  Understanding and modulating the cross-stream motion of a surfactant-coated
droplet in pressure driven flow has great implications in many practical
applications. A combination of interfacial viscosity and Marangoni stress
acting over a surfactant-coated droplet in pressure driven flow offers greater
flexibility to modulate the cross-stream motion of it. Despite the intense
theoretical and numerical research towards manipulating the surfactant-laden
Newtonian droplets in Poiseuille flow, the experimental investigations are
seldom explored. Herein, we report our study on understanding the influence of
interfacial viscosity on the cross-stream motion of a surfactant-coated
Newtonian droplet in both isothermal and non-isothermal Poiseuille flow from a
theoretical as well as an experimental perspective. A theoretical model has
been developed to understand the effect of interfacial viscosity on the lateral
migration of a droplet under the assumptions of no shape deformation and
negligible fluid inertia or thermal convection. Theoretical analysis is
performed under two limiting conditions: (i) when the transport of surfactants
is dominated by surface-diffusion and (ii) when the transportation of
surfactants is dominated by surface-convection. Our theoretical analysis shows
that both the dilatational as well as the shear surface viscosities suppress
the lateral migration velocity of the droplet. Experiments have been performed
to validate the theoretically predicted droplet trajectories and to understand
the influence of channel confinement on the lateral migration of the droplet.
It has been observed from the experiments that the droplet travels faster
towards the centerline of the flow in a highly confined domain. The results
presented in this study could provide new vistas in designing and analyzing
various droplet-based microfluidic, biomedical and bio-microfluidic devices.
