RHEOLOGY AND MICROSTRUCTURE OF MAGMATIC EMULSIONS - THEORY AND EXPERIMENTS

The rheological properties of viscous emulsions composed of melt plus vapor bubbles constitute a critical but largely uninvestigated aspect of magmatic transport phenomena. In this study, the rheological behavior of dilute emulsions of GeO2 containing from 0.8 to 5.5 vol.% air bubbles has been measured experimentally between 1100 and 1175-degrees-C at 100 kPa in a rotating rod rheometer at shear rates between 0.05 and 7 s-1. At constant bubble volume fraction, when the range of shear rates examined is greater than a factor of twenty, the rheological behavior of the emulsions can be modeled by a power-law constitutive relation. The power-law emulsions are pseudoplastic (shear-thinning), having a flow index of 0.87-0.93. A tentative correlation between relative viscosity and bubble volume fraction is given as eta(r) = 1 + 13.1(phi), with eta(r) = eta(e)/eta(m) eta(m) (eta(e) is the emulsion viscosity at constant shear stress and eta(m) is the viscosity of the pure Newtonian melt phase.) The strong variation of relative viscosity with volume fraction of bubbles is placed in the context of current theoretical and experimental understanding of the effects of shear on viscous emulsions, and is attributed to the deformation and eventual disruption of bubbles by shear forces. Bubble deformation is promoted by shear and opposed by surface tension. Two dimensionless parameters governing bubble deformation are the capillary number Ca = gamma-eta(m)(b)r/sigma and viscosity ratio lambda = eta(v)/eta(m) determined from melt viscosity eta(m), vapor viscosity eta(v), bubble radius r(b), shear rate gamma, and vapor-melt interfacial tension-sigma. The capillary number is a measure of the relative importance of shear and interfacial stresses. Low-lambda bubbles may attain very elongate stable shapes, and high shear rates are required before fragmentation occurs at a critical capillary number Ca(crit,f). The number of daughter bubbles formed during disruption is known to depend on Ca/Ca(crit,f) and to rise steeply as this ratio increases from 1 to 20. Bubbles are deformed into prolate ellipsoids with deformation parameter D = (l-b) / (l+b) where l and b represent the long and short axes of the ellipsoidal bubble; for small non-dimensional shear rate (Ca less-than-or-equal-to 0.4), D = Ca. The bubbles undergo transient oscillation with respect to both D and long-axis orientation relative to the shear direction. This may lead to variability of torque during a single experiment even when shear rate is held constant. Bubble fragmentation has consequences for observed bubble size distributions in post-experimental counts as well as in nature. However, bubble fragmentation by the fracture mechanism is unlikely (or at least, not dominant) in most natural magmatic flows. Instead a sub-critical instability known as tip-streaming can occur at a much lower capillary number, Ca(crit,)ts = 0.56. This mechanism produces much smaller daughter bubbles than that of fracture, but is much more relevant to magmatic flows which are characterized by capillary number between 0 and 100. The deformation of bubbles produces viscoelastic behavior in viscous emulsions. Normal stress differences amounting to several per cent of the total shear stress can be produced at shear rates of less than 10s-1. In rotating rod rheometry, this leads to rod-climbing behavior (Weissenberg effect) which permits the measurement of the normal stress differences by climbing rod viscometry. A preliminary assessment of the first normal stress difference (defined N1 = tau(theta-theta)-tau(rr) is made in one of our experiments, and is estimated to be about 2% of the total shear stress. Inferences drawn regarding the viscosity and discharge of lava flows may be misleading if allowance is not made for the effects of vapor bubbles on magma rheology.