Abstract:
The rheology of bubble-bearing magmas is investigated through a series of
three-dimensional boundary integral calculations in which the
effects of bubble deformation,
volume fraction, and strain rate are considered.
The behaviour of bubbles in
viscous flows is characterized by the capillary number, Ca,
the ratio of viscous
stresses that promote deformation to
surface tension stresses that resist deformation.
Estimates of Ca in natural flows are highly variable, reflecting
variations in strain rate and melt viscosity. In the low capillary number
limit (e.g., in carbonatite flows) bubbles remain spherical and may
contribute greater stress to the suspension than in high capillary number
flows, in which bubble deformation is significant.
At higher capillary numbers,
deformed bubbles become aligned in the direction of flow, and as a result,
contribute less stress to the suspension.
Calculations indicate that the effective 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.
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
viscosity of the suspension may be less than that of the liquid phase.
Results of this study may help explain previous experimental, theoretical,
and field based
observations regarding the effects of bubbles on flow rheology.