| The sheared wavy liquid films, as an important flow, have notably different hydrodynamics and flow stability under interfacial shear stress from those of free falling liquid films. Firstly, The Orr-Sommerfeld equation describing the flow stability of liquid films under shear draining down an inclined wall is established based on complete boundary conditions. The wave velocity is computed with the perturbation method. The stability of the sheared liquid films is investigated form the present model and the physical reasons for instability are discussed. Secondly, based on the boundary layer theory and complete boundary conditions, the linear stability equation of two-dimensional surface waves on the sheared liquid films is formulated in present paper with the integral approach and linearization theory. The effects of shear stress, Reynolds number, wave number, surface tension and inclination angle on the stability of the interfacial waves in different conditions are investigated with present model.
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