Study on the rheology of a dilute emulsion of surfactant-covered droplets using the level set and closest point methods

In this work, we study the effects of surfactant elasticity (E), coverage factor (X), and Péclet number (Pe) on the droplet shape and emulsion rheology. Our analysis considers a single two-dimensional surfactant-covered droplet in an immiscible liquid submitted to a simple shear flow. The numerical methodology combines the level set, to capture the interface, and the closest point method to solve the surfactant transport equation. We separate the dilute phase contribution to the bulk stress tensor in the capillary stress, associated with the normal stress jump, and the Marangoni stress, related to the stress tangent to the interface. Our results show that E and X affect the droplet shape more intensely than the Pe. On the other hand, Pe directly affects the emulsion's bulk viscosity. For Pe≫1, the capillary viscosity decreases with X, while the Marangoni viscosity grows with X. Such a compensation mechanism allows the increase in the bulk viscosity with X. We also present results for the first normal stress difference.