Effect of surfactant concentration and interfacial slip on the flow past a viscous drop at low surface Péclet number
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(2018)

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 Péclet 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 Péclet number. The analytical expressions for the migration velocity of the drop are also obtained in powers of the surface Péclet 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 Péclet number, Marangoni number etc.
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