The response of Li levels to the power interruption of an inductively coupled plasma (ICP) has been simulated by using a time dependent collisional radiative model of the Li system. To take the transport processes into account, a model for the inner channel (IC) was developed. It describes the temperature, the velocity and the evaporation of the droplets in the IC in relation to the conductive heat transport from the skin towards the IC. The same transport module provides the increase of the analyte density along the central axis as created by the evaporation of droplets. The results of the simulation show a good agreement with those of experiments and it turns out that the power interruption technique applied to the analyte emission is very useful to get insight in transport phenomena in the IC.