A new simple model for the puffing/micro-explosion of water-fuel emulsion droplets is suggested. The model is based on the assumption that a spherical water sub-droplet is located in the centre of a larger fuel droplet. The fuel is approximated by n-dodecane. The fuel droplet surface temperature is assumed to be fixed, and fuel evaporation is ignored. The heat conduction equation is solved inside this composite droplet with the Dirichlet boundary condition at the surface of the fuel droplet. The time instant when the temperature at the interface between water and fuel reaches the boiling temperature of water is associated with the start of the puffing process leading to micro-explosion. This time is referred to as the time to puffing, or micro-explosion delay time. When the fuel surface temperature is equal to the boiling temperature of fuel then this time is expected to be the shortest of the possible times. The predictions of the model are shown to be in agreement with available experimental data. The model predicts an increase in this time with increase in the fuel droplet size for fixed water and fuel mass fractions, in agreement with observations. © 2018 The Authors