Mathematical Modeling of Some Glass Problems
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In studying glass morphology one often uses models, which describe it as a strongly viscous Newtonian fluid. In this chapter we shall study two types of problems encountered in glass technology. One is dealing with so-called sintering, which plays a role in producing high-quality glasses, for example, and the other with producing packing glass by so-called pressing. We give a Stokes model to describe these processes and discuss various aspects of the evolution of both forming problems. The sintering problem is solved by a boundary element method, for which we use an interesting analytical tool to avoid numerical instabilities. The pressing problem actually deals with the morphology of a bottle or jar. Here we focus on simulating the glass flow. We first show how to deal with the temperature separately, by a suitable dimension analysis. Then we consider the flow of the glass in a domain with a partially free and partially moving boundary. We give a number of numerical examples to sustain our result.
KeywordsComplex Flow Contact Radius Excess Free Energy Liquid Glass Contact Conductance
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