The Hadamard-Rybczynski equation describes the steady-state buoyant rise velocity of an unconfined spherical bubble in a viscous liquid. This solution has been experimentally validated for the case where the liquid viscosity is held constant. Here, we extend this result for non-isothermal conditions, by developing a solution for bubble position in which we account for the time-dependent liquid viscosity, liquid and gas densities, and bubble radius. We validate this solution using experiments in which spherical bubbles are created in a molten silicate liquid by cutting gas cavities into glass sheets, which are stacked, then heated through the glass transition interval. The bubble-bearing liquid, which has a strongly temperature-dependent viscosity, is subjected to various heating and cooling programs such that the bubble rise velocity varies through the experiment. We find that our predictions match the final observed position of the bubble measured in blocks of cooled glass to within the experimental uncertainty, even after the application of a complex temperature-time pathway. We explore applications of this solution for industrial, artistic, and natural volcanological applied problems.

<p>The material behaviours that underpin artistic work with glass have striking similarities to those of volcanic glasses, silicate melts, and magmas. This similarity presents a compelling opportunity for collaboration between glass artists and volcanologists to better understand silicate melts, and thereby to elucidate volcanic processes.</p><p> </p><p>Using silicate melts as an experimental material is advantageous, because it allows us to investigate coupled thermorheological effects that are not well captured by the more widely used low-temperature magma analogue materials such as syrups and oils. Here we present work focussed on adapting and refining the artistic, kiln-based process of bubble entrapment and the precision manipulation of gas phases in glass. These techniques have previously been used to create glass art pieces involving complex bespoke figures formed from gas trapped within layers of glass. We expand the use of this technique to investigate bubble rise dynamics in soda-lime-silicate glass under non-isothermal conditions; varying temperature to slow or accelerate the bubble rise.</p><p>We present a scaled mathematical model that provides an excellent description of the experimental data even in case of complex changing temperature environments similar to the long, slow annealing stages of glass art production. Scaling analysis is used to show how our experiments using artistic soda-lime-silica glass can be scaled to volcanic environments. This allows a better understanding of bubble motion in magmas under variable temperature conditions, such as those in shallow basaltic lava lakes, flows, or the uppermost parts of magma plumbing systems.</p><p> </p><p>This art-science collaboration used artistic skills and knowledge to validated our model, and tested the limits of the artistic technique: the use of kiln-based heating programs and the glass used by artists. Overall, the advantages of using kiln-based art techniques and skills for volcanology is clear. But we also find that there is a deep mutuality to glass art collaborations, such that the art techniques can be refined via the scientific model development. Ultimately, when working to better understand the behaviours of a complex material such as glass, the approaches of the artist and the scientist are very similar, and our project shows that the presumed disciplinary divide may be less divisive than expected.</p>