On dynamic excitation of Marangoni instability in a liquid layer with insoluble surfactant on the deformable surface

This paper is a continuation of our previous work presented at the IMA-6, see [1]. We continue to analyze the parametric excitation of Marangoni instability by a periodic flux modulation in a liquid layer with insoluble surfactant. Contrary to the previous investigation here the upper free surface of the layer is deformable. The linear stability analysis for the disturbances with arbitrary wave numbers is performed. Three response modes of the system to an external periodic stimulation were found – synchronous, subharmonic, and quasi-periodic ones. Results for different Galileo and inverse capillary parameters are presented. It is shown that contrary to the situation with nondeformable interface, at small values of Galileo and inverse capillary parameters a new subharmonic instability region appears in the range of long waves.