Dresden 2003 – scientific programme
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DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.15: Poster
Thursday, March 27, 2003, 15:30–18:00, P1
Persistent random walk in a honeycomb structure: Light transport in foams — •Holger Stark1 and Mir Faez Miri1,2 — 1Universität Konstanz, Fachbereich Physik, D-78457 Konstanz — 2Institute For Advanced Studies in Basic Sciences, P.O. Box 45195-159, Zanjan, Iran
Milk, a common colloidal dispersion, appears white since incoming light is multiply scattered from fat droplets suspended in water. The theory behind this observation is complicated but becomes simple in the limit of many scattering events where the transport of light is diffusive. Foams also look white. Since they correspond to a random filling of space by cells with an average size much larger than the wavelength of light, we apply geometrical optics to model the light transport. A photon hitting a cell edge is reflected or transmitted with certain probabilities which results in a persistance random walk.
As the simplest model for a 2D foam, we use the honeycomb structure. With regard to the angle of incidence, we identify special cases for which we can analytically demonstrate the diffusive behavior and calculate the diffusion constants although the processes correspond to a twelfth-order Markov chain. We also present numerical simulations for arbitrary angles of incidence. They show a surprising dependence of the diffusion constant on the angle of incidence. In addition, they motivate a further analytically solvable case based on a two-state model.