A Multiscale Model of Partial Melts 2: Numerical Results

TL;DR

This paper numerically investigates the relationships between material properties and porosity in partially molten media, revealing that bulk viscosity is inversely proportional to porosity and predicting the vanishing of the compaction length as porosity decreases.

Contribution

It provides numerical estimates linking microstructural parameters to porosity and integrates these into a hybrid model for partially molten media.

Findings

Bulk viscosity inversely proportional to porosity

Compaction length vanishes with decreasing porosity

Numerical estimates inform the homogenized model

Abstract

In a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that the dependence of these parameters upon the microstructure is not self-evident. In particular, one seeks to relate them to the porosity. In this paper, we numerically solve ensembles of the cell problems from which these quantities emerge. Using this data, we estimate relationships between the parameters and the porosity. In particular, the bulk viscosity appears to be inversely proportional to the porosity. Finally, we synthesize these numerical estimates with the models. Our hybrid numerical--analytical model predicts that the compaction length vanishes with porosity.