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 o f bubble deformation, volume fraction, and shear rate are considered. The b ehaviour of bubbles in viscous flows is characterized by the capillary numb er, Cn, the ratio of viscous shear stresses that promote deformation to sur face tension stresses that resist bubble deformation. Estimates of Cn in na tural lava flows are highly variable, reflecting variations in shear rate a nd 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 deform ation is significant. At higher Cn, deformed bubbles become aligned in the direction of flow, and as a result, contribute less shear stress to the sus pension. Calculations indicate that the effective shear viscosity of bubbly suspensions, at least for Ca < 0.5, is a weakly increasing function of vol ume fraction and that suspensions of bubbles are shear thinning. Field obse rvations and qualitative arguments, however, suggest that for sufficiently large Ca (Cn greater than about 1) the effective shear viscosity may be les s than that of the suspending liquid. Bubbles reach their quasi-steady defo rmed shapes after strains of order one; for shorter times, the continuous d eformation of the bubbles results in continual changes of rheological prope rties. in particular, fur small strains, the effective shear viscosity of t he 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 rheo logy. (C) 1998 Elsevier Science B.V. All rights reserved.