Fluid demixing kinetics on spherical geometry: power spectrum and Minkowski functional analysis

Abstract

Dynamic density functional theory calculations of fluid–fluid demixing on spherical geometries are characterized via their angular power spectrum as well as via the Minkowski functionals (MFs) of their binarized fluid density fields. MFs form a complete set of additive, motion invariant and continuous morphological measures sensitive to nonlinear (spatial) correlations. The temporal evolution of the fluid density fields is analyzed for different sphere sizes and mixing compositions. The demixing process in the stages of early spinodal decomposition and consecutive domain growth can be characterized by both methods and a power-law domain growth $L(t)\propto {t}^{\alpha }$ is evidenced for the MF measures. The average domain size obtained by the structure factor only responds to the late stage domain growth of the demixing process. MFs provide refined insights into the demixing process: they allow the detection of distinct stages in the early spinodal decomposition, provide a precise measure of the relative species composition of the mixture and, most importantly: after a proper rescaling, they allow the detection of a universal demixing behavior for a wide range of mixture fractions and for different sphere sizes.

Keywords

• morphological data analysis
• demixing
• curved space
• spinodal decomposition