Beyond the D ² -law: a unified approach to unveiling shrinkage kinetics across diverse droplet vaporisation processes

Droplet vaporisation can exhibit distinct shrinkage kinetic laws depending on the experimental set-up and ambient conditions. In this work, we present a unified approach that combines experiment and theory to identify true shrinkage kinetics across a broad range of droplet vaporisation processes extending beyond the classical D 2 -law – particularly under realistic conditions involving support fibres or/and inevitable convective effects. Experimentally, we assume a power law $D^n= D_0^n- \textit{Kt}$ , where K is the vaporisation rate constant, and re-express it as $(D/D_0)^n = 1 - t/t_{\textit{life}}$ in terms of the normalised droplet diameter $D/D_0$ and time t $ / $ t life relative to the droplet’s initial diameter D 0 and lifetime t life . Taking D as the diameter of a volume-equivalent sphere, the exponent n can be reliably extracted from the slope of the log–log plot of $( 1 - t/t_{\textit{life}})$ against $D/D_0$ . The robustness of this method is demonstrated by re-confirming the D 2 -law for pure fuel droplet evaporation and validating the $D^{3/2} $ -law for droplet evaporation under forced convection. We further apply this method to droplet combustion, revealing a significant departure from the D 2 -law with n $=$ 2.56 ± 0.20–2.65 ± 0.17 across various liquid fuels, unaffected by the presence of support fibres. An even more pronounced departure, with n approaching 3, is observed in droplet combustion within a continuous flame sustained by an auxiliary burner. Theoretically, we develop a more general theory to describe these droplet combustion processes, showing that the observed positive departures mainly result from flame-driven buoyant convection with 2.33 < n < 3, capturing well the experimental data. The same theoretical framework can also account for the negative departures in convection-driven vaporisation processes without flame, thereby providing a unified interpretation for the fundamental distinctions between flame-driven and non-flame-driven droplet vaporisation processes. The present study not only identifies distinct shrinkage power laws that emerge from complexities in these processes, but also reveals the central role of an inherent length scale – arising from underlying convective mechanisms – in shaping the true shrinkage kinetics that lead to violations of the D 2 -law.