On the Interface Formation Model for Dynamic Triple Lines

TL;DR

This paper develops a thermodynamically consistent model for dynamic triple lines in three-phase fluids, extending interface formation theory with detailed balances and entropy principles, and proves energy stability.

Contribution

It introduces a comprehensive continuum thermodynamical model for dynamic triple lines, incorporating full interfacial physics and entropy principles, extending previous theories.

Findings

Derived balances for mass, momentum, energy, and entropy in three-phase systems.

Established the total energy as a Lyapunov function, ensuring stability.

Provided a nonlinear closure for sorption processes in the model.

Abstract

This paper revisits the theory of Y. Shikhmurzaev on forming interfaces as a continuum thermodynamical model for dynamic triple lines. We start with the derivation of the balances for mass, momentum, energy and entropy in a three-phase fluid system with full interfacial physics, including a brief review of the relevant transport theorems on interfaces and triple lines. Employing the entropy principle in the form given in [Bothe & Dreyer, Acta Mechanica, doi:10.1007/s00707-014-1275-1] but extended to this more general case, we arrive at the entropy production and perform a linear closure, except for a nonlinear closure for the sorption processes. Specialized to the isothermal case, we obtain a thermodynamically consistent mathematical model for dynamic triple lines and show that the total available energy is a strict Lyapunov function for this system.