The linear stability of a two-fluid shear flow with an insoluble surfactant on the flat interface is investigated in the Stokes approximation. Gravity is neglected in order to isolate the Marangoni effect of the surfactant. In contrast to all earlier studies of related fluid systems, we encounter (i) the destabilization (here, of a shear flow) caused solely by the introduction of an interfacial surfactant and (ii) the destabilization (here, of a system with a surfactant) caused solely by the imposition of a Stokes flow. Asymptotic long-wave expressions for the growth rates are obtained.
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