The use of the perimeter-area method to calculate the fractal dimension of aggregates

Florio, Brendan J.; Fawell, Phillip D.; Small, Michael

doi:10.1016/j.powtec.2018.11.030

Cited by 47 publications

(23 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The fractal dimension, determined from the dependency between the perimeter and surface area of a particle, indicates the extent of development of the surface of the analyzed particles and allows for precise and unbiased comparison of particle microstructures obtained at various drying temperatures. The fractal image analysis method has been used to analyze surfaces of particles or aggregates, but also to investigate crystallization properties of milk fat, yoghurt microstructure or properties of aggregates in wastewater (Staniewski et al 2015;Smoczyński and Baranowska 2014;Smoczyński et al 2016;Florio et al 2019). Results of image analysis are presented in Table 1, whereas an example of a logarithmic dependency between particle perimeter and surface area is shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

Fractal analysis of the microstructure of milk powders produced at various temperatures

Smoczyński

2020

J Food Sci Technol

View full text Add to dashboard Cite

The quality of milk powder is largely determined during it manufacture process by the morphological characteristics of powder particles. Considering that, the main research objective of this study was to determine whether parameters of the production process contribute to differences in the microstructure of the manufactured powders, and by this means affect their functional traits. To diversify the milk powder production process, various temperatures of the inlet air were used during drying, i.e. 140, 150 and 160°C. An image fractal analysis was employed and powder particle sizes were compared with respective results achieved in the instrumental analysis using the laser diffraction method. Values of fractal dimensions decreased slightly along with drying temperature increase, what demonstrates that the technological parameters are reflected in the microstructure of milk powders produced. Although particle sizes determined with both methods fitted within the same range of values, the contribution of particular fractions slightly differed and the choice of the appropriate approach may not always be unambiguous. Finally, the fractal dimension is a precise parameter which provides the accurate and explicit characteristics of milk powder microstructure and as such should be recommended for the characterization of irregular structures of different food products.

show abstract

Section: Resultsmentioning

confidence: 99%

Fractal analysis of the microstructure of milk powders produced at various temperatures

Smoczyński

2020

J Food Sci Technol

View full text Add to dashboard Cite

show abstract

“…The validities of these two approaches were also reported in previous studies. [ 19,25,28 ] The 2D fractal dimension

D_{f}^{2 D}

obtained by image analysis cannot be directly used as a parameter for the 3D structures but should be converted to the value in the 3D model

D_{f}^{3 D}

. Here, this is performed using an empirical correlation of Equation ) derived by Lee and Kramer [ 26 ] :

D_{f}^{3 D} = - 1.628 D_{f}^{2 D} + 4.6

…”

Section: Resultsmentioning

confidence: 99%

“…The area‐perimeter method is also frequently used for 2D fractal dimension estimation for images, [ 24,25 ] as it has a high correlation with the fractal dimension for the three‐dimensional (3D) structures. [ 26 ] The perimeter P and the area A of the projected surfaces can be measured by the ImageJ software as described in Figure 2D.…”

Section: Materials and Experimental Methodsmentioning

confidence: 99%

Experimental investigation on the microstructure of fluidized nanoparticle agglomerates by TEM image analysis

Liu

Yang

2020

Can J Chem Eng

View full text Add to dashboard Cite

In this paper, the hierarchical solid structures and multiscale pore structures inside fluidized nanoparticle agglomerates (FNPAs) are qualitatively revealed in the transmission electron microscope (TEM) images of ultrathin slices of solidified FNPAs from the bottom of the bed. The micromorphology of aggregates and simple agglomerates, the porosities of pores intra and inter simple agglomerates, and pore size distributions inside FNPAs are quantitatively analyzed by image analysis. The average fractal dimensions of aggregates of about 300 nm‐1000 nm and simple agglomerates of several micrometres are around 1.9 and 2.6 respectively. The pore structure of FNPAs is complex and heterogeneous and displays a multiscale feature. Nearly 50% of the pores intra simple agglomerates have sizes of tens of nanometers and more than half the pores between simple agglomerates are of micrometre scale. The porosities of the pores intra and inter simple agglomerates are about 0.82 and 0.85 respectively.

show abstract

“…The normally used method to extract the fractal feature of packaging materials is to employ the material micromorphology in the preparation process, surface, or fracture morphology of packaging material, and the test data in the property change process of packaging material (e.g., acoustic emission (AE) signal [ 18 ]) to carry out image gray processing and noise reduction processing, respectively. Common methods for calculating fractal dimension include the box counting method [ 19 ], correlation dimension method [ 20 ], Hurst index method [ 21 ], slit island method [ 22 ], yard stick method [ 23 ], area-perimeter method [ 24 ], Sierpiński carpet method [ 25 ], semi-variance method [ 26 ], and power spectral density [ 27 ] (PSD) method. The main methods to obtain object image are scanning electron microscope [ 28 ] (SEM), transmission electron microscope [ 29 ] (TEM), atomic force microscope [ 30 ] (AFM), and other imaging techniques.…”

Section: Basic Theory Of Fractalmentioning

confidence: 99%

Review about the Application of Fractal Theory in the Research of Packaging Materials

Duan

Mao

et al. 2021

Materials

View full text Add to dashboard Cite

The work is intended to summarize the recent progress in the work of fractal theory in packaging material to provide important insights into applied research on fractal in packaging materials. The fractal analysis methods employed for inorganic materials such as metal alloys and ceramics, polymers, and their composites are reviewed from the aspects of fractal feature extraction and fractal dimension calculation methods. Through the fractal dimension of packaging materials and the fractal in their preparation process, the relationship between the fractal characteristic parameters and the properties of packaging materials is discussed. The fractal analysis method can qualitatively and quantitatively characterize the fractal characteristics, microstructure, and properties of a large number of various types of packaging materials. The method of using fractal theory to probe the preparation and properties of packaging materials is universal; the relationship between the properties of packaging materials and fractal dimension will be a critical trend of fractal theory in the research on properties of packaging materials.

show abstract

The use of the perimeter-area method to calculate the fractal dimension of aggregates

Cited by 47 publications

References 20 publications

Fractal analysis of the microstructure of milk powders produced at various temperatures

Fractal analysis of the microstructure of milk powders produced at various temperatures

Experimental investigation on the microstructure of fluidized nanoparticle agglomerates by TEM image analysis

Review about the Application of Fractal Theory in the Research of Packaging Materials

Contact Info

Product

Resources

About