  We investigate the scenario of homogeneous nucleation for a first order
quark-hadron phase transition in a rapidly expanding background of quark gluon
plasma. Using an improved preexponential factor for homogeneous nucleation
rate, we solve a set of coupled equations to study the hadronization and the
hydrodynamical evolution of the matter. It is found that significant
supercooling is possible before hadronization begins. This study also suggests
that spinodal decomposition competes with nucleation and may provide an
alternative mechanism for phase conversion particularly if the transition is
strong enough and the medium is nonviscous. For weak enough transition, the
phase conversion may still proceed via homogeneous nucleation.
