title: Do dissolving objects converge to a universal shape?
abstract: Surprisingly, macroscopic objects such as melting ice cubes and growing stalactites approach nonintuitive geometric ideals. Here we investigate the shape of dissolving cylinders in a large volume of water. The cylinders are oriented vertically and consist of amorphous glucose or poly(ethylene glycol). The dissolution causes density differences in the surrounding fluid, which induce gravity-driven convection downward along the object. The resulting concentration gradient shapes the cylinder according to fast dissolution at the tip and slow dissolution at the base. The contour of the object approaches a power law of the form z ∝ R(2), where z is the vertical distance from the tip and R is the corresponding radius. We suggest that this paraboloidal shape is the geometric attractor for the dissolution of noncrystalline objects in the presence of gravity.
authors.affiliation: †Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States.
authors.forename: Elias
authors.initials: E
authors.lastname: Nakouzi
authors.affiliation: ‡DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom.
authors.forename: Raymond E
authors.initials: RE
authors.lastname: Goldstein
authors.affiliation: †Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States.
authors.forename: Oliver
authors.initials: O
authors.lastname: Steinbock