The boundary integral equation for curved solid/liquid interfaces propagating into a binary liquid with convection
- 11 January 2022
- journal article
- research article
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 55 (5), 055701
- https://doi.org/10.1088/1751-8121/ac463e
Abstract
The boundary integral method is developed for unsteady solid/liquid interfaces propagating into undercooled binary liquids with convection. A single integrodifferential equation for the interface function is derived using the Green function technique. In the limiting cases, the obtained unsteady convective boundary integral equation transforms into a previously developed theory. This integral is simplified for the steady-state growth in arbitrary curvilinear coordinates when the solid/liquid interface is isothermal (isoconcentration). Finally, we evaluate the boundary integral for a binary melt with a forced flow and analyze how the melt undercooling depends on Peclet and Reynolds numbers.Keywords
Funding Information
- Russian Science Foundation (21-71-00044)
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