Abstract
Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often, thermal fluctuations, modelled as stochastic noise, are present in the system and the phase segregation process occurs on a surface. In this work, the segregation process is modelled via the Cahn–Hilliard–Cook model, which is a fourth-order parabolic stochastic system. Coarsening is analysed on two sample surfaces: a unit sphere and a dumbbell. On both surfaces, a statistical analysis of the growth rate is performed, and the influence of noise level and mobility is also investigated. For the spherical interface, it is also shown that a lognormal distribution fits the growth rate well.
Highlights
Domains on curved surfaces are found in numerous industrial and biomedical applications such as chemical reactors [1], enhanced oil recovery [2] and pulmonary functions [3]
After the initial segregation phase, it is expected that the characteristic length grows at a particular growth rate, R (t) ∝ tα, where α is the growth rate
The CHC model is solved on smooth interfaces using a splitting method that converts the fourth-order partial differential equation into two coupled second-order partial differential equations
Summary
Domains on curved surfaces are found in numerous industrial and biomedical applications such as chemical reactors [1], enhanced oil recovery [2] and pulmonary functions [3]. These domains have the potential to change the dynamics of these systems significantly. In addition to biological membranes, other interesting phase dynamics on a curved surface includes crystal growth [7], phase separation within thin films [8] and phase separation patterns in diblock polymers [9]. The goal of this work is to study the phase segregation dynamics on a smooth curved surface
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