Acid polishing of lead glass
type: Item
instance of: scholarly article
title: Acid polishing of lead glass
zbMATH Open document ID: 1274.80017
DOI: 10.1186/2190-5983-1-1
author: Jonathan A. Ward
author: A. C. Fowler
author: Stephen B. G. O'Brien
published in: Journal of Mathematics in Industry
publication date: 2013-08-05T00:00:00Z
review text: The authors introduce and discuss a model which accounts for the acid polishing process of lead glass. They consider a molecularly rough surface composed of horizontal layers and submitted to a wet chemical etching process. They introduce the fraction \(\psi _{n}^{j}(t)\) of exposed surface at level \(n\) of species \(j\) and at time \(t\). They prove that the fractions \(\psi _{n}^{j}(t)\) are solutions of the coupled system of ordinary differential equations \( \overset{.}{\psi }_{0}^{j}(t)=-A_{j}\psi _{0}^{j}(t)\), \(\overset{.}{\psi } _{n}^{j}(t)=-A_{j}\psi _{n}^{j}(t)+f_{j}\sum_{k}A_{k}\psi _{n-1}^{k}(t)\), \( n\geq 1\). The initial conditions \(\psi _{0}^{j}(0)=f_{j}\), \(\psi _{n}^{j}(0)=0\), \(n\geq 1\), are added. Here \(f_{j}\) is the fraction of \(j\) molecules. For the resolution of this coupled linear system, the authors use the Laplace transform which leads to an algebraic system whose solution can be expressed in terms of the function \(g(\lambda )=\sum_{k}\frac{ A_{k}f_{k}}{\lambda +A_{k}}\). They then describe some properties of the solution. The paper ends with some considerations on a continuum model, the authors introducing the eigenvectors of the preceding algebraic system and ending with a nonsteady partial differential system.
reviewed by: Alain Brillard
Mathematics Subject Classification ID: 80A32
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 35K40
zbMATH DE Number: 6194779
zbMATH Keywords: crystal glass
zbMATH Keywords: etching rate multi-component
zbMATH Keywords: ordinary differential system
zbMATH Keywords: Laplace transform
zbMATH Keywords: eigenvector
zbMATH Keywords: continuum model
Wikidata QID: Q59255510
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1186/2190-5983-1-1
OpenAlex ID: W2110967954
cites work: Q4856154
cites work: Mathematical modelling of erosion by powder blasting
description: scientific article