A new bubble dynamics model to study bubble growth, deformation, and coalescence

Abstract

We propose a new bubble dynamics model to study the evolution of a suspension of bubbles over a wide range of vesicularity, and that accounts for hydrodynamical interactions between bubbles while they grow, deform under shear flow conditions, and exchange mass by diffusion coarsening. The model is based on a lattice Boltzmann method for free surface flows. As such, it assumes an infinite viscosity contrast between the exsolved volatiles and the melt. Our model allows for coalescence when two bubbles approach each other because of growth or deformation. The parameter (disjoining pressure) that controls the coalescence efficiency, i.e., drainage time for the fluid film between the bubbles, can be set arbitrarily in our calculations. We calibrated this parameter by matching the measured time for the drainage of the melt film across a range of Bond numbers (ratio of buoyancy to surface tension stresses) with laboratory experiments of a bubble rising to a free surface. The model is then used successfully to model Ostwald ripening and bubble deformation under simple shear flow conditions. The results we obtain for the deformation of a single bubble are in excellent agreement with previous experimental and theoretical studies. For a suspension, we observe that the collective effect of bubbles is different depending on the relative magnitude of viscous and interfacial stresses (capillary number). At low capillary number, we find that bubbles deform more readily in a suspension than for the case of a single bubble, whereas the opposite is observed at high capillary number.

Vesiculation in rhyolite at low H2O contents: A thermodynamic model

“…Exsolution of a fluid phase from oversaturated melts involves nucleation and growth of bubbles. The processes of bubble nucleation and growth in silicate melts have been studied from a variety of perspectives, including: high-temperature (T) experimentation [e.g., Hurwitz and Navon, 1994;Bagdassarov et al, 1996;Lyakhovsky et al, 1996;Navon et al, 1998;Gardner et al, 2000;Larsen and Gardner, 2000;Mourtada-Bonnefoi and Laporte, 2004;Gardner and Ketcham, 2011], theoretical modelling [e.g., Sparks, 1978;Toramaru, 1989Toramaru, , 1995Proussevitch and Sahagian, 1998;Blower et al, 2001;Lensky et al, 2004;L'Heureux, 2007;Gonnermann and Gardner, 2013;Huber et al, 2014], and inversion of field-based observations [e.g., Gaonac'h et al, 1996;Mangan and Cashman, 1996;Castro et al, 2005;Giachetti et al, 2010;Watkins et al, 2012]. These studies have elucidated a diversity of competing processes and rates inherent in the vesiculation process.…”

On the link between Earth tides and volcanic degassing

“…Bubbles typically vary in size following a power law (Cashman and Marsh, 1988;Blower et al, 2003) and in shape from spherical to ellipsoidal (Rust et al, 2003;Moitra et al, 2013). While models based on polydisperse bubble size distributions are available (Sahagian and Proussevitch, 1998;Huber et al, 2013;Mancini et al, 2016), a common starting point to analyse the temporal evolution of 25 the bubbles is nevertheless the assumption of a monodisperse size distribution of spherical bubbles (Prousevitch et al, 1993;Lensky et al, 2004).…”

Excitation and resonance of acoustic-gravity waves in a column of stratified, bubbly magma

“…Bubble growth in magma may be diffusively or viscously limited, depending on liquid phase composition, ambient pressure and temperature conditions, and melt viscosity (e.g. Proussevitch, Sahagian & Anderson 1993;Navon, Chekhmir & Lyakhovsky 1998;Huber et al 2014).…”