Polishing lead crystal glass
Problem raised by the University of
Oxford
Exposition of the problem:
Cut lead crystal glass is polished by immersion in a bath of sulphuric acid and
hydrofluoric acid. The cut creates roughness at a ten micron scale, and this
roughness is gradually removed by successive dipping. The acids react with the
glass to remove its two main constituents, lead oxide and silica, and the
problem for the modelling week is to describe the reaction process, and
describe how this leads to a smoothing of the surface. Of concern in the
glass manufacturing industry are the questions of why the process works, and
how one might achieve optimality in the polishing process.
Scheme of the work to be done:
1) Build a model of the reaction process.
2) Non-dimensionalise and simplify the model.
3) Describe how the model induces smoothing of the surface.
4) Solve the model numerically.