular materials. Granular materials are defined as collections of rigid, athermal grains that interact primarily via contact repulsion and, in real grains, dissipative friction. These materials exist across many size scales and are ubiquitous in agriculture, pharmaceuticals, and astrophysical systems like the rings of Saturn; examples include coffee beans, asteroids, and table salt (Figure 1). Understanding how these materials respond to applied stresses and strains in processes involving transport, mixing, or packaging is thus crucial for applications across society. The physics of grains at the single-grain scale is well characterized by classical mechanics and elasticity theory, but the collective behaviors of these far-from-equilibrium materials are fascinating and not completely understood. For instance, these materials can display the properties of non-Newtonian fluids or amorphous solids depending on environmental conditions, and when in the solid or jammed state, they transmit stress in heterogeneous force chains [2]. Because such systems are far from equilibrium, standard statistical mechanics methods cannot be straightforwardly applied to them.

Figure 1: Granular materials across size scales. (Credit: Top-left, Jim Gade; top-right, freestocks; bottom-left, Bannon Morrissy; bottom-right, Kevin Ortiz)

Figure 2: Sample photoelastic image from my experiment in which a single grain (blue) is driven counterclockwise through a disk packing.

Research experience

My dissertation work focused on stick-slip dynamics in slowly sheared granular materials. Stick-slip features stick phases, in which stress is slowly increased in a jammed granular packing by an external compliant load, and intermittent slip events, in which the medium temporarily flows as a fluid and releases stress through rearrangement and dissipation due to friction and inelastic collisions. Similar dynamics are observable in many systems spanning several orders of magnitude in length, from dragging AFM tips to the sliding of tectonic plates during earthquakes. In my experiments, a spring is used to pull a sled over or an intruding rod through a model granular system composed of quasi-2D disks or polygons. Goals of this work included (1) exploring the dependence of these dynamics on particle shape and friction and (2) uncovering the sources of and searching for predictive measures for slip, or unjamming, events. Sample videos from my work that demonstrate these dynamics can be found on my Youtube channel and in Figure 3; a sample image from one of my experiments is also shown in Figure 2.

In my first project, I explored the point-load response of a confined system of grains to a spring-driven rod. The most important aspect of this project was changing the friction between the grains and a glass base by either floating grains on a water-air interface or sitting grains on the table [3]. Many model experimental granular systems feature quasi-2D particles sitting on a base (as opposed to 3D systems) for the purpose of extracting the positions of every grain as well as intergrain forces through photoelasticity [4], so understanding basal friction’s stabilizing effects is important for designing and interpreting such experiments and their results. Studying constricted flow can also be useful in providing recommendations for designing efficient granular transport systems with hoppers and conveyer belts. Our primary finding was that, with a dense packing of grains, the intruding grain-sized rod (“intruder”) exhibited stick-slip dynamics when basal friction was present but exhibited intermittent flow dynamics when basal friction was not. Intermittent flow occurs when the intruder can freely flow through the medium but occasionally gets stopped by the formation of grain arches; these dynamics are similar to what is observed when granular media flow through constricted apertures [5] and are qualitatively distinguishable from stick-slip behavior.

Collaborators of mine have been running simulations of this system to explore parameter changes that are not feasible in the experiments. We recently published work [6] that shows excellent agreement between simulation and experiment on the above mentioned dynamics and then shows that dynamic basal friction, rather than static basal friction, determines whether the intruder will move in a stick-slip manner or will experience intermittent flow. This novel finding implies that the restriction of motion of grains during slip events is significantly more important for limiting the intruder’s flow than increased stability from static friction when the intruder is stuck. We meet weekly online and are currently preparing a manuscript on simulations and experiments exploring the scaling of intruder dynamics with the relative sizes of the channel and intruder.

My more recent experimental projects involve using grains that are polygonal rather than circular, introducing local rotational constraints that can significantly modify the behavior of the bulk material [7]. My manuscript describing the transmission of forces through locally loaded disk and pentagonal packings (pre-print available at [8]) was recently accepted for publication in Soft Matter with minor revisions. Another project is in progress with a focus on comparing both grain-scale dynamics and intergrain forces through photoelasticity for grains with varying angularity.

My future research plans involve experimental exploration of the flow of grains through constricted apertures with varying shape, concavity, size and shape dispersity, and stiffness. More broadly, I am open to new soft matter research, particularly studying colloidal glasses and discontinuous shear thickening, foams, or emulsions. I am interested in learning to use new imaging systems like confocal microscopy and techniques for manipulating smaller scale systems than I am accustomed to in addition to diving into new physics.

Figure 3: Left: Sample video of stick-slip as single-grain penetrates a quasi-2D bed of photoelastic disks. Right: Instead of sitting on a glass substrate, the disks now float in water, having no basal friction. Intermittent flow is observed rather than stick-slip.

Figure 4: The experimental system I have been using to study stick-slip dynamics with varying grain angularity.

Research and undergraduate instruction

Experimentation is, along with theoretical developments, the foundation of science by providing empirical tests of theoretical predictions and providing new findings for theories to describe. Small-scale, table-top experimentation also offers practical skill development for researchers of all experience levels, especially undergraduates. As a research mentor, I aim for my students to have experiences in asking questions, devising experiments to address questions, analyzing data with integrity, and sharing findings with both scientific and general audiences. I will guide my students in the specific projects that they work on as well as general scientific methods, discuss their research progress with them regularly, encourage them to apply for competitive research or internship programs that will broaden their research or career outlooks, and help them find and prepare for conference and other presentation opportunities. I received excellent training as an undergraduate researcher myself, and that inspiring experience was a major factor in my decision to attend graduate school. While I do not expect that all of my research undergraduates will continue in scientific research, I do hope that they will learn how to think scientifically and find the research that they do both exciting and relevant.

[1] S. R. Nagel, Rev. Mod. Phys. 89, 2 (2017).

[2] D. Howell, R. P. Behringer, and C. Veje, Phys. Rev. Lett. 82, 26 (1999).

[3] R. Kozlowski, et. al., Phys. Rev. E 100, 032905 (2019).

[4] K. E. Daniels, J. E. Kollmer, and J. G. Puckett, Rev. Sci. Inst. 88, 051808 (2017).

[5] C. C. Thomas and D. J. Durian, Phys. Rev. Lett. 114, 17 (2015).

[6] C. M. Carlevaro, et. al., Phys. Rev. E 101, 012909 (2020).

[7] Y. Zhao, et. al., Granular Matter 21 (2019); N. Estrada, et. al., Phys. Rev. E 84, 011306 (2011).

[8] R. Kozlowski, et. al., arXiv 2018.06235 (2021).