  Surface-active agents (surfactants) release potential energy as they migrate
from one of two adjacent fluids onto their fluid-fluid interface, a process
that profoundly impacts the system's energy and entropy householding. The
continuum thermodynamics underlying such a surfactant-enriched binary-fluid
system has not yet been explored comprehensively. In this article, we present a
mathematical description of such a system, in terms of balance laws, equations
of state, and permissible constitutive relations and interface conditions, that
satisfies the first and second law of thermodynamics. The interface conditions
and permissible constitutive relations are revealed through a Coleman-Noll
analysis. We characterize the system's equilibrium by defining equilibrium
equivalences and study an example system. With our work, we aim to provide a
systematically derived framework that combines and links various elements of
existing literature, and that can serve as a thermodynamically consistent
foundation for the (numerical) modeling of full surfactant-enriched
binary-fluid systems.
