The equations governing spherically symmetric phase growth in an infinite medium are first formulated for the general case and are then simplified to describe growth controlled by the transport of heat and matter. All assumptions and restrictions are recounted. Exact solutions of the equations are obtained for conditions typical of bubble growth in the nucleate boiling of(a) pure materials and (b) binary mixtures. The effect of radial convection resulting from unequal phase densities is established and the regions of applicability of previously reported approximate solutions are determined.