Formation of tube-pumice structure under pure shear: Insights from extension tests of solidifying foam

Tube pumice, the bubbles of which are highly elongated in one direction, is a common product of explosive silicic eruptions, especially caldera-forming eruptions. To understand the conditions necessary to generate tube-like bubbles, we performed extensional experiments on polyurethane foam, which experiences vesiculation, deformation, and solidification at room temperature. The strain and strain rate of pure shear deformation were controlled by the pull length and pull rate of the extension, respectively. The shapes of bubbles in the solidified polyurethane foam were analyzed in three dimensions by X-ray computed tomography. The experimental results demonstrate that strain and capillary number control the degree of bubble deformation. Highly deformed (tube-like) bubbles were found in the experiments with large strain and large capillary number. In each experimental sample, there is scatter in the relation between the degrees of bubble deformation and expected capillary numbers, which we interpret to be the result of the inhomogeneous shear field around individual bubbles and bubble coalescence. Despite the large scatter, the average deformation degree is predicted well by the dynamics of a single bubble, where the viscous stress acting on the bubble surface is taken as the product of bulk strain rate and effective viscosity. Using this approach, the average deformation degree of experimental bubbles in each sample was approximately calculated from the deformation model of a single bubble at least in the range of pure shear strain smaller than 1.5. Small bubbles in the samples extended at low viscosities tend to be less elongated than those calculated from the deformation model, due to shape relaxation. The effect of shape relaxation is quantified by a new dimensionless number, i.e., the quench number, which represents the ratio of the timescale of increasing viscosity and shape relaxation. Our experiment suggests that bubble shapes in highly vesicular pumice can be used to analyze their viscosity and strain rate during the elongation process. An analysis of the published data was presented as a test case.