Deformation and migration of a two-dimensional droplet enclosing active particles*

Active particles enclosed inside of a droplet or a  vesicle induce shape fluctuations [1,2] and in some cases cause spontaneous motion of the “soft container” [2]. In the experiment [2], the droplet is quasi two-dimensional (2D). To understand the propulsion mechanism, we derive and analyze the dynamics of a 2D droplet enclosing active particles modeled as Stokes-flow singularities. We derive an analytical solution for the fluid flow and drop deformation  driven by one singularity in the asymptotic limit of small shape distortions. Boundary integral method is implemented to explore the scenario of large drop shape deformations and many enclosed particles. We compare the motion of the enclosed active particle and the drop dynamics in 2D with the previous analysis in 3D [3]. 

  

[1] Takatori, S. C.,  and Sahu, A. (2020). Active contact forces drive nonequilibrium fluctuations in membrane vesicles. Physical Review Letters, 124(15), 158102.

[2] Kokot, G., Faizi, H.A., Pradillo, G.E., Snezhko, A. and Vlahovska, P.M. (2022). Spontaneous self-propulsion and nonequilibrium shape fluctuations of a droplet enclosing active particles. Communications Physics, 5(1), pp.1-7.

[3] Kawakami, S. and Vlahovska, P. M. (2024)  Migration and deformation of a droplet enclosing an active particle,   arXiv:2407.10009