5.2 Forward model demonstration of matrix vs. fluid dominated
rheological regimes
The model simulations also demonstrate the existence of two endmember
regimes: one where the rheology of the suspension is dictated by the
properties of the fluid and one that is dictated by the properties of
the matrix. These regimes can be readily understood by considering the
evolution of the load on the suspension, \(\Sigma\), as a function of
time. Eq. (13) demonstrates that the expression for Σ is
the sum of three forces: buoyancy, drag, and compaction. The buoyancy
force remains constant while the drag force scales as the inverse of the
hydraulic conductivity, and hence is proportional to the viscosity of
the fluid, \(\eta_{f}\). The compaction force, on the other hand, is
scaled by the effective matrix viscosity, \(\xi\). In the limit where
the drag term is small compared to the resistance to deform the matrix,
the load, \(\Sigma\), is limited by the compaction of the matrix. In
this rheologically-limited regime (Connolly & Podladchikov, 2000), the
absolute magnitude of \(\eta_{f}\) bears no consequence
on Σ (Fig. 4a ). The converse is true in the limit
where the resistance to deform the matrix (controlled by the effective
matrix viscosity) is negligible compared to the drag force and phase
separation is then limited by the permeable flow of the fluid through
the porous matrix. In this hydraulically limited regime (Connolly &
Podladchikov, 2000), \(\Sigma\) becomes independent of \(\xi\) and
instead solely depends on the segregation velocity, melt fraction,
permeability, and viscosity of the fluid (Fig. 4b). These
endmember regimes are demonstrated experimentally by Renner et
al. (2003) using high T + P compaction experiments on geologic
materials with melts of different viscosities.