Dynamical growth of the hadron bubbles during the quark-hadron phase transition

The rate of dynamical growth of the hadron bubbles in a supercooled baryon free quark-gluon plasma, is evaluated by solving the equations of relativistic fluid dynamics in all space. For a non-viscous plasma, this dynamical growth rate is found to depend only on the range of correlation ξ of order parameter fluctuation, and the radius R of the critical hadron bubble, the two length scales relevant for the description of the critical phenomena. Unlike Csernai-Kapusta result, this rate does not vanish in the limit of zero viscosity. Further, it is shown that the dynamical prefactor acquires an additive component when the medium becomes viscous. Interestingly, under certain reasonable assumption for the velocity of the sound in the medium, the viscous and the non-viscous parts of the prefactor are found to be identical to the results obtained by Csernai-Kapusta and Ruggeri-Friedman (for the case of zero viscosity) respectively. It is also demonstrated that the first order phase transition from QGP to hadron matter, which proceeds through supercooling, generates additional entropy even when the plasma is non-viscous. The correction to the growth rate due to the viscosity is found to be small though large amount of entropy is generated due to the slow evolution of the system. PACS number(s): 12.38.Mh, 64.60.Qb