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.