Swimming sheet near a plane surfactant-laden interface

In this work we analyze the velocity of a swimming sheet near a plane surfactant-laden interface by assuming the Reynolds number and the sheet's deformation to be small. We observe a nonmonotonic dependence of the sheet's velocity on the Marangoni number (Ma) and the surface Peclet number (Pe(s)). For a sheet passing only transverse waves, the swimming velocity increases with an increase in Ma for any fixed Pe(s). When Pe(s) is increasing, on the other hand, the swimming velocity of the same sheet either increases (at large Ma) or it initially increases and then decreases (at small Ma). This dependence of the swimming velocity on Ma and Pe(s) is altered if the sheet is passing longitudinal waves in addition to the transverse waves along its surface.