The results demonstrate the trade off between \(\phi_{m}\) and \(\xi_{\text{ref}}\) in that they both have the tendency to increase the
stiffness of the crystal column when raised. For instance, for a given
compaction length (and set of \(\phi_{m}\) and \(\xi_{\text{ref}}\))
that replicates the observed data well, to maintain a solution that
satisfies the experiments reasonably well after reducing \(\phi_{m}\), \(\xi_{\text{ref}}\) must increase. The inverse is true if \(\phi_{m}\)is raised. Fig. 3 also demonstrates that the inverted
rheological parameters are better constrained for more compacted samples
(height of crystal column is O(\(\delta_{c}\))), but that a wide variety
of parameters replicate the observed data well for less compacted
samples (Fig. 3b ). Finally, the results show how the compaction
length determines the curvature of the final melt fraction profile and
that the compaction length is in general large (> compacted
domain) for the case of the centrifuge experiments.