Towards an interpretation of the scale diffusivity in liquid atomization process: An experimental approach

Recent investigations have presented an application of the scale entropy diffusion theory to model liquid atomization process. This theory describes multi-scale behavior by a diffusion equation of the scale entropy function. In atomization, this function is related to the scale-distribution which provides a measurement of the specific-length of the eroded liquid system according to the scale of erosion. The present paper performs a detailed description of the scale diffusion mechanism for the atomization process of a liquid jet emanating from a gasoline injector with the objective of determining the scale diffusivity parameter introduced by the diffusion theory. The 2-D description of the gasoline jet as a function of the injection pressure reveals that the scale space is divided into two regions according to the sign of the scale specific-length variation rate: The small-scale region refers to the scales that undergo an elongation mechanism whereas the large-scale region concerns the scales that undergo a contraction mechanism. Furthermore, two phases of the atomization process are identified depending on whether the elongation mechanism is governed by the jet dynamics or surface tension effects. A non-dimensional number segregating these two phases is established. During the atomization process, the contraction mechanism diffuses in the small scale region. This manifests by a temporal decrease of the scale with a zero specific-length variation. It is found that the scale diffusivity parameter can be determined from the evolution of this characteristic scale in the second phase of the atomization process.