TY - JOUR

T1 - Free-convection-assisted shape-preserving dissolution or etching of a rotationally symmetric body

AU - Kuiken, H.K.

PY - 2000

Y1 - 2000

N2 - A rotationally symmetric body which is totally immersed in a liquid that contains reactants which dissolve the solid is considered. The body is in a vertical position, which means that the heavier liquid close to the body moves downwards under the action of the force of gravity. This free-convective motion creates a concentration field around the body, with the concentration gradient at the surface being proportional to the speed of dissolution or etch rate. A special body shape is sought for which the dissolution process results in a succession of body shapes which are all the same, that is, the etching process is shape-preserving. It turns out that a fully analytical solution describing the body shape can be obtained. The speed at which the body moves downwards as a result of etching is proportional to -1/4, where is the radius of curvature at the body apex. This analytical solution is ideally suited as a benchmark against which numerical codes can be tested.

AB - A rotationally symmetric body which is totally immersed in a liquid that contains reactants which dissolve the solid is considered. The body is in a vertical position, which means that the heavier liquid close to the body moves downwards under the action of the force of gravity. This free-convective motion creates a concentration field around the body, with the concentration gradient at the surface being proportional to the speed of dissolution or etch rate. A special body shape is sought for which the dissolution process results in a succession of body shapes which are all the same, that is, the etching process is shape-preserving. It turns out that a fully analytical solution describing the body shape can be obtained. The speed at which the body moves downwards as a result of etching is proportional to -1/4, where is the radius of curvature at the body apex. This analytical solution is ideally suited as a benchmark against which numerical codes can be tested.

U2 - 10.1093/qjmam/53.2.253

DO - 10.1093/qjmam/53.2.253

M3 - Article

SN - 0033-5614

VL - 53

SP - 253

EP - 261

JO - The Quarterly Journal of Mechanics and Applied Mathematics

JF - The Quarterly Journal of Mechanics and Applied Mathematics

IS - 2

ER -