An approach to geometrical and optical simulation of soap froth
Article Ecrit par: Icart, Isabelle ; Arques, Didier ;
Résumé: This paper deals with a complete computer simulation of structures that are of great interest to physicists and mathematicians: foams, and, peculiarly, soap froth. We "rst present a minimization algorithm, based on Plateau's rules, which allows to model the geometry of irregular patterns of bubbles. The resulting model accounts for the thickness variation of the films, and their tapering under gravity. It involves non-parallel plane "lms, in the shape of wedges. Then we derive the equations describing the interaction between a plane monochromatic electromagnetic wave and this kind of film. Assuming the material } soap } that constitutes these films is a linear, homogeneous isotropic dielectric medium, the expressions of the intensity reffection and transmission coeficients, also called reflectivity and transmissivity are deduced and simpli"ed in the case of soap "lms. The expressions given for wedge films can be applied more generally to the case of surfaces with gentle slope variations. The optical simulation of the interaction between light waves and soap froth is performed using a ray-tracing algorithm. We show in this paper how this algorithm had to be adapted, in order to integrate these new expressions of re#ectivity and transmissivity. Finally, the consistency of the results is analysed, studying the e!ect of a variation of the parameters, and making a comparison with reality.
Langue:
Anglais