Cosmology in a Test Tube: Theory of Domain Walls Formation in Binary Fluids

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Formation of domain walls during a rapid phase transition in a quasi one dimensional Cahn-Hiliard equation describing binary fluids in a thin tube is studied. Density of kinks scales like a sixth root of quench rate for equal concentrations and like a square root of quench rate for unequal concentrations of fluids. For a slow inhomogeneous transition the density is linear in velocity of temperature front. This paper is first theoretical study of topological defects formation in a system with conserved order parameter.