Gas Bubble Inflation in Compressible Viscous Fluid by Hubble-like Flow

Abstract

We analyze the dynamics of a gas bubble inflating in a compressible viscous fluid that flows according to a Hubble-like field, proportional to the radial coordinate. The equation of motion of the bubble wall is derived and the speed of sound on it, calculated. Numerical solutions are provided for suitable boundary conditions and meaningful physical parameters. Such a treatment inspires the obtaining of approximate analytical solutions in terms of families of conics. A two-dimensional Universe that lives on the wall of the bubble, whose points move away from each other according to the Hubble law, is then proposed. Cosmological fine-tuning problems are discussed in the light of such a toy-model. Possible extensions of our formulation, with basis on an analogy between surface tension and cosmological constant, are briefly addressed.