Effects of bulk elasticity on sheet formation and expansion

Abstract

The destabilization, fragmentation, and atomization of thin fluid sheets governs processes such as the aerosolization of sneeze ejecta, agrochemical spraying, and fuel injection in liquid rocket engines. Although the evolution, stability, and breakup of fluid sheets composed of a Newtonian liquid has been extensively studied, the morphology and dynamics of viscoelastic fluid sheets remains poorly understood. This manuscript provides a theoretical and numerical framework that integrates the effects of fluid elasticity, surface tension, inertia, and viscosity to predict the morphology, velocity, and stress within stable fluid sheets composed of viscoelastic fluids as a function of the dimensionless Weber, Reynolds, and Weissenberg numbers. We find a non-monotonic behavior in the sheet's size, velocity, and stress distribution as a function of the ratio between the Weissenberg and the Weber numbers. In particular, a minimum in the sheet's size and a maximum in the stress occur when such a ratio is of the order of unity. We interpret these results as the consequence of the competing effects of the growth-favoring inertia and the restoring elastic forces acting within the sheet.