Critical review and experimental validation of radiative transfer models for semitransparent media containing large gas bubbles

Abstract

Many materials manufacturing, photobiochemical, and photoelectrochemical processes involve radiation transfer through foams and bubbly fluids. Controlling and optimizing these processes require accurate predictions of radiation transfer through semitransparent media. Previously developed models treated the heterogeneous media as homogeneous plane-parallel slabs with some effective radiation characteristics while radiation transfer was governed by the one-dimensional radiative transfer equation (RTE). Unfortunately, their accuracy and range of validity remains unclear for lack of comparison with one another or against the same set of experimental data. This study aims to critically review and assess the validity of these models both numerically and experimentally. First, predictions of the transmittance and reflectance of heterogeneous slabs containing large randomly distributed bubbles were compared with those obtained from Monte Carlo ray-tracing (MCRT) method based on geometric optics. A new hybrid model was proposed that predicts the effective scattering coefficient and asymmetry factor using the Lorenz–Mie theory and the effective absorption coefficient as the volume-weighted sum of the bubbles and medium absorption coefficients and solves the RTE using the Monte Carlo method. Its predictions showed excellent agreement with those by the MCRT method for a wide range of bubble volume fractions (0%–30%) as well as slab thicknesses (2–40 mm) and medium absorption coefficients (0.1–100 m−1). Second, microcomputed X-ray tomography scans were performed on a fused silica sample containing bubbles with mean radius of 480 μm to retrieve the exact locations, diameters, and total volume fraction of bubbles. Here also, predictions of the hybrid model using the retrieved data agreed well with experimental measurements of the spectral normal-hemispherical reflectance and transmittance of the sample for wavelengths between 0.4 and 3 μm when silica ranges from weakly absorbing to absorbing.