A thermodynamic model of multiphase flows with moving interfaces and contact line

In this paper, we develop a general continuum description for thermodynamic multiphase flows with intersecting dividing surfaces, and three-phase common contact line, taking the contribution of the excess surface and line thermodynamic quantities into account. Starting with the standard postulates of continuum mechanics and the general global balance statement for an arbitrary physical quantity in a physical domain of three bulk phases including singular material or non-material phase interfaces and a three-phase contact line, we derive, in addition to the classical local balance equations for each bulk phase, the local conservation equations on the phase interfaces and at the contact line. Then, these additional interface and line balance laws are specified for excess surface and line physical quantities, e.g., excess mass, momentum, angular momentum, energy, and entropy, respectively. Some simplified forms of these balance laws are also presented and discussed.