Abstract
We show both experimentally and theoretically for the first time that the widely used D2-law for describing the shrinking kinetics of a vaporizing droplet is not the true law for single burning droplets under the influence of gravity. Experimentally, the instantaneous diameter D for such a droplet is identified to obey a new kinetic law: Dn decreases linearly with time t, with the exponent n=2.53±0.30−2.69±0.14 for a variety of common liquid fuels such as alkanes and alcohols of low and high boiling hydrocarbons. Theoretically, we develop a phenomenological theory to show n=8/3≈2.67 well capturing the experimental values. The burning rate constant in this new D8/3-law no longer behaves like the thermal diffusivity α of the gas phase but turns into α3ℓ−7/3/g due to the additional inherent fluid-property-determined buoyancy length ℓ under the influence of the gravitational acceleration g. This non-square power law is purely transport determined. It is a consequence of simultaneous momentum, heat, and mass transfer resulted from buoyant convection setup by the blazing flame around the droplet, insensitive to combustion chemistry and detailed reaction kinetics. This study provides not only renewed insights into the multifaceted droplet combustion phenomenon but also possibly new paradigms for a better understanding or characterization of actual fuel droplet combustion processes in normal gravity environments.
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