Elasto-hydrodynamics of droplet-pool-interactions

Abstract

In Newtonian fluids, impact of a droplet on a liquid pool births a cavity, crown, capillary waves, and Worthington jet. The corresponding hydrodynamic events for elastic or Boger fluids, however, remain an uncharted domain of comprehension and exploration. We thoroughly investigate, via experiments, theory, and simulations, how elastic energy storage, fluid relaxation, and competitive inertio elasto capillarity govern the spatio temporal evolution of the cavity, the crown, and the ensuing Worthington jet in polymeric elastic fluids. The events are systematically explored over a wide range of impact Weber and Deborah numbers, considering varied Newtonian and elastic fluid droplet pool combinations, and revealing new, and distinct morphological regimes compared to Newtonian counterparts. We illustrate that these new findings are purely driven by fluid elasticity, and not by viscosity or interfacial tension. We derive a theory for cavity radius evolution, using energy conservation within potential-flow framework. We show that 30-40 % of the droplets kinetic impact energy may be stored as elastic energy by the stretching polymer chains during cavity expansion. Appealing to the FENE P model, we derive a theory for the temporal evolution of the radius of the elongated Worthington jet. We show that in elasto capillary regime, competitive elastic and capillary stresses lead to exponential decay of the jet radius. The role of elastic stresses and the local velocity field in governing cavity evolution, morphology, and jet formation are further elucidated through computer simulations. Our findings significantly advance the uncharted paradigm of interplay between inertia, capillarity, and elasticity in droplet-pool interaction elastohydrodynamics.