Light scattering by radially inhomogeneous spheres to study droplet evaporation

In the last years, many optical systems, based on the measure of the properties of elastically scattered light, have been developed to determine in non intrusive way the velocity, the size and the optical properties of single droplets inside sprays. The Lorenz-Mie theory, which is strictly valid for homogeneous spheres, is usually used as base of these techniques. However, in real sprays, due to the heating of the droplets, the real part n of the refractive index of the liquid phase changes for the reduction of its density, while the imaginary part k increase if absorbing species are formed inside the droplets. In these cases the Lorenz-Mie theory is not adequate and more sophisticated models to interpret the light scattering by inhomogeneous sphere must be employed. In the present paper a theoretical analysis of the history of a vaporizing droplet via optical measurements will be discussed. The relevant features present in the computed light scattering angular patterns will be outlined. The possibility of inferring by light scattering methods the properties (diameter and temperature) of vaporising droplets will be critically revised. The considerations here drawn in a particular case nevertheless are common to other cases that are not here discussed for shortness.