The objective of this study is to elucidate the physical mechanisms by which the Marangoni number Ma influence the stability of thick liquid film flow with insoluble surfactants on a vertical fiber. Through nondimensionalization and the long-wave approximation, the original two-dimensional model is successfully reduced to a one-dimensional simplified model whose validity is verified by high consistency with fully linearized results in the long-wave region. Linear stability analysis reveals three stability mechanisms governed by Ma. The Rayleigh–Plateau instability mode dominates at low Ma, Marangoni instability mode prevails at high Ma, and complete stability is exhibited at intermediate Ma. The nonlinear numerical method reveals that the competition between Marangoni convection and the difference between the interface velocity and the wave speed $c_w$ results in diverse outcomes at different Ma values. At low Ma, the effect of advection by $c_w$ is much greater than that of Marangoni convection, such that Marangoni convection primarily serves to mitigate the Rayleigh–Plateau instability. At high Ma, Marangoni convection becomes stronger and induces Marangoni convection instability.

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• Flow instability
• Instability control
• Instability of free-surface flows
• Low Reynolds number flows
• Marangoni convection
• Thin fluid films