On the Threshold of Shear-thinning Drop Fragmentation under Impulsive Acceleration

Through our previous works, we extensively explored the threshold of droplet fragmentation under impulsive acceleration, and its dependence on non-dimensional parameters such as Weber number, drop Ohnesorge number (Oh_d), ambient Ohnesorge number (Oh_a), and density ratio. We discovered that all four non-dimensional numbers could affect the appearance of non-trivial forward and backward-plume fragmentation morphologies (as opposed to the trivial backward bag breakup). Specifically, Oh_d (representative of drop viscosity) was found to be primary parameter controlling the appearance of instability driven plumes at the upstream pole, as well as delaying and possibly preventing the fragmentation process for drops. Incidentally, shear-thinning fluids (a special class of general viscous fluids) whose viscosity decreases when exposed to large strain rates, could show many orders of magnitude variance in local drop viscosities in different regions of a drop under aerodynamic stress, depending on local strain rates. The strain rates are expected to be the lowest at the droplet core, and hence expected to show the highest local drop Ohnesorge numbers (zero strain). Through this work, we explore the role of this inhomogeneity of local strain rates and corresponding local viscosities. Carreau constitutive model is the model of choice for the present work (since it allows finite zero and non-zero infinite strain rate viscosities, respectively) and is implemented in the open-source VOF based incompressible NS solver Basilisk. A range of zero-shear and infinite-shear Ohnesorge numbers are simulated, and the resulting deformation and fragmentation is analyzed.