Progress in the Application of Fractal Porous Media Theory to Property Analysis and Process Simulation in Melt Crystallization

Abstract

The application of fractal porous media (FPM) theory in melt crystallization is a novel concept to be developed extensively, which has received wide attention in recent years. The primary advantage of FPM theory is the ability to describe the complex, random structure of porous crystal layers with fewer parameters. This review will introduce aspects of the property analysis of porous crystal layers grown in the heterogeneous thermal field. For the first time, the existing flow model of FPM theory will be outlined and an overview of the general issues, model modification, and validation of the separation process in melt crystallization will be discussed in detail. Kinetic and model research on separation evaluation and optimized operation will be mentioned to unfold the promising application field. Finally, the paper will conclude with perspectives on the future research directions, key challenges, and issues in this area.

Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation

“…(4) with the experimental data by several investigators and found that the ratio of 3 10 ξ − = best fits the experimental data for different porous media. Similar conclusions can be also found in other applications of fractal theory [66,[72][73][74]. Considering that the pores in porous media are analogous to the particles in nanofluids, Eq.…”

Recent advances in melt crystallization, towards process intensification and technique development

“…Several authors discussed the fractal parameters, including porosity, effective porosity, characteristic factor, permeability, etc. 36–39 Recently, several evaluated parameters have been proposed to correlate the sweating process with separation results. Generally, the separation results consist of the yield and purity of the target products, and the sweating process parameters include temperature, heating rate, and sweating time.…”

A Discussion on Fractal Models for Transport Physics of Porous Media

“…Over the past three decades, fractal geometry theory has sparked considerable interest in many disciplines to characterize irregular or disordered objects such as porous media, rough surfaces, fractures, aggregates, granular materials, melt crystallization, etc. [2][3][4][5][6][7][8][9][10] It has been shown by numerous experimental studies that many natural and some synthetic porous media are fractal, i.e. they are self-similar or self-affine over several length scales.…”

“…of porous media. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Table 1 lists the fractal models for number-size distribution of porous media. As can be seen in Table 1, different fractal models for the relationship between the porosity and fractal dimension were proposed by different researchers, and the definitions of fractal dimension are also diverse.…”