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 ).