  We propose a theoretical approach to describe quantitatively the heating
process in aqueous solutions of dispersed TiN nanoparticles under solar
illumination. The temperature gradients of solution with different
concentrations of TiN nanoparticles are calculated when confinement effects of
the container on the solar absorption are taken into account. We find that the
average penetration of solar radiation into the solution is significantly
reduced with increasing the nanoparticle concentration. At high concentrations,
our numerical results show that photons are localized near the surface of the
solution. Moreover, the heat energy balance equation at the vapor-liquid
interface is used to describe the solar steam generation. The theoretical time
dependence of temperature rise and vaporization weight losses is consistent
with experiments. Our calculations give strong evidence that the substantially
localized heating near the vapor-liquid interface is the main reason for the
more efficient steam generation process by floating plasmonic membranes when
compared to randomly dispersed nanoparticles. The validated theoretical model
suggests that our approach can be applied towards new predictions and other
experimental data descriptions.
