Cross-stream migration of a surfactant-laden deformable droplet in a Poiseuille flow

摘要

The motion of a viscous deformable droplet suspended in an unboundedPoiseuille flow in the presence of bulk-insoluble surfactants is studiedanalytically. Assuming the convective transport of fluid and heat to benegligible, we perform a small-deformation perturbation analysis to obtain thedroplet migration velocity. The droplet dynamics strongly depends on thedistribution of surfactants along the droplet interface, which is governed bythe relative strength of convective transport of surfactants as compared withthe diffusive transport of surfactants. The present study is focused on thefollowing two limits: (i) when the surfactant transport is dominated by surfacediffusion, and (ii) when the surfactant transport is dominated by surfaceconvection. In the first limiting case, it is seen that the axial velocity ofthe droplet decreases with increase in the advection of the surfactants alongthe surface. The variation of cross-stream migration velocity, on the otherhand, is analyzed over three different regimes based on the ratio of theviscosity of the droplet phase to that of the carrier phase. In the firstregime the migration velocity decreases with increase in surface advection ofthe surfactants although there is no change in direction of droplet migration.For the second regime, the direction of the cross-stream migration of thedroplet changes depending on different parameters. In the third regime, themigration velocity is merely affected by any change in the surfactantdistribution. For the other limit of higher surface advection in comparison tosurface diffusion of the surfactants, the axial velocity of the droplet isfound to be independent of the surfactant distribution. However, thecross-stream velocity is found to decrease with increase in non-uniformity insurfactant distribution.