Journal of Fluid Mechanics



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Interfacial conditions between a pure fluid and a porous medium: implications for binary alloy solidification


M. LE BARS a1 and M. GRAE WORSTER a1
a1 Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK

Article author query
le bars m   [Google Scholar] 
worster mg   [Google Scholar] 
 

Abstract

The single-domain Darcy–Brinkman model is applied to some analytically tractable flows through adjacent porous and pure-fluid domains and is compared systematically with the multiple-domain Stokes–Darcy model. In particular, we focus on the interaction between flow and solidification within the mushy layer during binary alloy solidification in a corner flow and on the effects of the chosen mathematical description on the resulting macrosegregation patterns. Large-scale results provided by the multiple-domain formulation depend strongly on the microscopic interfacial conditions. No satisfactory agreement between the single- and multiple-domain approaches is obtained when using previously suggested conditions written directly at the interface between the liquid and the porous medium. Rather, we define a viscous transition zone inside the porous domain, where the Stokes equation still applies, and we impose continuity of pressure and velocities across it. This new condition provides good agreement between the two formulations of solidification problems when there is a continuous variation of porosity across the interface between a partially solidified region (mushy zone) and the melt.

(Published Online February 27 2006)
(Received December 17 2004)
(Revised August 8 2005)



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