Thermally modulated cross-stream migration of a surfactant-laden deformable drop in a Poiseuille flow

TL;DR

This study analyzes how temperature gradients and surfactant transport mechanisms influence the cross-stream migration of deformable droplets in non-isothermal Poiseuille flow, revealing conditions for migration reversal and velocity dependence.

Contribution

It introduces an asymptotic approach to model thermally modulated droplet migration considering surfactant effects and identifies critical parameters affecting migration direction and magnitude.

Findings

Droplet always migrates towards the flow centerline in convection-driven surfactant transport.

Migration direction reverses for highly viscous droplets or above a critical temperature gradient.

Cross-stream velocity is larger and viscosity-independent in surface convection-dominated surfactant transport.

Abstract

In the present study, we investigate the cross-stream migration of a deformable droplet suspended in a non-isothermal Poiseuille flow in the presence of bulk-insoluble surfactants. Owing to the non-linearity present in the system of governing equations, an asymptotic approach is adopted, in an effort to capture the intricate and non-trivial coupling between the various influencing parameters. With the assumption of negligible inertia in fluid flow and convective transport of thermal energy, we obtain the droplet migration velocity through small-deformation perturbation analysis for two different limiting cases, namely, convection-driven-surfactant transport and surface-diffusion-dominated surfactant transport. Under each of these limiting cases, the cross-stream migration of droplet is studied for a constant temperature gradient applied in the same direction as well as in a direction opposite to the imposed flow. For the former limiting case, the droplet is always migrates towards the centerline of flow. For a highly viscous droplet, the direction of its cross-stream migration reverses. When the temperature decreases in the direction of the imposed flow, cross-stream migration velocity reduces with increase in the applied temperature gradient till a critical point is reached at which there is no cross-stream migration. Beyond the critical point, there is a gradual increase in the magnitude of the cross-stream velocity. The droplet, below the critical temperature gradient, migrates towards the flow centerline; however, above it the droplet moves away from the centerline. For the other limiting case of surfactant transport dominated by surface convection, the magnitude of the cross-stream velocity is found to be significantly larger and at the same time independent of the droplet-carrier phase viscosity ratio.