Regular Article

Multifractal analysis of biodiesel droplet imprints and estimation of the fractal surface energy of the spray

Zhytomyr State Technological University, Chernyakhovsky Street, 103, Zhytomyr 10005, Ukraine

^a e-mail: moskvinpavel56@gmail.com

Received: 19 January 2017
Revised: 16 May 2017
Accepted: 24 May 2017
Published online: 14 June 2017

Abstract

The multifractal (MF) analysis of the surface areas and the volumes of fuel spray droplet imprints, which formed on the surface of a glass plate covered with a soot layer, is presented. The input information for the MF analysis was obtained from photographic images of imprints of droplets of biodiesel, diesel and their mixtures. The parameters for the MF spectra of the surface areas and the volumes of fuel droplet imprints are calculated for different biodiesel and diesel ratios in the mixtures. The correspondence of the multifractal functions to their canonical forms is demonstrated. Quantitative relationships between the parameters of MF spectra and the composition of dispersed fuels are revealed. On the basis of a formal approach and data on the multifractal parameters for the volume and the area of imprints of atomized fuel droplets the mathematical expression which takes into account the contribution of the fractal surface structure of the spray into its surface energy was proposed. The behavior of the surface energy of the system depending on the fractal parameters that describe the volume and the area of the fractal surface was discussed.