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 a counterpart of the Hertz???Knudsen???Langmuir equation familiar from conventional theories of evaporation-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, like crystalline solids, that 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 a comprehensive discussion of configurational forces, the balance of configurational momentum, and configurational thermodynamics that 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, the transport of surfactant and momentum within the interface, and the transport of solute, momentum, kinetic energy, and heat across the interface. Due to the complexity of these equations, we provide approximate equations which we compare to relations that appear in the literature.published or submitted for publicationis peer reviewe

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