Morphology of spinodal decomposition

The morphology of homogeneous phases during spinodal decomposition, i.e., the scaling of the content, shape, and connectivity of spatial structures is described by a family of morphological measures, known as Minkowski functionals. Besides providing means to determine the characteristic length scale $L$ in a statistically robust and computationally inexpensive way, the measures allow also one to define the crossover from the early stage decomposition to the late stage domain growth. We observe the scaling behavior $L\sim t^{\alpha }$ with $\alpha =1/3,$ $\alpha =1/2,$ and $\alpha =2/3\mathrm{}$ depending on the viscosity. When approaching the spinodal ${\rho }_{\mathrm{sp}},$ we recover the prediction $L\sim (\rho -{\rho }_{\mathrm{sp}}{)}^{-1/2}$ for the early time decomposition.