Modelling the formation of metallic foams

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Modelling the formation of metallic foams
Simon Cox, Wiebke Drenckhan, Denis Weaire and
John Banhart
Department of Physics, Trinity College, Dublin 2,
Ireland (e-mail Simon.Cox_at_tcd.ie) and
Hans-Meitner-Institute Berlin, Glienicker Str.
100, D-14109 Berlin.
We describe the formation of metallic foams with
a powder-metallurgical process1. A foamed
liquid metal, which has been fully expanded in
the liquid state, is simultaneously subjected to
liquid drainage, which leads eventually to
rupture and collapse, and to cooling from the
sides, which solidifies the structure. The
process is therefore governed by a "race against
time" as the drainage acts to destroy the foam
before it can freeze.
The illustration on the right shows the result of
numerical calculations that find the final
profile of relative density. Also shown is the
profile predicted from a theoretical analysis
based upon conservation of energy and matter. The
agreement is encouraging. Drainage occurs at the
top of the foam, so that F decreases slightly
there. At the same time, the freezing front
descends and solidifies the top part of the foam.
A similar process occurs at the bottom of the
sample, this time due to an accumulation of
liquid above the encroaching frozen base. At the
centre of the foam, F shows the equilibrium form
of a normal liquid foam.
Reproduced from Duarte Banhart (2000) Acta
Mater.
The theoretical model allows us to derive a
criterion for obtaining uniform samples of frozen
metal foam, in terms of the physical and material
parameters of the sample
Latent heat (liquid density)2 gravity
sample length initial F ltlt thermal
conductivity melting temperature liquid
viscosity
The image on the left shows a screenshot of the
graphical user interface for the one-dimensional
drainage program. The numerical code is accessed
through this java interface to allow interactive
input of all relevant material properties and
physical parameters (e.g. value of liquid density
etc.) and of the required computational
parameters. The display shows the dynamic
evolution of the liquid fraction F and the
temperature profile in the sample.
We have also modelled the solidification and
drainage process in three-dimensions. For
example, on the right is a cube of metal foam
that has been cooled from all six sides. One
quarter of the cube has been removed to show the
centre of the sample.The distribution of metal in
the final, frozen foam is denoted by false
colour blue/red denotes less/more dense foam.
The simulation shows the transfer of metal from
the top to the bottom of the sample. The amout of
homogeneous (green) foam depends upon the aspect
ratio of the cell increasing the height will
increase the degree of homogeneity, which is
perhaps counter-intuitive. Thus, orientation is
important in the fabrication process a foam will
be more uniform if it has been fabricated with
its long side aligned in the direction of gravity.
References 1 J. Banhart and D. Weaire, Physics
Today, July 2002. 2 S.J. Cox, G. Bradley and D.
Weaire, Euro. J. Phys Appl. Physics 1487
(2001). 3 D. Weaire and S. Hutzler, The
Physics of Foams, Clarendon Press, Oxford (1999).
Acknowledgements This research was supported by
the Prodex programme of ESA, and is a
contribution to ESA contract C14308 / AO-075-99.
SC was supported by a Marie Curie fellowship.