Rheology of bubble-bearing magmas

The rheology of bubble-bearing suspensions is investigated through a series of three-dimensional boundary integral calculations in which the effects of bubble deformation, volume fraction, and shear rate are considered. The behaviour of bubbles in viscous flows is characterized by the capillary number, Ca, the ratio of viscous shear stresses that promote deformation to surface tension stresses that resist bubble deformation. Estimates of Ca in natural lava flows are highly variable, reflecting variations in shear rate and melt viscosity. In the low capillary number limit (e.g., in carbonatite flows) bubbles remain spherical and may contribute greater shear stress to the suspension than in high capillary number flows, in which bubble deformation is significant. At higher Ca, deformed bubbles become aligned in the direction of flow, and as a result, contribute less shear stress to the suspension. Calculations indicate that the effective shear viscosity of bubbly suspensions, at least for Ca<0.5, is a weakly increasing function of volume fraction and that suspensions of bubbles are shear thinning. Field observations and qualitative arguments, however, suggest that for sufficiently large Ca (Ca greater than about 1) the effective shear viscosity may be less than that of the suspending liquid. Bubbles reach their quasi-steady deformed shapes after strains of order one; for shorter times, the continuous deformation of the bubbles results in continual changes of rheological properties. In particular, for small strains, the effective shear viscosity of the suspension may be less than that of the liquid phase, even for small Ca. Results of this study may help explain previous experimental, theoretical, and field based observations regarding the effects of bubbles on flow rheology.