On the Compatibility of Sharp and Diffuse Interfaces Out of Equilibrium

Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 369-405, March 2024.
Abstract. There are two main approaches to modelling interfaces within nonequilibrium thermodynamics, the so-called sharp and diffuse interface models. Both of them are based on the local equilibrium assumption (LEA) in the bulk, but the latter additionally assumes the validity of this concept also within the interface itself (as the thermodynamic description is available and smoothly varying even within the interface), that is, on a finer length scale, which we call super-LEA. Instead of testing the two approaches against molecular dynamic simulations, we explore the mutual compatibility of these two descriptions of an interface in a nonequilibrium situation. Based on the level of detail in the two frameworks, one naturally cannot reconstruct a diffuse interface model from a sharp interface counterpart. One can test, however, whether diffuse interface models are indeed a more detailed description of the interface. Namely, assuming that both approaches are valid, we use the diffuse interface model (van der Waals entropy together with the Cahn–Hilliard type energy with the mass density as the order parameter) and its sharp interface counterpart (with the additional set of interfacial state variables subjected to known thermodynamic constraints) to test their mutual compatibility and indirectly verify the correctness of the additional super-LEA of the diffuse models. That is, thanks to super-LEA, we define five interfacial temperatures that should be equal. However, when we analyze diffuse interface results like experimental or simulation data in terms of sharp interfaces, we show that, contrary to molecular simulation data, they do not yield equal interfacial temperatures. We argue that the culprit is the super-LEA which is most prominently expressed in the accessibility of the entropy density profile. Nevertheless, it is observed that there is an inconsistency between diffuse and sharp interface descriptions; they cannot both be correct. The sharp interface framework has been recently tested against molecular dynamics and the obtained results suggest that super-LEA is the potential weakness of the diffuse framework. In this sense, sharp interfaces are found to be superior to diffuse interfaces in their general ability to model physical systems with interfaces.