Equilibrium, stability and evolution of bubbles in a finite melt volume

Abstract

We consider a simple model of the simultaneous expansion and/or contraction of multiple bubbles, initially having the same size, immersed in a finite melt volume. The bubble growth is due to the presence of a dissolved gas within the melt. The model has multiple equilibria, and we examine the stability of each equilibrium state, via linear stability analysis and numerical experiment. We show that in every case it is the largest bubble size that is stable. Finally, we consider a generalisation of the model which allows a demonstration of the process of Ostwald ripening, where smaller bubbles contract while larger bubbles expand. The model has application to a diverse range of phenomena, including the head on a glass of beer, magma systems and the conversion of coal into coke. References

• H. M. Gonnermann and M. Manga, The fluid mechanics inside a volcano. Annu. Rev. Fluid Mech. 39 (2007) 321--356. doi:10.1146/annurev.fluid.39.050905.110207
• K. Malysa, Wet foams: formation, properties and mechnism of stability. Adv. Colloid Interface Sci. 40 (1992) 37--83. doi:10.1016/0001-8686(92)80071-5
• R. Loison, P. Foch, A. Boyer, Coke: Quality and Production. 2nd Ed. 1989. Butterworths.
• K. Yamada, H Emori, K Nakazawa, Time-evolution of bubble formation in a viscous liquid. Earth Planets Space (2008) 60, 661--679.
• A. A. Proussevitch, D. L. Sahagian, A. T. Anderson, Dynamics of diffusive bubble growth in magmas: Isothermal case. J. Geophys. Res. (1993) 98(B12), 22283--22307. doi:10.1029/93JB02027
• A. A. Proussevitch, D. L. Sahagian, Dynamics and energetics of bubble growth in magmas: analytical formulation and numerical modeling. J. Geophys. Res. (1998) 103(B8), 18223--18251. doi:10.1029/98JB00906
• P. Stevenson, Inter-bubble gas diffusion in liquid foam. Current Opinion in Colloids and Interface Sci. (2010) 15, 374--381. doi:10.1016/j.cocis.2010.05.010
• C. A. Ward, P. Tikuisis, R. D. Venter. Stability of bubbles in a closed volume of liquid-gas solution. J. Appl. Phys. (1982) 53(9), 6076--6084. doi:10.1063/1.331559
• A. van der Net, W. Drenckhan, D. Weaire, S. Hutzler, The crystal structure of bubbles in the wet foam limit. Soft Matter (2006) 2, 129--134. doi:10.1039/b515537a
• A. van der Net, G. W. Delaney, W. Drenckhan, D. Weaire, S. Hutzler, Crystalline arrangements of microbubbles in monodisperse foams. Coll. Surf. A: Physicochem. Eng. Aspects (2007) 309, 117--124. doi:10.1016/j.colsurfa.2006.11.056