  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.
