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.