A mathematical model of the evaporation of a polydisperse ensemble of drops, with allowance for a nonlinear 'diffusion' term in the kinetic equation for the population density distribution function, is developed. The model describes the interaction of a gas phase with vaporizing drops: it has great potential for application in condensed matter physics, thermophysics and engineering devices (e.g. spray drying, cooling, power engineering). The kinetics of heat transfer between phases is theoretically studied. An analytical solution to the integro-differential equations of the process of droplet evaporation is found in a parametric form. Analytical solutions in the presence and absence of the 'diffusion' term are compared. It is shown that the fluctuations in particle evaporation rates ('diffusion' term in the Fokker-Planck equation) play a decisive role in the evolutionary behaviour of a polydisperse ensemble of vaporizing liquid drops. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.
Keywords: distribution function; evaporation; metastable state; particulate assemblage; phase transformation; superheat.