Viscosity of magmas containing highly deformable bubbles

The shear viscosity of a suspension of deformable bubbles dispersed within a Newtonian fluid is calculated as a function of the shear rate and strain. The relative importance of bubble deformation in the suspension is charact erized by the capillary number (Ca), which represents the ratio of viscous and surface tension stresses. For,mall Ca, bubbles remain nearly spherical, and for sufficiently large strains the viscosity of suspension is greater than that of the suspending fluid, i.e. the relative viscosity is greater t han 1. If Ca > O(1) the relative viscosity is less than one. In the limit t hat Ca --> infinity (surface tension is dynamically negligible), numerical calculations for a suspension of spherical bubbles agree well with the expe rimental measurements of Lejeune et al. (1999, Rheology of bubble-bearing m agmas. Earth Planet. Sci. Lett., vol. 166, pp. 71-84). In general, bubbles have a modest effect on the relative viscosity, with viscosity changing by less: than a factor of about 3 for volume fractions up to 50%. (C) 2001 Els evier Science B.V. All rights reserved.