Droplet deformation in secondary breakup: Transformation from a sphere to a disk-like structure

Abstract

Deformation of a droplet from an initial spherical shape to a disk-like structure is common during its secondary breakup. Characterizing this initial deformation is important to develop accurate secondary breakup models. In the present study, the initial droplet deformation until initiation time (where the droplet attains a disk-like structure) was investigated by experiments with a variety of test liquids offering wide ranges of surface tension (0.022–0.71 N/m), viscosity (0.86–3.63 mPa⋅s), and density (788–6900 kg/m3). The test liquids included molten metals along with classical water-like liquids. To characterize the initial droplet deformation until the initiation time, the droplet’s displacement, relative velocity, deformation, and drag coefficient (CD) were measured. A non-dimensional parameter named the displacement–relative velocity–deformation (DVD) parameter was introduced and a mathematical expression for its temporal evolution, which could be useful for validating simulation results, was obtained. The temporal evolution of the DVD parameter and the droplet’s displacement, relative velocity, and deformation (in non-dimensional forms) for molten metals were observed to be significantly different from those for the other liquids at similar Weber numbers. A correlation for the non-dimensional droplet deformation at the initiation time is also presented by studying the relationship between an instantaneous Weber number defined at the initiation time (Weini) and the corresponding conventional Weber number (We). It is observed that the temporal evolution of CD until the initiation time for ∼30<We<∼70 (where dual-bag and sheet-thinning breakup modes are observed) is significantly different in comparison to that for ∼10<We<∼30 (where bag and bag-stamen breakup modes are observed).