Time-Varying Oscillatory Response of Burning Gel Fuel Droplets

Gel fuel droplets exhibit disruptive burning due to the rupture of their gellant shell, which causes the release of unreacted fuel vapors from the droplet interior to the flame in the form of jets. In addition to pure vaporization, this jetting allows convective transport for fuel vapors, which accelerates gas-phase mixing and is known to improve droplet burn rates. Using high-magnification and high-speed imaging, this study found that the viscoelastic gellant shell at the droplet surface evolves during the droplet's lifetime, which causes the droplet to burst at different frequencies, thereby triggering a time-varying oscillatory jetting. In particular, the continuous wavelet spectra of the droplet diameter fluctuations show that the droplet bursting exhibits a nonmonotonic (hump-shaped) trend, where the bursting frequency first increases and then decreases to a point where the droplet stops oscillating. The changes in the shell structure are captured by tracking the temporal variation of the area of rupture sites, spatial movement of their centroid, and the degree of overlap between the rupture areas of successive cycles. During the initial period (immediately following its formation) when the shell is newly formed, it is weak and flexible, which causes it to burst at increasingly high frequencies. This is because the area at and around the rupture site becomes progressively weaker with each rupture in an already weak shell. This is shown by a high degree of overlap between the areas of successive ruptures. On the other hand, the shell flexibility during the initial period is demonstrated by a reversal in the motion of rupture site centroids. However, at later stages when the droplet has undergone multiple ruptures, the depletion of the fuel vapor causes accumulation of gellant on the shell, thus causing the shell to become strong and rigid. This thick, strong, and rigid shell suppresses droplet oscillations. Overall, this study provides a mechanistic understanding of how the gellant shell evolves during the combustion of a gel fuel droplet and causes the droplet to burst at different frequencies. This understanding can be used to devise gel fuel compositions that result in gellant shells with tailored properties, and therefore, control the jetting frequencies to tune droplet burn rates.