6.3 Transitions from mechanical repacking to grain-boundary diffusion-controlled creep regimes
From the parameters tabulated in table 3 and 4 , the effective matrix viscosity (eq. (16)) as a function of melt fraction are calculated and plotted in Fig. 12 . An important observation of the MCMC results is that the viscosities calculated by fitting the numerical model to the data of Hoyos et al. (2022) show reasonable agreement (within approximately one order of magnitude) with those obtained by analyzing the centrifuge data with the compaction model (Fig. 12 ).
Also included in Fig. 12 are the effective matrix viscosities inferred from experiments of C423 and C372 (data points) of Renneret al. (2003) and an optimization of an alternate expression for the effective matrix viscosity to those experiments:
\begin{equation} \left(20\right)\ \xi_{\text{GBD}}=\ 3\eta_{s}\left(1-\sqrt{\frac{\phi}{\phi_{\text{dis}}}}\right)^{2}.\nonumber \\ \end{equation}
Here, \(\eta_{s}\) is the matrix shear viscosity at \(\phi=0\) and\(\phi_{\text{dis}}\) is the melt fraction at which the crystal matrix disaggregates. Eq. (20) assumes that matrix deformation is accommodated by GBD. To satisfy the break in slope observed in the viscosities measured in Renner et al. (2003), the disaggregation melt fraction needs to be set to ca. 0.36. This value is not consistent with the centrifuge experiments which suggest it is ca. 0.58 (Connolly & Schmidt, 2022). Furthermore, we note that the effective viscosity inferred by analysis of the centrifuge experiments (intermediate melt fractions) is several orders of magnitude lower than that measured in Renner et al. (2003) (low melt fractions) (Fig. 12 ).