Collaborative Research: Surface and Bulk PDE Modeling of the Propulsion of an Active Drop

This collaborative project explores how a tiny droplet, powered by internal and surface activity, can propel itself—serving as a simplified model for how primitive cells, or "protocells", move. In experiments, such systems can be created by building networks of actin proteins inside and along the membrane of giant vesicles. To understand how this motion arises, the research team develops mathematical models that describe how forces inside the droplet and on its surface interact with the surrounding fluid. A key focus is to understand how this active droplet pushes against its environment to generate sustained forward motion—behavior that is fundamental to many forms of movement in soft materials and living cells. The project supports graduate education at Florida State University and New Jersey Institute of Technology, and promotes collaboration and dissemination of scientific knowledge through scientific workshops and seminars. The project aims to elucidate the role of steric alignment interactions in the nematic fluid on drop propulsion. The project combines analytical theory, numerical simulations, and comparisons with experimental data from active vesicle systems. The primary investigator Young leads the development of mathematical models and analytical methods, including theory of partial differential equations (PDE), dynamical systems analysis, differential geometry, and asymptotic techniques. The primary investigator Quaife develops efficient numerical algorithms for solving coupled surface-bulk PDEs on both rigid and deforming geometries. These numerical methods include solvers for surface PDEs on evolving interfaces and bulk-surface coupling across moving boundaries. A central challenge is modeling steric alignment interactions at the continuum level and calibrating their strength using experimental observations. The resulting framework has broad applicability to active matter systems described by coupled surface-bulk dynamics on moving domains. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.