  The motion of a viscous drop is investigated when the interface is fully
covered with a stagnant layer of surfactant in an arbitrary unsteady Stokes
flow for the low surface P\'eclet number limit. The effect of the interfacial
slip coefficient on the behavior of the flow field is also considered. The
hydrodynamic problem is solved by the solenoidal decomposition method and the
drag force is computed in terms of Faxen's laws using a perturbation ansatz in
powers of the surface P\'eclet number. The analytical expressions for the
migration velocity of the drop are also obtained in powers of the surface
P\'eclet number. Further instances corresponding to a given ambient flow as
uniform flow, Couette flow, Poiseuille flow are analyzed. Moreover, it is
observed that, a surfactant-induced cross-stream migration of the drop occur
towards the centre-line in both Couette flow and Poiseuille flow cases. The
variation of the drag force and migration velocity is computed for different
parameters such as P\'eclet number, Marangoni number etc.
