Numerical Simulation of Viscous Sintering
G.A.L. van de Vorst
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A method to produce glass fibres for the telecommunication
industry is heating a porous pure glass to a sufficiently high
temperature so that the glass becomes a highly viscous fluid: the
flow causes densification of the glass. This process is usually
referred to as viscous sintering. The porous pure glass is
produced by the so-called sol-gel technique.
The driving force for the sintering phenomenon is the excess
of free surface energy of the porous glass compared to a same
quantity of a fully dense glass. Ideally, one wants to produce a
dense and homogeneous glass, free from voids and impurities this
way. Therefore, a good theoretical understanding is needed of the
densification kinetics of the porous glass, i.e. the viscous
sintering phenomenon. In particular, one is interested in the
shrinkage rate of the glass as a function of the viscosity and
particle size, which reflects how time, temperature and
microstructure influence the development of the densification
process. Another question is what kind of structural
configuration leads to a higher densification rate.
Mathematically, the sintering is described as a viscous
incompressible Newtonian volume flow. The numerical solution of
this model consists of formulating the problem by a system of
integral equations and solving these by applying a Boundary
Element Method. This yields the surface velocity field at a fixed
time. In order to obtain the motion of the flow domain in time,
an implicit multistep method is used (BDF).
A simple approach of describing the sintering phenomenon is to
consider the behaviour of so-called unit problems only, like the
coalescence of two equal spheres or cylinders, which can be used
to understand the behaviour of macroscopic systems. Recently, a
more sophisticated approach is developed by the determination of
a representative unit cell within the porous glass and to
consider the densification of it. This unit cell has to be chosen
so that it reflects the sintering of the porous glass as a whole
realistically. An example of such a two-dimensional numerical
simulation is shown below.
Reference:
G.A.L. van de Vorst: Modelling and Numerical Simulation of
Viscous Sintering, PhD thesis, Eindhoven University of
Technology, 1994.
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