Coupled Bubble-Flame Dynamics in Burning Emulsion Droplets

We explore the coupled dynamics of bubble behavior and flame evolution in burning stable emulsion droplets. Two distinct flame response modes, i.e., varicose and sinuous, are revealed using high-speed imaging, governed by the interplay between the flame front, ejected vapor, and secondary droplets. Varicose mode dominates during bubble growth, while sinuous mode emerges following bubble collapse. These recurring growth-collapse cycles result in a self-tuning instability that alternates between the two modes. We employ Continuous Wavelet Transform (CWT), Proper Orthogonal Decomposition (POD), and Spectral POD to characterize two combustion phases. Phase I exhibits low- and high-frequency broadband spectra (O(10⁰) and O(10²) Hz), linked to evaporation. In contrast, Phase II displays a wider high-frequency range (O(10¹) to O(10³) Hz), attributed to droplet breakup. The number of modes required to capture 90% of system energy remains nearly constant in Phase I but rises significantly in Phase II, indicating increased spatio-temporal complexity. The results show that emulsified fuels exhibit higher modal energy across a broader frequency range compared to pure fuels, highlighting the role of bubble dynamics in enhancing coherent flame structures and frequency-dependent instabilities.