Journal of Mathematics in Industry (2011) 1:1 DOI RESEARCH Open Access Acid polishing of lead glass Jonathan A Ward · Andrew C Fowler · Stephen BG O’Brien Received: 11 November 2010 / Accepted: 3 June 2011 / Published online: 3 June 2011 © 2011 Ward et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License Abstract Purpose: The polishing of cut lead glass crystal is effected through the dowsing of the glass in a mixture of two separate acids, which between them etch the surface and as a result cause it to be. | Journal of Mathematics in Industry 2011 1 1 DOI 2190-5983-1-1 Journal of Mathematics in Industry a SpringerOpen Journal RESEARCH Open Access Acid polishing of lead glass Jonathan A Ward Andrew C Fowler Stephen BG O Brien Received 11 November 2010 Accepted 3 June 2011 Published online 3 June 2011 2011 Ward et al. licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License Abstract Purpose The polishing of cut lead glass crystal is effected through the dowsing of the glass in a mixture of two separate acids which between them etch the surface and as a result cause it to be become smooth. In order to characterise the resultant polishing the rate of surface etching must be known but when this involves multicomponent surface reactions it becomes unclear what this rate actually is. Methods We develop a differential equation based discrete model to determine the effective etching rate by means of an atomic scale model of the etching process. Results We calculate the etching rate numerically and provide an approximate asymptotic estimate. Conclusions The natural extension of this work would be to develop a continuum advection-diffusion model. Keywords Etching rate multi-component crystal glass mathematical model ordinary differential equation asymptotics numerics Laplace transform 1 Introduction Wet chemical etching or chemical milling is a technique which allows the removal of material from a substrate via chemical reaction. In many applications selective attack by the chemical etchant on different areas of the substrate is controlled by removable layers of masking material or by partial immersion in the etchant. Etching is used in JA Ward AC Fowler SBG O Brien ỊSI MACSI Department of Mathematics and Statistics University of Limerick Limerick Ireland e-mail JA Ward e-mail AC Fowler e-mail 0 Springer Page 2of19 Ward et al. a wide variety of .
