A numerical simulation of liquid oxygen droplets igniting in hot gaseous hydrogen during break-up is used to examine effects of Reynolds and Weber numbers on the ignition regime. The simulation is based on a volume of fluid (VOF) description of the liqui-gas, interface. Surface tension and internal liquid motion were taken into account to allow simulations of the droplet breakup and secondary atomization. The VOF technique was also modified to include the droplet vaporization, assuming thermodynamic equilibrium at the interface. Gas-phase combustion was treated in the thermodiffusive approximation. This simulation technique makes it possible to deal with complex geometries, and liquid-gas interface topology. A parametric study for different Weber and Reynolds numbers showed that, if ignition always takes place in premixed areas, the transition to a non-premixed flame around the drop strongly depends on the relative velocity between the two phases. A coupling was found with secondary droplet dispersion and vaporization in the case of breakup. In order to study more precisely the mixture at ignition and burning of the drop, the dependence of temperature and species mass fraction with mixture fraction was examined. The calculation may be used to distinguish premixed and non-premixed combustion during ignition and breakup regimes. Finally, the time evolution of the variance of the mixture fraction was compared with the solution of the corresponding balance equation found in the literature. A good agreement was found between our simulations and the balance equation for the mixture fraction and its variance, justifying standard assumptions made in these equations.