Physics
Scientific paper
Dec 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002georl..29x..23l&link_type=abstract
Geophysical Research Letters, Volume 29, Issue 24, pp. 23-1, CiteID 2170, DOI 10.1029/2002GL015697
Physics
10
Tectonophysics: Rheology-General, Volcanology: Lava Rheology And Morphology, Volcanology: Magma Migration
Scientific paper
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.
Llewellin E. W.
Mader Heidy M.
Wilson D. R. S.
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