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W. G. Pritchard Lab Seminar: 3:30-4:30 PM, 104 McAllister Building
**Monday April 19, 2004**
Dynamics of cooling viscoplastic fluids
Neil Balmforth
Department of Mathematics
Massachusetts Institute of Technology
Abstract:
Many problems in geophysics involve the flow of a non-Newtonian fluid.
Examples include mudslides (clay slurries are one of the most frequently
cited examples of viscoplastic fluids), the spreading of lava (which
acquires a yield stress once it begins to cool and silicates crystallize),
and the movement of ice (according to Glenn's flow law, ice is a shear-
thinning non-Newtonian material). There are also counterparts of these
problems in chemical engineering, where, although the emphasis typically
shifts towards different objectives, the need to understand the fundamental
fluid mechanics remains the same. In this talk I will describe efforts to
model these kinds of fluid flows, beginning with some mathematical analysis
of the governing fluid equations which furnishes a simpler system of
equations to describe the flow dynamics; a ``shallow lava model'' in the
context of volcanology. The simplified model enables a concise exploration
of how viscoplastic fluids spread over inclined planes, and how domes that
cool from their surface expand on a flat surface.
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