The Dynamics of Secondary Fragmentation of Viscoplastic and Shear-Thinning Droplets

A liquid droplet undergoes secondary breakup under impulsive acceleration when the flow Weber number is greater than critical Weber number (We_cr). For a Newtonian droplet, its We­_cr depends on density ratio (ρ) as well as drop (Oh_d) and ambient (Oh_o) Ohnesorge numbers. However, in many physical applications, the droplet fluid is non-Newtonian in nature. Aerial Firefighting is a prime example of one such application where shear-thinning and viscoplastic fluids such as Xanthan gum and Guar gum solutions are used as fire retardants. Such a change in droplet fluid rheology can have a significant impact on its deformation and breakup as well as its We_cr. Through this work, we explore the role of shear-thinning and viscoplastic rheology on secondary fragmentation using multiphase Direct numerical simulations. To facilitate this exploration, Carreau-Yasuda and Modified Herschel-Bulkley constitutive models for shear-thinning and Viscoplastic rheology respectively are implemented for Volume-of-Fluid Direct numerical simulations and validated against analytical and experimental works. A parameter sweep across Weissenberg number (Wi) and power-law exponent n for some benchmark Newtonian fragmentation cases is performed. Analysis of the simulations reveal the importance of the nominal viscosity and corresponding nominal Drop Ohnesorge number in the droplet's fragmentation dynamics, and its connection to Wi and n is also highlighted.