Microstructural heterogeneity drives reaction initiation in granular materials

Abstract

Thermal localization leads to reaction initiation in granular materials. Observations show that it occurs in the vicinity of large pores and, thus, depends on a material's microstructure. Since the spatial variability of the latter cannot be ascertained in all its relevant details, we treat the material's initial porosity as a random field. The so-called "hotspots" are then modeled as rare events in a complex nonlinear dynamical system. Their probability of occurrence is quantified by the tails of the distributions of the temperature and the corresponding reaction rate. These are computed via Monte Carlo simulations of a two-phase five-equation dynamic compaction model, which are supplemented with a mesoscale model of the thermal localization at the solid-gas interface. Our results demonstrate a strong nonlinear dependence of the probability of hotspot initiation on the variance of the initial porosity.

Crystal Shape Control on the Repacking and Jamming of Crystal‐Rich Mushes

“…We observe, in general, a greater frequency and magnitude of load drop events for bigger and more elongated particles. Further experiments are needed to better constrain the factors that control load drop events and study how they modify the rheology of the granular medium before and after disruption. Recent advances in developing stochastic rheology models in granular media (e.g., Bakarji & Tartakovsky, 2020) may allow for a continuum scale parameterization of these discrete and episodic events.…”

Stochastic Pore Collapse Models in Granular Materials

“…The concept of plastic potential was introduced by Mises in 1928 by analogy to the elastic potential which has a similar form to Eqn. (3). Likewise, we propose a stochastic extension to thermoelasticity and apply it to plasticity.…”

“…In such situations, increasing the complexity of a continuum model will not be enough to capture the behavior of the system itself. Earlier work has shown that simply adding fluctuations to the initial microstructure accounts for the sensitivity of reactionrate on the pore size [3]. Motivated by the fluctuating Lifschitz-Landau fluctuating Navier-Stokes equation, we * tartkovsky@stanford.edu posit that one can account for unpredictable microscale phenomena in granular materials by introducing a fluctuation term into the continuum equations.…”

Data-driven discovery of coarse-grained equations

“…Many engineering problems require knowledge of the full PDF. For example, estimating the probability of rare events is only possible when the tails of the distribution are accurately modeled (Bakarji and Tartakovsky, 2019).…”