For a very volatile liquid, a generally used quasi-steady diffusion model often fails in representing accurately an evaporation phenomenon. The substrate thermal diffusivity and the liquid volatility rule this assumption. The present study uses an unsteady diffusion model to analyze the effect of these two parameters. Heat diffusion in solid, liquid and gas phases and mass diffusion in the surrounding air are solved by a finite volume method associated with an ADI scheme. In order to investigate the effects of volatility, water, ethanol and methanol are considered on very thin substrates of aluminum or PTFE. Thicker substrates are then used to analyze the effect of their thermal properties under non-heating and heating conditions. For an unheated substrate, the volatility reduces the droplet lifetime, but has little influence on the unsteady effects. But, the thermal diffusivity of a heated substrate strongly affects the evaporation rate. Unsteady effects are important for a small substrate thermal diffusivity. Their duration can be more than 80% of the drop lifetime for an ethanol droplet on PTFE. Consequently, the quasi-steadiness assumption does not hold in this case, while it remains valid on a heated aluminum substrate. (C) 2015 Elsevier Ltd. All rights reserved.