Collaborative Research: Statistical mechanics of dense suspensions - dynamical correlations and scaling theory

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This award supports research and education on dense suspensions, specifically a collection of rough particles suspended in a fluid like water: cornstarch is a good example of such a system. Similar dense suspensions include cement, ceramics, and mud. These suspensions are often so packed with particles that small changes in flow rate may cause them to stop flowing and jam into a solid. Surprisingly, a predictive theory for this behavior is lacking. One obstacle is figuring out how interactions between two particles cause the behavior seen when many particles are put together. The research supported by this award is focused on creating understanding using a combination of theory, numerical simulations, and analysis of experimental data. Since the behavior of suspensions is easily accessible in experiments and numerical simulations that show good agreement, they are an ideal system for exploring the larger question of how materials change properties due to flow conditions. The team is committed to outreach and diversity-in-education efforts: a novel approach to exposing the basic science through on-stage dramatization will be undertaken with collaborators in New York City, while both investigators will mentor undergraduate research students with recruitment from under-represented groups a priority.This award supports research and education to develop understanding of microscopic correlations and macroscopic behavior in dense, shear-thickening suspensions. Using a discrete-particle simulation approach that incorporates particle frictional contact at stress above a threshold level, the behavior of the discontinuous shear thickening (DST) and shear jamming (SJ) transitions will be explored. The focus will be on measuring dynamical, or motion variable, correlations such as the spatial and temporal correlation of fluctuating velocities and rotational motions. This will be complemented by analysis of divergent shear and normal stress as jamming is approached; the analysis will apply methods of crossover scaling, a renormalization group method especially useful when behavior is influenced by two singular points: this is seen in the current system as it undergoes two forms of jamming, one due to geometrically-determined frictionless contacts at vanishing stress and the other due to stress-induced frictional contacts at large stress. The continuum description of suspension flow in a novel direction, by extension of recent approaches to describe the emergent elasticity of jammed amorphous packings will also be investigated. This direction of work is based on a postulate that rigidity on progressively larger scales is induced by increase of the stress, which in a sufficiently dense suspension leads to a percolation of rigidity and jamming; the continuum theory is based in the investigation of motion correlations by simulation. To explore more complex kinematics, simulation of a spatially varying flow mimicking active microrheology, in which a probe particle is pulled through a dense suspension, will be undertaken.This 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.