Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-13T01:41:07.725Z Has data issue: false hasContentIssue false
  • English
  • Français

Melting of a sphere in hot fluid

Published online by Cambridge University Press:  26 April 2006

Paul Mcleod ,
David S. Riley  and
R. Stephen. J. Sparks
Paul Mcleod
Affiliation:
Department of Geology, University of Bristol, Wills Memorial Building, Queen's Road, Bristol, BS8 1RJ, UK
David S. Riley
Affiliation:
Department of Theoretical Mechanics, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
R. Stephen. J. Sparks
Affiliation:
Department of Geology, University of Bristol, Wills Memorial Building, Queen's Road, Bristol, BS8 1RJ, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

Solid bodies immersed in hot fluids may melt. The molten material produced can then mix with, and be assimilated into, the fluid influencing its compositional and thermal states. Compositional convection of melt and thermal convection of cooled fluid around the solid determine the heat flux from the fluid to the solid's surface. This, together with the thermal properties of the solid, controls the rate of melting. Experiments on melting wax spheres into water are described; these have shown how variations in the nature of melt flow round the sphere cause differing melting rates and hence the development of a distinctive melting morphology. Melting rates are calculated by a simple theoretical analysis which estimates melt layer thickness and the heat flux from the fluid. Melting rate predictions agree well with the experimental data. A geological application occurs when magma incorporates blocks of its surrounding wall rock. Relatively rapid melting rates are estimated, typically in the order of a half metre per day. Such fast rates indicate that this method of contamination may be an important influence on magmatic evolution in continental environments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 327 , 25 November 1996 , pp. 393 - 409
Copyright
© 1996 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Campbell, I. H. & Turner, J. S. 1987 A laboratory investigation of assimilation at the top of a basaltic magma chamber. J. Geol. 95, 155–172.Google Scholar
Fang, D. & Hellawell, A. 1988 The surface morphology of crystals melting under solutions of different densities. J. Cryst. Growth 92, 364–370.Google Scholar
Furlong, K. P. & Myers, J. D. 1985 Thermal-mechanical modelling of the role of thermal stresses and stoping in magma contamination. J. Volc. Geotherm. Res. 24, 179–191.Google Scholar
Hildreth, W. & Moorbath, S. 1988 Crustal contributions to arc magmatism in the Andes of Central Chile. Contrib. Min. Petrol. 98, 455–489.Google Scholar
Huppert, H. E. & Sparks, R. S. J. 1988a Melting the roof of a chamber containing a hot turbulently convecting fluid. J. Fluid Mech. 188, 107–131.Google Scholar
Huppert, H. E. & Sparks, R. S. J. 1988b The generation of granitic magmas by intrusion of basalt into continental crust. J. Petrol. 29, 599–624.Google Scholar
Huppert, H. E. & Sparks, R. S. J. 1988c The fluid dynamics of crystal melting by injection of basaltic sills. Phil. Trans. R. Soc. Edinburgh: Earth Sci. 79, 237–243.Google Scholar
Jafarpur, K. & Yovanovich, M. M. 1992 Laminar free convective heat transfer from isothermal spheres: a new analytical method. Intl. J. Heat Mass Transfer. 35, 2195–2201.Google Scholar
Kerr, R. C. 1994a Melting driven by vigorous compositional convection. J. Fluid Mech. 280, 255–285.Google Scholar
Kerr, R. C. 1994b Dissolving driven by vigorous compositional convection. J. Fluid Mech. 280, 287–302.Google Scholar
Kerr, R. C. & Lister, J. R. 1992 Further results for convection driven by the differential sedimentation of particles. J. Fluid Mech. 243, 227–245.Google Scholar
Kranse, A. A. & Schenk, J. 1965 Thermal free convection from a solid sphere. App. Sci. Res. A 15, 397–403.Google Scholar
Lister, J. R. & Kerr, R. C. 1987 The effect of geometry on the gravitational instability of a buoyant region of viscous fluid. J. Fluid Mech. 202, 577–594.Google Scholar
Martin, D. & Campbell, I. H. 1988 Laboratory modelling of convection in magma chambers: crystallisation against sloping floors. J. Geophys. Res. 93, 7974–7988.Google Scholar
Ryan, M. P. 1987 Neutral buoyancy and the mechanical evolution of magmatic systems. In Magmatic Processes: Physiochemical Principles (ed. B. O. Mysen). Geochem. Soc. Spec. Publ., vol. 1, pp. 259–287.
Schenk, J. & Schenkels, F. A. M. 1968 Thermal free convection from an ice sphere in water. Appl. Sci. Res. 19, 465–476.Google Scholar