Determining flow type, shear rate and shear stress in magmas from bubble shapes and orientations

We interpret the shear environments that produced bubble textures in obsidian samples using the results of theoretical, numerical and experimental studies on the deformation of bubbles in shear flows. In particular, we use the shapes and orientations of bubbles (vesicles) in obsidian to estimate shear rates and shear stresses, and assess flow type (simple vs. pure shear). This technique can be used to determine shear rates in volcanic conduits, the origin of pyroclastic obsidian, and the emplacement history and dynamics of obsidian flows. A spherical bubble in a viscous fluid subjected to a low Reynolds number, steady flow field deforms until it reaches a steady shape and orientation. Bubble deformation is governed by the competing stresses from shearing that deforms, and surface tension that rerounds. The ratio of these stresses is the capillary number, Ca. Because the relationships among Ca, bubble orientation and shape differ for pure and simple shear, we can distinguish between these flow types using preserved bubble geometries. Furthermore, because Ca is a function of shear rate, we can use relationships between Ca and the magnitude of deformation to calculate shear rates when melt viscosity and surface tension are known. To demonstrate the potential of the technique, we examine three obsidian samples chosen for diversity of origin and texture. Two of the samples have low crystallinities and banding defined by layers of different vesicularity. Bubble geometries in a spatter-fed obsidian flow sample record deformation by pure shear, whereas a juvenile obsidian clast from a pyroclastic fall deposit records predominantly simple shear. A third sample from an obsidian flow has banding marked by variable concentrations of microlites, and shows bubble deformation most consistent with dominantly simple shear and some bubble relaxation. The highest shear rate and shear stress are recorded by the pyroclastic obsidian (shear rate=0.01 s−1, shear stress=60 kPa). The spatter-fed obsidian flow sample deformed by pure shear records the lowest shear stress (4.9 kPa). The obsidian flow sample, deformed by simple shear, records the lowest shear rates (10−6.6–10−6.9 s−1) despite high shear stresses (22–36 kPa) because of the high viscosity of the degassed rhyolite (0.13 wt% water).