Numerical studies of liquid sprays and other particle laden flows for practical systems of interest traditionally involve an Eulerian-Lagrangian framework,in which the Navier-Stokes equations are used to model the continuous phase and the dispersed phase particles,and droplets are tracked using Newton's second law of motion.The source terms in the Lagrangian equations of motion require knowledge of the forces acting on the discrete phase.For solid particles,there are several models that describe the flow physics for a wide range of operating conditions.There are,however,no reliable models available to describe the dynamics of deformable objects,such as droplets.The present paper investigates the child droplet statistics resulting from the deformation and fragmentation of Newtonian and non-Newtonian liquid droplets.The working fluids under consideration are water(Newtonian)and a 0.5%carboxymethyl cellulose(CMC)-water solution(shear thinning non-Newtonian).Weber numbers up to 1400 for the Newtonian and from 2000 to 10000 for the non-Newtonian fluids are investigated at room temperature conditions.An Eulerian-Eulerian formulation based on the one-fluid approach is used to model the breakup process,along with a volume-of-fluid(VOF)interface capturing algorithm to resolve the multi-fluid interface on an octree mesh.An adaptive mesh refinement(AMR)technique is employed to ensure computational efficiency and reasonable turn-around times.It is found that the dynamics of Newtonian and non-Newtonian liquid droplets differ significantly in terms of the processes that lead to their deformation and fragmentation.Results show that the child droplet sizes follow a universal log-normal distribution for Newtonian liquids.The shear-thinning non-Newtonian fluids are governed by a Gaussian curve for the range of Weber numbers under investigation.The drag coefficient of deforming and fragmenting water droplets shows a monotonically decreasing trend as a function of Weber number.A generalized regime diagram is developed to predict the breakup mechanisms of water droplets over a wide range of pressures.The predicted value of the Sauter mean diameter corresponding to droplet size distribution resulting from shear breakup of water droplets at atmospheric pressure compares well with experimentally measured values.