Degenerate Mobilities in Phase Field Models are Insufficient to Capture Surface Diffusion
This corrects a long-standing misconception in phase field modeling, impacting researchers who use these models to simulate surface diffusion in materials science.
The authors show that degenerate Cahn-Hilliard models, contrary to prior belief, exhibit coarsening due to bulk diffusion rather than pure surface diffusion, revealing a fundamental limitation of these models for capturing surface diffusion.
Phase field models frequently provide insight to phase transitions, and are robust numerical tools to solve free boundary problems corresponding to the motion of interfaces. A body of prior literature suggests that interface motion via surface diffusion is the long-time, sharp interface limit of microscopic phase field models such as the Cahn-Hilliard equation with a degenerate mobility function. Contrary to this conventional wisdom, we show that the long-time behaviour of degenerate Cahn-Hilliard equation with a polynomial free energy undergoes coarsening, reflecting the presence of bulk diffusion, rather than pure surface diffusion. This reveals an important limitation of phase field models that are frequently used to model surface diffusion.