HADRON BUBBLE EVOLUTION INTO THE QUARK SEA

A solution is presented for the evolution of hadron bubbles which nucleate in the quark sea if there is a first-order quark-hadron phase transition at a temperature Tc on the order of 100 MeV. We make three assumptions: (1) the dominant mechanism for transport of latent heat is radiative, e.g., neutrinos; (2) the distance between nucleation sites is greater than the neutrino mean free path; and (3) the effects of hydrodynamic flow can be neglected. Bubbles nucleate with a characteristic radius 1 fm, where is a dimensionless parameter for the undercooling (we take 10-4, so that the expansion of the Universe can be neglected). We argue that bubbles grow stably and remain spherical until the radius becomes as large as the neutrino mean free path, 10 cm. The growth then becomes diffusion limited and the bubbles become unstable to formation of dendrites, or finger-like structures, because latent heat can diffuse away more easily from long fingers than from spheres. We study the nonlinear evolution of structure with a "geometrical model" and argue that the hadron bubbles ultimately look like stringy seaweed. The percolation of seaweed-shaped bubbles can leave behind regions of quark phase that are quite small. In fact, one might expect the typical scale to be LQ=l10 cm. Protons can easily diffuse out of such small regions (and neutrons back in). Thus, these instabilities can lead to important modifications of inhomogeneous nucleosynthesis, which requires LQ1 m. © 1990 The American Physical Society.