Size Distribution Function of Droplet in Liquid-Liquid Mixing and Bubble in Gas-Liquid Mixing, Crystal in Crystallization and Crushed Product in Crushing.

Abstract

The size distribution function of particles that present as droplets in liquid-liquid mixing, bubbles in gas-liquid mixing, crystals in crystallization, and crushed materials in crushing, is examined based on consideration of the balance of the external and the internal force/energy of the particle, and from the viewpoint of information entropy. Then, a new size distribution function (PSF), which is the product of the original size distribution function and the realizable probability function of the size of particles, is presented. The same formula style as that of newly presented PSF can be derived also by balancing the external energy calculated from the energy spectrum density distribution function (ESF) for the turbulent flow field and the internal force/energy of particles. Additionally, it is clarified that the size distribution of eddies in the turbulent flow can be deduced from the same viewpoint by considering that a large eddy is segmented by external force/energy and the style of the distribution is isomorphic with that of ESF. In addition, the usefulness of newly presented PSF is clarified by fitting it to the data generated by the traditional three common unimodal PSF; Rosin-Rammler, Normal and Log-Normal size distribution functions. The main advantages of the newly presented PSF are that it is defined based on a clear physical background and that, for all practical purposes, it can replace the three common PSF. Therefore, this newly presented PSF provides a means of presenting and comparing the different size distribution patterns in terms of a single mathematical expression.