Marangoni-induced hydrodynamics of a non-Newtonian liquid droplet

This study investigates the migration of a spherical droplet described by a nonlinear, memoryless viscous model. Unlike linear formulations, this approach captures steady inelastic flow behavior without assuming a proportional relationship between stress and strain rate. The droplet is immersed in an axisymmetric, non-isothermal Stokes flow and is coated with surfactants along its interface. Using a stream-function approach, we determine the drag force and corresponding migration velocity, considering thermocapillary and surfactant-induced Marangoni stresses. Our findings reveal that droplet migration is significantly influenced by the droplet's non-Newtonian characteristics and the Marangoni stresses. We provide an in-depth analysis within the specific context of Poiseuille flow, showing that the interplay between thermocapillary forces and non-Newtonian properties enhances droplet migration. Conversely, when the surfactant Marangoni number is small, the droplet migrates faster, but for high values, it creates resistance, reducing migration velocity. The critical thermal Marangoni number is also calculated at which droplet motion ceases, observing a nonlinear dependency on the non-Newtonian parameter. Finally, streamline patterns are analyzed to illustrate how non-Newtonian rheology primarily reorganizes the internal recirculation and perturbs the near-field exterior flow. These insights have practical implications in biomedical engineering, where non-Newtonian flows are frequently encountered in design and analysis.