Patterns and Their Large-Scale Distortions in Marangoni Convection with Insoluble Surfactant

Nonlinear dynamics of patterns near the threshold of long-wave monotonic Marangoni instability of conductive state in a heated thin layer of liquid covered by insoluble surfactant is considered. Pattern selection between roll and square planforms is analyzed. The dependence of pattern stability on the heat transfer from the free surface of the liquid characterized by Biot number and the gravity described by Galileo number at different surfactant concentrations is studied. Using weakly nonlinear analysis, we derive a set of amplitude equations governing the large-scale roll distortions in the presence of the surface deformation and the surfactant redistribution. These equations are used for the linear analysis of modulational instability of stationary rolls.

Automated summary

This study investigates the nonlinear dynamics of patterns near the threshold of long-wave monotonic Marangoni instability of conductive state in a heated thin layer of liquid covered by insoluble surfactant. It analyzes pattern selection between roll and square planforms and studies the dependence of pattern stability on heat transfer and gravity at different surfactant concentrations. Using weakly nonlinear analysis, a set of amplitude equations governing the large-scale roll distortions are derived for the linear analysis of modulational instability of stationary rolls.