A free-convection boundary-layer model for the centrifugal etching of an axisymmetric cavity (Q1287081)

The author considers the etching of an axisymmetric cavity under the influence of artificial acceleration field generated inside a centrifuge. From a fluid-mechanical point of view, the centrifugal etching involves a free-convection boundary layer and a moving boundary. This combination has not been studied extensively in the literature before. Here the basic boundary layer equations are continuity, momentum and concentration equations written in the \((s,n)\) coordinates, where \(s\) is the arc length along the cavity wall in an azimuthal plane with \(s=0\) denoting the apex of the cavity, and \(n\) denotes the distance from the wall as measured inwards the normal direction. These equations endowed with appropriate boundary conditions are first transformed into a non-dimensional form, and then are solved numerically as ordinary differential equations. The author shows that the moving-boundary equations admit a family of similarity solutions. A good qualitative agreement is found between the author's similarity results and earlier fully numerical results reported in the literature.