Optical measurement uncertainties due to refractive index mismatch for flow in porous media

Abstract

Application of optical techniques such as PIV, PTV, and LDA for velocity field estimation in porous media requires matching of refractive indices of the liquid phase to that of the solid matrix, including the channel walls. The methods most commonly employed to match the refractive indices have been to maximize the transmitted intensity through the bed or to rely on direct refractometer measurements of the indices of the two phases. Mismatch of refractive indices leads to error in estimation of particle position, e PD, due to refraction at solid–liquid interfaces. Analytical ray tracing applied to a model of solid beads placed randomly along the optical path is used to estimate e PD. The model, after validating against experimental results, is used to generate expression for e PD as a function of refractive index mismatch for a range of bead diameters, bed widths, bed porosity, and optical magnification. The estimate of e PD, which is found to be unbiased, is connected to errors in PIV measurement using the central limit theorem. Mismatch in refractive indices can also lead to reduction in particle density, N s, detected light flux, J, and degrade the particle image. The model, verified through experiments, is used to predict the reduction in N s and J, where it is found that particle defocusing caused by spherical beads in refractive index mismatched porous bed is the primary contributor to reductions of N s and J. In addition, the magnitude of e PD is determined for the use of fluorescent dye emission for particle detection due to wavelength-dependent index of refraction.