Faraday waves at the surfactant-covered free surface of the vertically vibrated non-isothermal liquid

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We consider a deep-water container, which is vibrated vertically and subjected to a vertical gradient of temperature. Parametric excitation generated by the vibration leads to the appearance of Faraday ripples on the surface of the liquid. The vertical heating of the liquid is an additional mechanism of interfacial instability. The previous studies of the combined action of these two destabilization mechanisms lack the analysis of the parametric excitation of waves with wavenumbers close but different from that excited in the isothermal case. Closing that gap leads to a qualitatively different prediction: near the threshold of the oscillatory Marangoni instability, parametric resonance appears for arbitrary small driving amplitudes. It is shown also that insoluble surfactant spread over the free surface can significantly change the interval of interfacial instabilities.