The double-mass model of drop deformation and secondary breakup

In the paper, a new analytical model of drop deformation and secondary breakup is presented. The model is a direct extension of the TAB (Taylor Analogy Breakup) model of O’Rourke and Amsden P. O’Rourke, A.A. Amsden, The TAB method for numerical calculation of spray droplet breakup, SAE Paper No 872089, 1987] 9]. The drop is represented by the system of two masses connected by a spring, allowed to oscillate and move along a specified axis. Two versions of the model are analyzed: linear – offering analytical solution for drop oscillations, and nonlinear – defined in terms of parameters with clear, physical interpretation, and more interesting from the point of view of applications. Conditions of stability of a drop subjected to impulsive acceleration by ambient flow are discussed and a new criterion is introduced including droplet Weber number, Ohnesorge number and density ratio. The role of the density ratio proves to be prominent for large Ohnesorge numbers or when the drop density approaches the ambient density.