6.2 Hydrodynamic and particle-particle interface contributions to
the effective matrix viscosity
The empirically-found closed form expression used for the effective
matrix viscosity for repacking follows Boyer et al. (2011). At
constant volume fraction of solids (or alternatively, constant melt
fraction), shear and normal stresses scale viscously with macroscopic
strain rate (Boyer et al. , 2011). The dependence of shear and
normal viscosity on melt fraction is included in eq. (14) and (15). Eq.
(14) includes a friction coefficient, \(\mu_{\text{friction}}\), taken
to be 0.3 (Boyer et al. , 2011), while both eq. (14) and (15)
depend on the maximum packing, \(\phi_{m}\), and are scaled by a
reference viscosity, \(\xi_{\text{ref}}\), in eq. (16). The effective
matrix viscosity, eq. (16), is the sum of the viscous resistance
provided by introducing rigid, non-touching particles into a deforming
fluid (hydrodynamic contribution) and that due to touching particles
sharing a common interface and dissipating energy by rubbing against one
another (friction). Using the most likely solution from the MCMC
inversions, we calculate the relative contribution of particle-particle
dissipation (includes friction) in the loading curves for the
experiments of Hoyos et al. (2022). This quantity is calculated
as the relative contribution of eq. (15) and the third term in eq. (14)
to the total expression of eq. (16). The relative contribution of
particle-particle dissipation for EXP009, for example, is shown inFig. 8 . Fig. 8 demonstrates that the relative
contribution of particle-particle dissipation is large compared to
hydrodynamic contribution (the relative contribution of the first two
terms of eq. (14) to the total expression of eq. (16)). This observation
suggests that while at large melt fractions the rheology of magmas may
be controlled by hydrodynamic contributions, at intermediate melt
fractions the contribution of particle-particle dissipation caused by
friction to the matrix rheology is considerable and should be included
in regimes where repacking is relevant (i.e., at intermediate melt
fractions above the maximum close packing where relative motion between
particles isn’t entirely restricted).