The constitutive equation and flow dynamics of bubbly magmas

Llewellin, E.W.; Mader, H.M.; Wilson, S.D.R.

doi:10.1029/2002gl015697

The constitutive equation and flow dynamics of bubbly magmas

Llewellin, E.W.; Mader, H.M.; Wilson, S.D.R.

Authors

Professor Edward Llewellin ed.llewellin@durham.ac.uk
Professor

H.M. Mader

S.D.R. Wilson

Abstract

A generalized constitutive equation for bubbly liquids is presented which successfully reproduces the expected viscosity response for both steady flows with varying capillary number Ca (a measure of the bubble deformation) and unsteady flows with varying dynamic capillary number Cd (a measure of the steadiness of the flow) previously given in separate studies. The constitutive equation is given in terms of observable material and flow parameters and is valid at least up to Ca ∼ O(1000) and Cd ∼ O(10). Analytical solutions are presented for steady, simple-shearing flow (Ca variable) and oscillatory flow with small total-strains (Cd variable). The special case of steady flow in a circular pipe—analogous to magma flow in a volcanic conduit—is investigated. Velocity profiles across the conduit are found to be parabolic or plug-flow depending on a dimensionless number, the conduit capillary number Cc. Plug flow is predicted for Cc ≈ 4 which is in the mid-range for volcanic-eruption conditions.

Citation

Llewellin, E., Mader, H., & Wilson, S. (2002). The constitutive equation and flow dynamics of bubbly magmas. Geophysical Research Letters, 29(24), https://doi.org/10.1029/2002gl015697

Journal Article Type	Article
Publication Date	2002-12
Deposit Date	Oct 6, 2008
Publicly Available Date	Mar 18, 2010
Journal	Geophysical Research Letters
Print ISSN	0094-8276
Publisher	Wiley
Peer Reviewed	Peer Reviewed
Volume	29
Issue	24
DOI	https://doi.org/10.1029/2002gl015697
Keywords	Tectonophysics, Lava, Rheology, Morphology, Volcanology, Magma migration.

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Copyright Statement
© 2002 American Geophysical Union.
Llewellin, E. W. and Mader, H. M. and Wilson, S. D. R., (2002), 'The constitutive equation and flow dynamics of bubbly magmas.', Geophysical research letters., 29 (24), Article 2170, 10.1029/2002GL015697 (DOI). To view the published open abstract, go to http://dx.doi.org and enter the DOI.