The convective Stefan problem: Transitional shapes under natural convection
Abstract
Fluids sculpt many of the shapes we see in the world around us, from melting ice cubes to ``stone forests'' of limestone rock spires. We present a new mathematical model describing the shape evolution of a body that dissolves or melts under gravitationally stable buoyancy-driven convection, driven by thermal or solutal transfer at the solid-fluid interface. For high Schmidt number, the system is reduced to a single integro-differential equation for the shape evolution. Focusing on the case of an initially conic or wedge-shaped body, we derive complete predictions for the underlying self-similar shapes, intrinsic scales and descent rates that apply to bodies that melt or dissolve in a quiescent ambient fluid. The theoretical predictions show excellent agreement with the results of a new series of laboratory experiments.
- Publication:
-
APS Division of Fluid Dynamics Meeting Abstracts
- Pub Date:
- 2020
- Bibcode:
- 2020APS..DFDT01004P