Conservation laws of surfactant transport equations

Abstract

Equations of the interfacial convection and convection-diffusion describing the transport of surfactants, and more general interfacial balance laws, in the context of a three-dimensional incompressible two-phase flow are considered. Here, the interface is represented implicitly by a zero level set of an appropriate function. All interfacial quantities and operators are extended from the interface to the three-dimensional domain. In both convection and convection-diffusion settings, infinite families of conservation laws that essentially involve surfactant concentration are derived, using the direct construction method. The obtained results are also applicable to the construction of the general balance laws for other excess surface physical quantities. The system of governing equations is subsequently rewritten in a fully conserved form in the three-dimensional domain. The latter is essential for simulations using modern numerical methods.