We posit that for melt fractions > ca. 0.3, repacking
contributes significantly to the ability of the crystal columns to
resist compaction. At high melt fractions, hydrodynamic interactions
dominate and crystal-melt separation is accomodated by hindered
settling. As melt fraction decreases, contiguity increases and
eventually particle-particle interactions dominate and grain
rearrangements are important (repacking dominated) (Fig. 12 ).
Eventually, as melt fraction continues to decrease, the effective matrix
viscosity increases rapidly as the maximum packing fraction is
approached and particles no longer have any degrees of freedom for
rotation and translation (Fig. 12 ). At low melt fractions
(<0.3), column shortening is likely limited by GBD, or if
conditions allow, some other creep mechanism. This is consistent with
the results of Renner et al. (2003), who found their experiments
to have a stress exponent of 1, indicating compaction in the experiments
was accommodated by grain boundary diffusion-controlled creep. The
rheological laws for this regime approximate grains for a variety of
geometries and assume fixed center of masses (Arzt, 1982, Rudge, 2018,
Takei & Holtzman, 2009). These models therefore do not account for the
effects of grain rearrangements and are likely only appropriate when the
melt fraction is lower than the maximum packing fraction. A transition
from GBD to repacking is likely controlling the abrupt decrease in
effective compaction viscosity at melt fractions of ca. 0.3 measure in
Renner et al. (2003) (Fig. 12 ) and would avoid the issue of an
inferred disaggregation melt fraction that is inconsistent with the
centrifuge experiments.
To illustrate this point, we consider a composite GBD and repacking
rheology. We use the experimental dataset C423 of Renner et al. (2003)
which records a rapid increase in inferred viscosities as a function of
decreasing melt fraction between melt fractions of 0.25-0.3. We use the
results from the previous section to parameterize the composite rheology
to model the experimental compaction rates (Fig. 13a ). The
total strain rate is equivalent to the sum of strain rate for the
repacking (parameters included in table 3 for olivine
centrifuge experiments assuming both \(\xi_{\text{ref}}\) and\(\phi_{m}\) are material parameters) and GBD rheology. The latter is
constrained by a MCMC inversion parameterized with an expression for the
effective matrix viscosity expressed in eq. (20). The optimized
disaggregation melt fraction in this case is a more plausible value of
0.62. The strain rates predicted by the composite rheology and that
measured by experiment C423 of Renner et al. (2003) show good
agreement (Fig. 13a ). Furthermore, Fig. 13billustrates that repacking accommodates the majority of compaction at
melt fractions larger than the maximum packing fraction inferred from
the analysis of the centrifuge experiments, while GBD controls
compaction below at melt fractions below the maximum packing fraction.
While we assume a single value for the maximum packing fraction, a
jamming state can be reached in granular suspensions anywhere from the
random lose packing to the maximum close packing. The exact transition
from repacking accommodated compaction to that accommodated by GBD,
therefore, may also vary within this range (for example, due to the
details in how specimens with different starting melt fractions are
prepared). Despite this, we find the maximum packing fractions obtained
by analyzing the centrifuge experiments are commensurate with the
transition in compaction rate in the Renner et al. (2003)
experiments as well as the minimum trapped melt fractions inferred
geochemically in the cumulates feeding high silica granites discussed by
(Lee & Morton, 2015). This agreement suggests that the longevity of
intrusive systems may limit melt loss at the maximum packing fraction
because further melt loss would exceed the (thermal) lifespan of these
bodies.