Model of traveling wave formed by autonomous motion of contact line with oil/water interface

A model for the spontaneous traveling wave in oil/water system is proposed. The present model is to explain the traveling wave generated by chemical reactions between a cationic surfactant and oil-soluble anions. This is an extension of the previous model which describes the oscillatory motion of the contact line formed by the oil/water interface and a glass surface. The oscillations at different places are coupled to each other by an effect that diminishes the interfacial energy. The numerical calculations reveal that the traveling wave with a specified direction is reproduced under several assumptions for the noise term.