From singularity phenomena in thin films to chemically driven active matter
Fan Yang, Princeton Mechanical and Aerospace Engineering


Unlike conventional jet and drop breakup, which forms a cylindrical liquid column, the dripping of a viscous film will form a liquid
annulus, which then ruptures and heals due to surface tension and the inner surface forms a retracting tip. We apply a one-dimensional model
to analyze the healing dynamics, which predicts a universal thinning curve and shows good agreement with experimental measurements. The shape of the tip is documented to be conical and the retraction speed is determined by the balance of viscous and capillary stresses.

In the second part of the talk, I will introduce a reduced-order model to describe a system of interacting active particles suspended in a
viscous fluid. An approximate theory is developed for spheres in the semi-dilute regime, including hydrodynamic interactions up to the level
of force-quadrupoles. The results obtained are broadly applicable to collections of chemically active spheres and accurately describe the
autophoresis of two spheres, for which exact solutions are available. Numerical simulations of multi-body dynamics with chemical
inhomogeneities reveal self-organization and collective motion.