  We study the nucleation of a quark gluon plasma (QGP) phase in a hadron gas
at low temperatures and high baryon densities. This kind of process will
presumably happen very often in nuclear collisions at FAIR and NICA. When the
appropriate energy densities (or baryon densities) and temperatures are reached
the conversion of one phase into another is not instantaneous. It is a complex
process, which involves the nucleation of bubbles of the new phase. One
important element of this transition process is the rate of growth of a QGP
bubble. In order to estimate it we solve the Relativistic Rayleigh$-$Plesset
equation which governs the dynamics of a relativistic spherical bubble in a
strongly interacting medium. The baryon rich hadron gas is represented by the
nonlinear Walecka model and the QGP is described by the MIT bag model and also
by a mean field model of QCD.
