Computational Analysis of the Effects of Surface Films on the Scattering Properties of Bubbles in Water

摘要

A scattering algorithm for coated spheres was developed using the partial wave series of Aden and Kerker to theoretically determine if surface films on air bubbles in water have a significant effect on optical scattering patterns. The air bubbles were modeled as spheres (of radius a) coated by a film of uniform thickness h and complex refractive index n sub c surrounded by water of refractive index sub vw equal to 4/3. Size parameters of ka (where 2 pi/k equals the optical wavelength in water) equal to 100, 500, 1000, and 2500 (corresponding to radii a approx. = 7.5 micron to 189 micron for lambda sub in air = 632.8 nm) were modeled for values of h ranging from 0 to 3 micron. Irradiance results are plotted as a function of scattering angle theta with emphasis on the critical scattering region. Comparison is made with known results from Mie theory for noncoated spheres as well as a physical-optics approximation developed by Marston and Kingsbury. Some modeling is done in terms of geometric ray optics, in order to explain observed effects. Finally, observations regarding the use of noncoated versus coated bubble results for the sizing and detection of microbubbles in various experimental applications is discussed.