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Abstract Geophysical fluid‐granular flows, such as pyroclastic currents and debris flows, owe much of their runout and hazard behavior to the occurrence and time‐variant decay of a flow‐internal fluid pore pressure. However, modeling the effects of fluid pore pressure to forecast hazards is challenging because a unified method in Earth Sciences to quantitatively determine the permeability of these natural mixtures is currently missing. Here we combine experiments on fluidization and defluidization of pyroclastic materials, eolian sediments, and glass beads mixtures with numerical multiphase simulations to compare previous attempts to compute the permeability of complex natural particle‐fluid mixtures. In analogy to particle‐engineering studies on simple gas‐particle mixtures, we demonstrate that the effective length‐scale in the characterization of the fluid‐particle interaction of complex natural mixtures is the product of the Sauter mean diameter and the particle sphericity. Its use in the Kozeny‐Carman equation allows accurate prediction of mixture permeability, and we suggest the routine calculation of the Sauter mean from grain size distributions of the deposits of geophysical mass flows in Earth Sciences. We also show, through defluidization experiments, that the duration of gas retention in natural mixtures is well described when using the Sauter mean as the effective particle size. Further, we show through multiphase simulations that initial bed expansion extends the pore pressure diffusion timescale up to nine times. These results can be applied to small‐to‐large volume dense pyroclastic currents where the ranges of Sauter mean diameter predict gas retention for long duration and to debris flows and snow avalanches.
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Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding
We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in d = 3 dimensions and, thus, obtain an estimate of the random close packing volume fraction, ϕRCP, as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributions. For binary systems, we show agreement between our predictions and simulations using both our own results and results reported in previous studies, as well as agreement with recent experiments from the literature. We then apply our approach to systems with continuous polydispersity using three different particle size distributions, namely, the log-normal, Gamma, and truncated power-law distributions. In all cases, we observe agreement between our theoretical findings and numerical results up to rather large polydispersities for all particle size distributions when using as reference our own simulations and results from the literature. In particular, we find ϕRCP to increase monotonically with the relative standard deviation, sσ, of the distribution and to saturate at a value that always remains below 1. A perturbative expansion yields a closed-form expression for ϕRCP that quantitatively captures a distribution-independent regime for sσ < 0.5. Beyond that regime, we show that the gradual loss in agreement is tied to the growth of the skewness of size distributions.
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- Award ID(s):
- 2226387
- PAR ID:
- 10440212
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 158
- Issue:
- 4
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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