Diffusive fractionation of volatiles and their isotopes during bubble growth in magmas

Abstract

Bubbles grow in decompressing magmas by simple expansion and by diffusive supply of volatiles to the bubble/melt interface. The latter phenomenon is of significant geochemical interest because diffusion can fractionate elements and isotopes (or isotopologues) of dissolved components. This raises the possibility that the character of volatile components in bubbles may not reflect that of volatiles dissolved in the host melt over the lifetime of a bubble—even in the absence of equilibrium vapor/melt isotopic fractionation. Recent experiments have confirmed the existence of an isotope mass effect on diffusion of the volatile element Cl in silicate melt [Fortin et al. (Isotopic fractionation of chlorine during chemical diffusion in a dacitic melt and its implications for isotope behavior during bubble growth (abstract), 2016 Fall AGU Meeting, 2016)], so there is a clear need to understand the efficacy of diffusive fractionation during bubble growth. In this study, numerical models of diffusion and mass redistribution during bubble growth were implemented for both “passive” volatiles—those whose concentrations are generally well below saturation levels—and “active” volatiles such as CO2 and H2O, whose elevated concentrations and limited solubilities are the cause of bubble nucleation and growth. Both diffusive and convective bubble-growth scenarios were explored. The magnitude of the isotope mass effect on passive volatiles partitioned into bubbles growing at a constant rate R in a static system depends upon R/DL, Kd and DH/DL (Kd = bubble/melt partition coefficient; DH/DL = diffusivity ratio of the heavy and light isotopes). During convective bubble growth, the presence of a discrete (physical) melt boundary layer against the growing bubble (of width xBL) simplifies outcomes because it leads to the quick onset of steady-state fractionation during growth, the magnitude of which depends mainly upon R∙xBL/DL and DH/DL (bubble/melt fractionation is maximized at R∙xBL/DL ≈0.1). Constant R is unrealistic for most real systems, so other scenarios were explored by including the solubility and EOS of an “active” volatile (e.g., CO2) in the numerical simulations. For plausible decompression paths, R increases exponentially with time—leading, potentially, to larger isotopic fractionation of species partitioned into the growing bubble. For volatile species whose isotope mass effects on diffusion have been measured (Cl, Li), predicted isotope fractionation in the exsolved vapor can be as large as −4‰ for Cl and −25‰ for Li.