Surfactant-induced instability of a sheared liquid layer

The surfactant-induced instability of a sheared liquid layer coated on a horizontal plane underneath a semi-infinite fluid is examined under conditions of Stokes flow. Linear stability analysis reveals that the surfactant induces a Marangoni instability for perturbations with sufficiently long wavelength. The predictions of the linear stability analysis are confirmed by boundary integrals simulations of the non-linear motion in the case of fluids with equal viscosity. In the case of steady shear flow over a liquid layer coated on a wall with sinusoidal undulations, the surfactant promotes the interfacial deformation. Comparison with corresponding results for infinite shear flow and two-layer channel flow suggest that the presence of a wall, and most likely a fluid interface, is necessary but not sufficient for the onset of a surfactant-induced instability.