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). p. 2170.
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.
|Keywords:||Tectonophysics, Lava, Rheology, Morphology, Volcanology, Magma migration.|
|Full text:||(VoR) Version of Record|
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|Publisher Web site:||http://dx.doi.org/10.1029/2002GL015697|
|Publisher 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.|
|Date accepted:||No date available|
|Date deposited:||18 March 2010|
|Date of first online publication:||December 2002|
|Date first made open access:||No date available|
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