An approach to geometrical and optical simulation of soap froth
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 first 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 films, 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 reflection and transmission coefficients, also called reflectivity and transmissivity are deduced and simplified in the case of soap films. 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 reflectivity and transmissivity. Finally, the consistency of the results is analysed, studying the effect of a variation of the parameters, and making a comparison with reality. (C) 1999 Elsevier Science Ltd. All rights reserved.