Some theoretical considerations in modeling laser-induced incandescence at low-pressures

Laser-induced incandescence (LII) of nanoparticles at low pressures has received some attention in recent years as a particle sizing technique or a technique for inferring the mean value of the absorption function of the particle material. In this paper, we are concerned with some fundamental issues in the theory of LII with particular attention paid to those encountered at very low pressures. The commonly adopted Rayleigh approximation for particle laser energy absorption and subsequent thermal emission is critically evaluated against the Mie solution in the range of size parameter relevant to LII. The Rayleigh approximation can cause significant error in particle laser energy absorption rate, especially when shorter wavelengths are used, and potentially in the particle temperature inferred from the two-color LII. We also demonstrate that claims that low-pressure LII can be used for particle sizing are flawed, due to the use of an incorrect expression for radiation heat loss rate from the particles in this regime, and unjustified neglect of particle sublimation heat loss. Using the currently best available carbon sublimation rate expression and physical parameters, the relative importance of heat conduction, thermal radiation, and sublimation heat loss from an isolated carbon particle was investigated for different ambient pressures, particle temperatures and particle diameters. To ensure particle radiation heat loss is dominant over conduction and sublimation the ambient pressure and the particle temperature should be kept respectively lower than 10^-4 atm and below about 2800 K. Under these conditions the effective temperature of a particle ensemble containing non-aggregated polydisperse primary particles to the power of -4 is proportional to the mean value of the particle absorption function, provided the particles are in the Rayleigh regime in the near infrared. The effect of aggregation on particle absorption and emission is briefly discussed. PACS 44.10.+i; 44.40.+a; 61.46Df