Sub-Newtonian coalescence in polymeric fluids

Abstract

We present a theoretical framework for capturing the coalescence of a pendant drop with a sessile drop in polymeric fluids. The framework is based on the unification of various constitutive laws under high Weissenberg creeping flow limit. Our results suggests that the phenomenon comes under a new regime namely, the sub-Newtonian regime followed by the limiting case of arrested coalescence with the arrest angle ${\theta }_{arrest}\propto E{c}^{-1/2}$, where $Ec$ is the Elasto-capillary number. Further, we propose a new time scale $T^{\ast }$ integrating the continuum variable $Ec$ and the macromolecular parameter $N_e$, the entanglement density to describe the liquid neck evolution. Finally, we validate the framework with high speed imaging experiments performed across different molecular weights of Poly(ethylene oxide) (PEO).