scholarly journals Fractal Properties of Pore Distribution of Electrospun Nanofiber Membrane

2020 ◽  
pp. 96-105
Author(s):  
Bai Chun- Yu ◽  
Chen Ying ◽  
Liu Yong ◽  
Shi Luo- Yi ◽  
Chen Ru- Dong
Keyword(s):  
Fractal Dimension ◽  
Flow Resistance ◽  
Fractal Theory ◽  
Pore Width ◽  
Electrospun Nanofiber ◽  
Nanofiber Membrane ◽  
Average Pore ◽  
Fractal Properties ◽  
Width Distribution ◽  
The Relationship

Due to the complex and chaotic characteristics of elecrtospun nanofiber membrane, fractal theory is a suitable mathematical framework. Using the fractal theory, Matlab and other computer software in Mathematics, the fractal properties of pore distribution of elecrtospun nanofiber membrane and the relationship between the fractal dimension and the physical properties of nonwovens are studied. Thirty samples were produced by using polyvinyl alcohol (PVA)on the DXES-01 automatic electrostatic spinning machine; BMP images of 30 samples were obtained by TM-1000 table scanning electron microscope; The scanning electron micro-scope images were grayed by digital image processing technology, and the average pore width of the samples was further calculated by Matlab software from the gray value matrix; G-P algorithm is used to calculate the fractal dimension of pore width distribution; The relationship between air flow resistance and the fractal dimension of pore width distribution of electrospun nanofiber membrane was analyzed. Finally, the correlation fractal dimension of the average pore width of electrospun nanofiber membrane has a quadratic function relation with the air flow resistance; The correlation fractal dimension of the average pore width obtained is consistent with the fractal dimension of porosity obtained by Ting Wang under the meaning of the relative error less than 10%is the same.

scholarly journals Blood physiological and flow characteristics within coronary artery circulatory network for human heart based on vascular fractal theory

2020 ◽  
Vol 12 (7) ◽  
pp. 168781402093338
Author(s):  
Yan-li Chen ◽  
Gui-Qiang Bai ◽  
Liu-xing Ren ◽  
Yang Bai ◽  
Meng-yao Sun ◽  
...  
Keyword(s):  
Blood Flow ◽  
Fractal Dimension ◽  
Coronary Artery ◽  
Flow Resistance ◽  
Fractal Theory ◽  
Flow Characteristics ◽  
Fractal Dimensions ◽  
Vascular Network ◽  
Capillary Diameter ◽  
The Relationship

To analyze the fractal form of the vascular network in the human circulatory system, the optimal transport effect has been achieved from the point of view of biological evolution. The blood flow mathematical models based on the fractal theory for capillary network and arteriole–capillary vascular fractal network were established using theory derivation, and the blood flow characteristics, dynamic flow resistance effects, and vascular fractal physiology property based on the fractal porous medium theory for the coronary artery circulatory network were analyzed under the consideration of some influencing factors, namely, non-Newtonian fluid characteristics of blood, hemocoagulation and embolization effect in capillaries, and plasma mass flow effects. Moreover, the Poiseuille flow equation is modified by introducing the correction function, and the flow model of blood in the vascular network is established. Obviously, the relationship characteristics between blood flow and bifurcation grade in fractal vascular, fractal dimension in the arteriole–capillary vascular network, fractal dimensions of the diameter of capillary tubular diameter, fractal dimensions of capillary blood vessels, blood Casson yield stress, and ratio of red blood cell radius to capillary diameter can be obtained. And the relationship characteristics between blood flow resistance and ratio of erythrocyte radius to capillary diameter, ratios of the distance between adjacent red blood cells to the radius of red cells, and bifurcation grade can be obtained. Finally, the clinical verification tests were accomplished to verify the theory is worthy of authenticity and rationality where the curve tendencies are very similar with those obtained by numerical simulations based on the theoretical models and experimental test showed that the theoretical calculation and simulation analysis of blood circulation system of fractal vascular network were reasonable and applicable by means of experimental relative method because of the maximum relative error is less than 10%, whatever fractal dimension m changes under different conditions.

EFFECT OF FRACTAL FRACTURES ON PERMEABILITY IN THREE-DIMENSIONAL DIGITAL ROCKS

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940015 ◽  
Author(s):  
WEIFENG LV ◽  
GUOLIANG YAN ◽  
YONGDONG LIU ◽  
XUEFENG LIU ◽  
DONGXING DU ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Fractured Reservoirs ◽  
Three Dimensional ◽  
Absolute Permeability ◽  
Fracture Aperture ◽  
Fracture Networks ◽  
Discrete Fracture Networks ◽  
Discrete Fracture ◽  
The Relationship

The fracture has great impact on the flow behavior in fractured reservoirs. Fracture traces are usually self-similar and scale-independent, which makes the fractal theory become a powerful tool to characterize fracture. To obtain three-dimensional (3D) digital rocks reflecting the properties of fractured reservoirs, we first generate discrete fracture networks by stochastic modeling based on the fractal theory. These fracture networks are then added to the existing digital rocks of rock matrixes. We combine two low-permeable cores as rock matrixes with a group of discrete fracture networks with fractal characteristics. Various types of fractured digital rocks are obtained by adjusting different fracture parameters. Pore network models are extracted from the 3D fractured digital rock. Then the permeability is predicted by Darcy law to investigate the impacts of fracture properties to the absolute permeability. The permeability of fractured rock is subject to exponential increases with fracture aperture. The relationship between the permeability and the fractal dimension of fracture centers is exponential, as well as the relationship between permeability and the fractal dimension of fracture lengths.

PORE STRUCTURE CHARACTERIZATION FOR A CONTINENTAL LACUSTRINE SHALE PARASEQUENCE BASED ON FRACTAL THEORY

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940006 ◽  
Author(s):  
LEI ZHANG ◽  
XUEJUAN ZHANG ◽  
HAO CHAI ◽  
YAOCAI LI ◽  
YONGJIE ZHOU
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Clay Mineral ◽  
Mineral Content ◽  
Fractal Theory ◽  
Average Pore Size ◽  
Structure Characterization ◽  
Imaging Method ◽  
Average Pore

Fractal dimension is an important parameter in the evaluation of tight reservoirs. For an outcrop section of the Nenjiang formation in the Songliao Basin, China, the pore structure and pore fractal characteristics of shale parasequences were investigated using fractal theory. In addition, factors causing pore structure changes were analyzed using the results of low-temperature nitrogen adsorption and scanning electron microscope (SEM) experiments. Conducive to gas migration and secondary pores development such as dissolution, results showed that nanoscale pores dominated by fracture-like morphology and consequent good internal connectivity were observed in each pore size section within the target layer. Each parasequence is characterized by a sequential upward decrease of average pore size and an upward increase of total pore volume, with an increasing number of pores from 2[Formula: see text]nm to 50[Formula: see text]nm. Pores are isolated from each other, with poor connectivity and relatively complex composition of brittle minerals and clay minerals. Main components of the brittle minerals, quartz and feldspar, occur in 20–50% and higher clay mineral content ranging from 50% to 70%. In the parasequence cycle, clay mineral gradually decreases while the brittle mineral content increases. Fractal dimension is negatively correlated with clay mineral content and positively correlated with brittle mineral (quartz and feldspar) content. The fractal dimension calculated by the imaging method and the FHH method shows an upward increasing tendency in each of the parasequence cycles. This is as a result of different phenomena, varied sediment hydrodynamic forces leading to particle size differences and increased brittle minerals resulting in microcracks, therefore, the fractal dimension of the large pores (imaging method) increases upward in the parasequence. Simultaneously, with increased content and accompanied dissolution of brittle minerals causing an increase of small pores from base to top of the parasequence, the fractal dimension of the small pores (FHH method) grows.

scholarly journals Experimental Study on Pore Characteristics and Fractal Dimension Calculation of Pore Structure of Aerated Concrete Block

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Jun Fu ◽  
Yue Yu
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Fractal Theory ◽  
Concrete Block ◽  
Average Diameter ◽  
Pore Characteristics ◽  
Average Pore ◽  
X Ray ◽  
Matlab Program ◽  
Aerated Concrete

It is important to control and predict the macroscopic properties through pore structure parameters of cement-based materials. Microscopic pore structure of concrete has many characteristics, such as sizes and disordered distribution. It is necessary to use fractal theory to describe the pore structure of concrete. In order to establish the relationship between the pore structure characteristics of aerated concrete and porosity, shape factor, pore superficial area, average pore diameter, and average diameter, the fractal dimension of the pore structure was used to evaluate the pore structure characteristics of aerated concrete. The X-ray computed tomography (CT) images of the aerated concrete block pore structure were obtained by using the XTH320 series X-ray three-dimensional microscope. The pore characteristics of aerated concrete block were studied according to Image-Pro Plus (IPP). Based on the research of the fractal dimension measurement methods, the proposed MATLAB program automatically determined the fractal dimension of the aerated concrete block pore structure images. The research results indicated that the small pores (20 μm∼60 μm) of aerated concrete block account for a large percentage compared with the large pores (60 μm∼400 μm or more) from pore diameter distribution and the pore structure of aerated concrete block has obvious fractal features and the fractal dimension of aerated concrete block pore structure images were calculated to be in the range of 1.775–1.805. The pore fractal dimension has a strong correlation with the pore fractal characteristics of aerated concrete blocks. The fractal dimension of the pore structure linearly increases with porosity, shape factor, and pore surface area. The fractal dimension of the pore structure decreases with the average pore size and average diameter. Thus, the fractal dimension of the pore structure that is calculated by the MATLAB program based on fractal theory can be assumed as the integrative evaluation index for evaluating the pore structure characteristic of aerated concrete block.

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

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 860
Author(s):  
Qingshan Duan ◽  
Jiejie An ◽  
Hanling Mao ◽  
Dongwu Liang ◽  
Hao Li ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Theory ◽  
Inorganic Materials ◽  
Packaging Materials ◽  
Analysis Method ◽  
Characteristic Parameters ◽  
Fractal Characteristic ◽  
Fractal Characteristics ◽  
The Relationship

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.

Study about Characteristics of Cement Paste on Fractal Theory

2013 ◽  
Vol 423-426 ◽  
pp. 1051-1054
Author(s):  
Tian Yang Zhai
Keyword(s):  
Compressive Strength ◽  
Fractal Dimension ◽  
Cement Paste ◽  
Permeability Coefficient ◽  
Fractal Theory ◽  
Fractal Model ◽  
Concrete Compressive Strength ◽  
Internal Pore Structure ◽  
The Relationship ◽  
Internal Pore

A fractal model to simulate cement paste internal pore structure, and on this basis deduce that fractal dimension is D and the corresponding pore is r, the relationship between porosity is P. MIP was measured test. Then calculated the different ages of the fractal dimension of cement and concrete compressive strength, tensile strength and permeability coefficient. The results showed that: compressive strength, permeability and fractal dimension has a good correlation. Whey in cement in the process of hydration of cement products continue to fill the pores, making the compressive strength increased 70%, permeability is declining.

Particles Gradation Optimization of Blasting Rockfill Based on Fractal Theory

2011 ◽  
Vol 366 ◽  
pp. 469-473 ◽  
Author(s):  
Sheng Zhu ◽  
Yan Ming Feng ◽  
Shu Rong Feng ◽  
Wu Yi Chen
Keyword(s):  
Fractal Dimension ◽  
Test Data ◽  
Fractal Theory ◽  
Average Diameter ◽  
Optimization Method ◽  
Dry Density ◽  
Rock Blasting ◽  
Rockfill Dam ◽  
Under Construction ◽  
The Relationship

Based on fractal theory, used the index of rockfill compaction characteristics(granularity fractal dimension) which conforms to Talbot curve distribution, combined with blasting schemes and rolling test data of several domestic rockfill dams, the relationship is established between compacted rockfill’s dry density and rock blasting parameters by rockfill granularity fractal dimension and its average diameter, and that provided the basis for rockfill particle grading optimization method. The method is applied by rockfill of JIANGPINGHE dam under construction, and the results show that this method can well reflect the intrinsic relation between rock blasting and rockfill compaction, which can be applied to particle grading design of rockfill dam.

scholarly journals A study on the effects of the fractal characteristics of aggregates on the mechanical behavior of cemented sand and gravel

2021 ◽  
Vol 71 (342) ◽  
pp. e250
Author(s):  
L. Guo ◽  
S. Li ◽  
L. Zhong ◽  
L. Guo ◽  
L. Wang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Elastic Modulus ◽  
Fractal Theory ◽  
Peak Stress ◽  
Aggregate Gradation ◽  
Cemented Sand ◽  
Ordinary Concrete ◽  
Fractal Characteristics ◽  
Sand And Gravel ◽  
The Relationship

Owing to complex aspects of cemented sand and gravel (CSG), such as included unscreened aggregates, CSG properties differ from those of ordinary concrete. Fractal theory is introduced to study the effects of aggregate characteristics on CSG properties, quantifying aggregate gradation and shape. Numerical simulation and analyses show that: (1) improved aggregate gradation decreases the gradation fractal dimension and increases the CSG peak stress and elastic modulus; (2) more irregularly shaped aggregates increase the shape fractal dimension and decrease the CSG peak stress and elastic modulus; (3) the relationship quantified between aggregate characteristics and CSG mechanical properties provides a theoretical basis for aggregate allocation in engineering design and construction. Mixing artificial aggregates can improve aggregate gradation but reduces CSG performance. Appropriately blending artificial and on-site aggregates achieves optimal CSG performance; in this study, this is attained using 20% artificial aggregates added under standard gradation.

Fractal Characteristics of the Middle-Upper Ordovician Marine Shale Nano-Scale Porous Structure from the Ordos Basin, Northeast China

2021 ◽  
Vol 21 (1) ◽  
pp. 274-283
Author(s):  
Liang Liu ◽  
Wuling Mo ◽  
Min Wang ◽  
Nengwu Zhou ◽  
Yu Yan ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Ordos Basin ◽  
Fractal Dimensions ◽  
Upper Ordovician ◽  
Average Pore ◽  
Marine Shale ◽  
Fractal Characteristics ◽  
The Relationship

The fractal characteristics of marine shale from the Middle-Upper Ordovician Wulalike Formation (O2w) in the southwest margin of the Ordos Basin are studied. Based on low-temperature nitrogen adsorption experiments, the FHH (Frenkel-Halsey-Hill) model was employed to investigate the relationship between the marine shale composition, such as TOC, mineral content and shale gas content, and pore structure parameters, such as BET specific surface area, average pore diameter, porosity and fractal dimension. The results show that the pore size distribution curve of shale slowly decreased after the pore size was greater than 50 nm, the pore size distribution showed multiple peaks, and the peak value was mainly in the range of 2–10 nm. Most pores are nanopores, although the pore type and shape are different. Two different fractal dimensions D1 and D2 are obtained from the two segments with relative pressures of 0–0.5 and 0.5–1.0, respectively: the D1 range is 2.77–2.82, and the D2 range is 2.63–2.66. As D1 is larger than D2, the pore structure of small pores is more uniform than that of large pores in the shale samples. The relationship between the fractal dimensions D1 and D2 and the total organic carbon (TOC) content is a convex curve. Fractal dimension D reaches its maximum when TOC is 0.53 wt.%. Fractal dimension D decreases with increasing specific surface area, porosity and average pore size. The fractal dimension has a different influence on the gas storage and migration in shale; the larger the fractal dimension is, the stronger the heterogeneity and the more complex the pore structure, and this outcome is conducive to the storage of gas in shale but not beneficial to the permeability and production of gas.

Study on the Distribution Law of the Crashed Coal Fragmentation

2011 ◽  
Vol 189-193 ◽  
pp. 1834-1839
Author(s):  
Jia Jia Zhang ◽  
Chang Long Du ◽  
Song Yong Liu ◽  
Hao Jiang
Keyword(s):  
Fractal Dimension ◽  
Weibull Distribution ◽  
Fractal Theory ◽  
Mathematic Model ◽  
Distribution Functions ◽  
Distribution Law ◽  
Characteristic Index ◽  
Fractal Distribution ◽  
The Relationship ◽  
Fragmentation Degree

In order to find the distribution law of coal fragmentation, mathematic model of size distribution was built according to fractal theory. Based on this, the experiments of impactive crash were carried out under different impact rate and different Protodikonov's hardness. The comparison between Weibull distribution and fractal distribution was done so as to find the relationship between the influence parameters and the coal fragmentation characteristic index, the coal fragmentation degree coefficient and the fractal dimension. The results indicate that both two types of distribution functions are suitable for the distribution discipline of coal fragmentation, but the relationship of the coal fragmentation degree and impact parameter is not reacted correctly by the coal fragmentation characteristic index and coal fragmentation degree coefficient in the Weibull distribution while the coal fragmentation degree could be expressed by the fractal dimension in fractal distribution. The relationships between the fractal dimension and the rate, the Protodikonov's hardness of coal are linear.

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