Squirming inside a liquid droplet with surface viscosities

Encapsulating active particles within droplets to drive their motion presents exciting possibilities for biomedical applications, such as targeted drug delivery. In realistic biological and environmental settings, droplet interfaces often exhibit complex rheological behaviors that influence propulsion. This work investigates how surface shear and dilatational viscosities affect the motion of an active droplet, where a liquid droplet encloses an active particle modeled as a squirmer. The findings provide insights into the behavior of microswimmer-driven droplets in complex environments, paving the way for their potential biomedical and environmental applications.