Theory for solvent, momentum, and energy transfer between a surfactant solution and a vapor atmosphere

We develop a complete set of equations governing the evolution of a sharp interface separating a volatile-solvent/nonvolatile-surfactant solution from a vapor atmosphere. In addition to a sorption isotherm equation and the conventional balances for mass, linear momentum, and energy, these equations include an alternative to the Hertz-Knudsen-Langmuir equation familiar from conventional theories of evaporation and condensation. This additional equation arises from a consideration of configurational forces within a thermodynamical framework. While the notion of configurational forces is well developed and understood for the description of materials that, like crystalline solids, possess natural reference configurations, very little has been done regarding their role in materials, such as viscous fluids, that do not possess preferred reference states. We therefore provide comprehensive developments of configurational forces, the balance of configurational momentum, and configurational thermodynamics. Our treatment does not require a choice of reference configuration. The general evolution equations arising from our theory account for the thermodynamic structure of the solution and the interface and for sources of dissipation related to the transport of surfactant, momentum, and heat in the solution and within the interface along with the transport of solute, momentum, kinetic energy, and heat across the interface. Moreover, the equations account for the Soret and Dufour effects in the solution and on the interface and for observed discontinuities of the temperature and chemical potential across the interface. Due to the complexity of these equations, we provide approximate equations which we compare to equations preexistent in the literature.