Abstract: The present paper develops a simplifiedLiquid-Solid-Gas-Fog (LSGF) model in the solidification of dispersed liquiddroplets on the basis of mean field concept to obtain the uniformly validasymptotic solution of the initial value problem at small supercooling. Theresults show that the whole dynamics process can be divided into two stages,the transient transition stage and the solidification stage. In thetransient stage without phase transition, the initial temperaturedistribution prescribed in the system is quickly to be special spatial. Inthe solidification stage, there is the solid/liquid phase conversion processtill to the vanish of the liquid phase. In addition, the case of the liquidcopper droplets is simulated to obtain the duration and the temperaturedistribution of the solidification under various growth conditions.