Rheology of subliquidus magmas: 1. Picritic compositions

The relationship between the rheology and phase equilibria of a picritic basalt from Kilauea Iki has been investigated at 1 atm along the QFM buffer. Between 1270° and 1180°C olivine and minor spinel are the only liquidus phases, and the melt volume decreases from 85 to 74 vol %. At the ol-sp-pc-cpx cotectic, melt is consumed more rapidly dropping to 47 vol % at 1139°C. The rheology of the magma is non-Newtonian, is characterized by time-dependent, pseudoplastic behavior, and is consistent with power law flow or Bingham pseudoplastic behavior. Non-Newtonian effects are most apparent when the crystal volume is greater than 25% and the shear rate is increasing. Once stirred, the magma approaches Newtonian rheology with decreasing shear rate. At 1170°C (approximately 25% suspended crystals) the apparent activation energy (calculated at unit shear rate) increases from 123 ± 10 kcal mol−1 to 452 ± 21 kcal mol−1. When the change in liquid composition along the liquidus is included, the observed viscosities are in good agreement with those calculated from the Einstein-Roscoe equation for a serial size distribution of crystals. A quadratic fit to the shear stress-strain rate data yields a nonzero intercept indicative of a finite yield strength. The apparent yield strength increases with decreasing temperature reaching ≈800 Pa at 1149°C. These extrapolated (and model dependent) values are in good agreement with those determined by other methods (Shaw et al., 1968; McBirney and Murase, 1984). The yield strengths can be fit by a power law expression, σ0 = 6500Φ2.85, where σ0 is the yield strength and Φ the crystal volume fraction. This expression recovers the yield strength estimates for other basalts, suggesting that it may be generally applicable to magmas in which the melt is of broadly basaltic composition. The magmas exhibit heating due to viscous dissipation during shearing. However, this effect is not large enough to produce the observed pseudoplasticity. We conclude that the non-Newtonian behavior in these magmas is due to reorientation of solids in the flow field and solid-solid interactions. We develop a model in which the time-dependent pseudoplasticity and yield strengths are produced by the relationship between solid phase contiguity (the fraction of solid internal surface area snared with other solids) and grain dispersive pressure due to shearing. Increased contiguity is related to increased apparent viscosities and yield strengths, while increased grain dispersive pressure due to shearing acts to diminish contiguity.