Modelling of Droplet Breakup via Nonlinear Hydrodynamic Insabilities

Interactions of liquid droplets with shock waves and the ensuing high-speed, post-shock flows occur in a variety physical systems. In these environments, a liquid droplet deforms from aerodynamic forces, assuming an oblate shape. Concurrent to the deformation, a progression of fluid instabilities develop on the surface. Both Kelvin-Helmholtz (KH) and Rayleigh-Taylor (RT) type instabilities arise due to the strong shear velocity and strong acceleration across the surface, respectively. These instabilities occur across a range temporal and spatial scales, from the immediate surface stripping of small droplets to large- wavelength perturbations that ultimately cause the droplet to fragment violently later in time. Various attempts have been made to characterize these instabilities, generally utilizing the framework of linear hydrodynamic stability theory. Here a theory of droplet breakup is presented that considers the combined effects of the non-linear KH & RT instabilities. This theory allows for estimation of the perturbation width and amplitude growth in time, utilizing extant drag, deformation, and external flow models to establish the boundary conditions. Experimental comparison data is provided by a series of experiments whereby droplets are accelerated with gaseous detonations travelling at Mach ~ 7.6 (~2350 m/s ). The development of the droplet in the post-detonation flow is imaged at both high-resolution and high-framerate with shadowgraph and Laser-Induced-Fluorescence techniques. From this imagery information on the droplet deformation and the size and growth of surface perturbations is extracted. Initial results from the experiments show agreement with the models. The findings presented are a promising first step towards the development of a nonlinear hydrodynamic instability driven model of droplet breakup.