Current work is inspired by bio--medical research for mass transport across liquid layer with surfactant that is expanded or compressed by moving barrier. The horizontal velocity of surfactant is a linear function of parallel coordinate. Our aim is to investigate if linear surface velocity distribution can affect stability of the liquid. It should be emphasized that we are interested not in phenomena connected to changing surface tension

like for instance Marangoni effect. Our objective is to study instability due to specific velocity profile across the liquid layer.

Starting point of our model is one of the simplest and also best known systems namely combined plane Couette-Poiseuille flow. Stability of such kind of flows were intensively researched since the beginning of our century using different methods and miscellaneous approximations. Linear analysis for plane Poiseuille

flow gives critical Reynolds number R_=5772 and for plane Couette flow critical Reynolds number is infinity so this flow is absolutely stable with respect to ifinitesimal amplitude disturbances. For combination of these two

kinds of flow as Couette component is increased from zero the flow becomes stable. Critical Reynold number increases (non monotonically) from R=5772 to infinity. Most interesting from point of view this paper the case

when total forizontal flux vanishes is absolutely stable. Nonlinear analysis and simulations reveal for both plane Couette and Poiseuille flows undercritical instability. For plane Poiseuille flow instability with respect to finite disturbances occurs when R>264. Linear stability analysis yields criteria sufficient only for instability and says nothing definite about stability. In turn the energy method predicts only the sufficient condition for stability

and says nothing definite about instability Energy analysis shows that Poiseuille flow is stable for R< 81.5 and plane Couette flow for R< 82.6.

In current work the case of combination Poiseuille and Couette flow for that total horizontal flux vanishes was generalized by introducing into model constant surface velocity gradient. Above sentence means that velocity of the upper surface assumed by boundary condition is a linear function of horizontal coordinate. Because our aim is to estimate upper limit of critical parameters for instability using simple method we chose linear analysis. Equation that for our model corresponds to Orr--Sommerfeld equation was derived. Using numerical method the problem was solved and instability that enhances mass transport was found.