Rainbow refractometry applied to radially inhomogeneous spheres: the critical case of evaporating droplets

A detailed study of rainbow thermometry and its application to droplets in reactive systems is presented. To this end the light-scattering history of a vaporizing droplet under unsteady conditions is discussed. Unlike in previous papers, the reduction of the droplet's diameter is also taken into account in addition to the variation of the refractive-index profile. A finely stratified sphere model with thousands of layers (i.e., 20,000) is used to compute the scattering patterns of a radially inhomogeneous evaporating droplet at different heating times and therefore with different diameters and refractive-index profiles. In the studied case the temperatures inferred from rainbow thermometry do not represent the actual temperatures inside the droplet. They do not represent an average internal temperature or even the surface or the core temperature. For droplets with a temperature that increases from the core to the surface, the inferred values are always lower than the minimum temperature inside the droplet. Therefore the rainbow technique should be applied with caution in all cases in which droplet inhomogeneities are suspected. In addition, a careful analysis of the scattering in the rainbow region is presented. Because of the physical structure of the rainbow, a marked uncertainty in the inferred temperatures also has to be considered in the case of homogenous droplets. For inhomogeneous spheres this intrinsic uncertainty has to be added to the effects caused by the internal profiles of the refractive index.