基于图像的多孔材料特征分析与物性测量研究
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摘要
多孔材料是一种性能优异的新型工程材料,其微观结构是影响宏观物性和使用效果的关键因素之一。多孔材料微观结构的定量表征及其对物性的影响一直是材料科学与工程领域的焦点和难点。大多数商业软件和仪器设备都没有涉及该领域,不具备物性测量的功能。本文采用图像测量技术分析并测量多孔材料的微观特征量。主要研究内容如下：
首先分析了目前多孔材料微观结构测量方法的优缺点,提出了基于图像算法测量多孔材料微观结构参数,采用分形表征多孔材料微观特征,建立物性与微观特征之间的关联,以实现物性测量。
目前测量多孔材料微观结构参数主要采用实验方法,存在周期长、成本高、易受环境影响的缺点,本文基于多孔材料的扫描电镜图片,分析比较了迭代法和递归法标记孔洞的缺点,利用回溯孔洞标记法测量出多孔材料的孔面积、孔周长、孔隙率等微观结构参数。
多孔材料复杂的微观结构难以用欧氏几何准确表征,而分形理论在描述各种无序或随机结构上颇具优势。本文对比分析了5种分形维数测定方法,选择盒维法作为多孔材料分形维数的测定方法,并用该方法测量图像的孔隙面积分形维数。
在分析国内外研究进展的基础上,推导了多孔材料渗透率与微观结构参数和分形维数之间的函数关系式,结合多孔材料的微观结构参数和孔隙面积分形维数、曲线分形维数可以预测多孔材料的渗透率,理论值和实验数据吻合较好。
本文基于分形技术来表征多孔材料的微观特征,结合图像算法测量得到其微观结构参数,实现了多孔材料的物性测量。
Porous media is a new engineering material with high performance. Its microstructure is one of the key factors which affect macro material property and performance. The description of microstructure of porous media and its connection with material property have always been the focus and difficulty in the field of materials science and engineering. However, Most commercial software and equipments don't have material parameters measurement function. The studies as follow:
Firstly, the current measurement methods of microstructure have been analyzed and compared. Then the author of this paper uses image algorithms to measure micro-structure parameters, and applies fractal to describe micro-features of porous media, and establish the connection between material property and micro features.
The author of this paper analyzes and compares iterative method, recursive method, and presents a new backtracking algorithm to mark the pore regions based on the scanning electron microscope. Then microstructure parameters such as area of pore, the perimeter of pore and porosity are measured.
Five kinds of methods are adopted to compute fractal dimension. The measuring data are processed and analyzed so as to choose a suitable method. Box-counting method is chosen in the fractal dimension computation of porous media, and then the pore area fractal dimensions are determined by this method.
Fractal model of permeability is presented based on the world progress. The permeability parameter of porous media can be predicted by using the microstructure parameters, pore area fractal dimension and tortuosity fractal dimension. The computed result agrees well with the experimental data.
In this paper, fractal theory and image processing are combined to realize measurement of porous media.
首先分析了目前多孔材料微观结构测量方法的优缺点,提出了基于图像算法测量多孔材料微观结构参数,采用分形表征多孔材料微观特征,建立物性与微观特征之间的关联,以实现物性测量。
目前测量多孔材料微观结构参数主要采用实验方法,存在周期长、成本高、易受环境影响的缺点,本文基于多孔材料的扫描电镜图片,分析比较了迭代法和递归法标记孔洞的缺点,利用回溯孔洞标记法测量出多孔材料的孔面积、孔周长、孔隙率等微观结构参数。
多孔材料复杂的微观结构难以用欧氏几何准确表征,而分形理论在描述各种无序或随机结构上颇具优势。本文对比分析了5种分形维数测定方法,选择盒维法作为多孔材料分形维数的测定方法,并用该方法测量图像的孔隙面积分形维数。
在分析国内外研究进展的基础上,推导了多孔材料渗透率与微观结构参数和分形维数之间的函数关系式,结合多孔材料的微观结构参数和孔隙面积分形维数、曲线分形维数可以预测多孔材料的渗透率,理论值和实验数据吻合较好。
本文基于分形技术来表征多孔材料的微观特征,结合图像算法测量得到其微观结构参数,实现了多孔材料的物性测量。
Porous media is a new engineering material with high performance. Its microstructure is one of the key factors which affect macro material property and performance. The description of microstructure of porous media and its connection with material property have always been the focus and difficulty in the field of materials science and engineering. However, Most commercial software and equipments don't have material parameters measurement function. The studies as follow:
Firstly, the current measurement methods of microstructure have been analyzed and compared. Then the author of this paper uses image algorithms to measure micro-structure parameters, and applies fractal to describe micro-features of porous media, and establish the connection between material property and micro features.
The author of this paper analyzes and compares iterative method, recursive method, and presents a new backtracking algorithm to mark the pore regions based on the scanning electron microscope. Then microstructure parameters such as area of pore, the perimeter of pore and porosity are measured.
Five kinds of methods are adopted to compute fractal dimension. The measuring data are processed and analyzed so as to choose a suitable method. Box-counting method is chosen in the fractal dimension computation of porous media, and then the pore area fractal dimensions are determined by this method.
Fractal model of permeability is presented based on the world progress. The permeability parameter of porous media can be predicted by using the microstructure parameters, pore area fractal dimension and tortuosity fractal dimension. The computed result agrees well with the experimental data.
In this paper, fractal theory and image processing are combined to realize measurement of porous media.
引文
[1]Gibson L J, Ashby M F. Cellular Solids:Structure and properties-Second edition[M]. Cambridge:Cambridge university Press,1997:12-28.
[2]Davies G J, Shu Z. Metallic foams their production properties and applications[M]. China J Mater Sci,1983:1899-1911.
[3]Liu P S, Liang K M. Functional materials of porous metal made by P/M electroplating and some other techniques[J]. Journal of Materials Science,2001,36(1):5069-5072.
[4]Banhart J, Manufacture characterization and application of cellular metals and metal foams[J]. Progress in Materials Science,2001,46(1):559-632.
[5]Liu P S, Yu B, Hu A M, etal. Development in application of porous metals[J].Trans. Nanferrous Met Soc.,2001,11(5):629-638.
[6]Liu W, Peng S W, Mizukami K. A general mathematical modeling for heat and mass transfer in unsaturated porous media:an application to free evaporative cooling[J]. Heat and Mass Transfer,1995,31(l):49-55.
[7]蒋林华,朱卫华,夏颂佑.粉煤灰水泥浆体的分形结构研究[J].河海大学学报,1999,1(1)：58-62.
[8]刘小君.表面形貌的分形特征研究[J].合肥工业大学学报,2000,23(2)：236-239.
[9]Mandelbrot B B. The fractal geometry of nature [M]. San Francisco:Freeman,1982:23-57.
[10]许祥在,翟秋兰.多孔材料的孔径分布与渗透性测定[J].分析仪器,1999,(4)：48-52.
[11]施斌,李生林.粘性土微观结构SEM图象的定量研究[J].中国科学(A辑),1995,25(6)：666-672.
[12]熊承仁,唐辉明,刘宝琛,张家生利用SEM照片获取土的孔隙结构参数[J].地球科学-中国地质大学学报,2007,32(3)：415-419.
[13]浦红,杨峥,陈斌.用计算机图像处理软件定量分析SEM图像[J].物理测量,2004,(1)：30-32.
[14]Zhang J R, Liu Y Z, Liu Z D. Quantitative Analysis of Micro-porosity of Eco-material by Using SEM Technique [J]. Journal of Wuhan University of Technology——Mater Sci Ed, 2004,19(2):35-37.
[15]张季如,祝杰,黄丽,黄文竞.土壤微观结构定量分析的IPP图像技术研究.武汉理工大学学报,2008,30(4)：80-83.
[16]Chang J, Yortsos YC. Pressure Transient Analysis of Fractal Reservoirs[J]. SPEFE,1990,5(1):31-38.
[17]Katz A J, Thompson A H. Fractal sandstone pores:Implications for conductivity and pore formation[J]. Phys. Rev. Lett,1985,""(54):1325-1328.
[18]Acuna J A, Ershagghi I, Yortsos Y C. Practical Application of Fractal Pressure Transient Analysis of Naturally Fractured Reservoirl. soc. Pet EngForm Eval,1995,10(3):173-179.
[19]孔祥言,李道伦,卢德唐.分形渗流基本公式及分形油藏样板曲线[J].西安石油大学学报(自然科学版),2007,22(2)：1-3.
[20]郁伯铭.多孔介质输运性质的分形分析研究进展[J],力学进展,2003,33(3)：333-346.
[21]刘晓丽,梁冰,薛强.多孔介质渗流率的分形描述[J],水科学进展,2003,14(6)：769-772.
[22]刘俊亮,田长安,曾燕伟,董彪.分形多孔介质孔隙微结构参数与渗透率的分维关系[J].水科学进展,2006,17(6)：812-817.
[23]陈永平,施明恒.基于分形理论的多孔介质渗透率研究[J].清华大学学报,2001,40(12)：94-97.
[24]Pitchumani R, Yao S C. Correlation of thermal conductivities of unidirectional fibrous composites using local fractal technique. ASME J. Heat Transfer,1991,113(4):788-796.
[25]Shi Y, Xiao J S, Pan M, Yuan R Z. A fractal permeability model for gas diffusion layer of PEM fuel cells[J]. Journal of Power Sources,2006,""(160):277-283.
[26]熊承仁,唐辉明,刘宝琛,张家生.利用SEM照片获取土的孔隙结构参数[J].地球科学——中国地质大学学报,2007,32(3)：415-419.
[27]毛灵涛,薛茹,安里千.MATLAB在微观结构SEM图像定量分析中的应用[J].电子显微学报,2004,23(05)：579-583.
[28]秦宣云,崔彩虹,谷成玲,郑洲顺.双重分形多孔介质孔隙率的研究[J].佳木斯大学学报,2008,26(05)：680-682.
[29]李小川,施明恒.多孔介质热导率的数值计算[J].工程热物理学报,2008,29(02)：291-293.
[30]章毓晋.图像处理和分析[M].北京：清华大学出版社,1998：19-21.
[31]Mandelbrot B B. The Fractal Geometry of Nature[M]. New York:Freeman,1982:23-57.
[32]张济忠.分形[M].北京：清华大学山版社,1995：41-65.
[33]K.法尔科内著.分形几何-数学基础及其应用[M].沈阳：东北大学出版社,1991：147-183.
[34]Zhang J R, Liu Y Z, Liu Z D. Quantitative Analysis of Micro-porosity of Eco-material by Using SEM Technique [J]. Journal of Wuhan University of Technology——Mater Sci Ed, 2004,19(2):35-37.
[35]朱名江.递归算法[J].中文信息,2002,(08)：36-39.
[36]俞杰,许化溪.一种易于实现的适于细胞图像连通区域的标记算法[J].江苏大学学报医学版,2005,15(2)：152-155.
[37]严蔚敏,陈文博编著.数据结构及应用算法教程[M].北京：清华大学出版社,2001：158-161.
[38]赵玲.回溯在多孔介质孔径测量中的应用研究[J].武汉理工大学学报信息与管理工程版,2010,32(2)：280-283.
[39]董远.图像分形维数计算技术[J].计算机应用与软件,2001,18(6)：208-212.
[40]胡可乐,李平.Logistic映射中奇怪吸引子的盒维数计算[J].江苏理工大学学报,1998,19(5)：62-65.
[41]Thompson A H, Katz A J, Kroch C E. The Micro geometry and Transport Properties of Sandstones [J]. Advances in Physics,1987,36(5):625-694.
[42]Yu B M, Cheng P. A fractal permeability model for bi-dispersed porous media[J]. Int. J. Heat Mass Transfer,2002,45(1):2983-2993.
[43]Yu B M, Li J H. Some fractal characters of porous media[J]. Fractals,2001,9(3):365-372.
[44]Keller J M, Chen S, Crownover R M. Texture Description and Segmentation through Fractal Geometry[J]. Computer Vision, Graphics, and Image Processing,1989,""(45):150-166.
[45]汪富泉,李后强.分形几何与动力系统[M].哈尔滨：黑龙江教育出版社,1993：125-181.
[46]雷树业,王利群,贾兰庆等.颗粒床孔隙率与渗透率的关系[J].清华大学学报,1998,38(5)：20-28.
[47]Adler P M, Thovert J F. Real porous media:local geometry and macroscopic properties[J]. Appl. Mech. Rev,1998,51(9):537-585.
[48]B M Yu, L J Lee, H Q Cao, A fractal in-plane permeability model for fabrics[J]. Polymer Composites,2002,22(2):201-221.
[49]A.E.薛定愕.多孔介质中的渗流物理[M].北京：石油工业出版社,1982：43-45.
[50]何斌,马天予,朱红莲.Visual C++数字图像处理[M].北京：人民邮电出版社,2004：445-447.
[51]刘培生,马晓明.多孔材料检测方法[M].北京：冶金工业出版社,2006：1-56.
[2]Davies G J, Shu Z. Metallic foams their production properties and applications[M]. China J Mater Sci,1983:1899-1911.
[3]Liu P S, Liang K M. Functional materials of porous metal made by P/M electroplating and some other techniques[J]. Journal of Materials Science,2001,36(1):5069-5072.
[4]Banhart J, Manufacture characterization and application of cellular metals and metal foams[J]. Progress in Materials Science,2001,46(1):559-632.
[5]Liu P S, Yu B, Hu A M, etal. Development in application of porous metals[J].Trans. Nanferrous Met Soc.,2001,11(5):629-638.
[6]Liu W, Peng S W, Mizukami K. A general mathematical modeling for heat and mass transfer in unsaturated porous media:an application to free evaporative cooling[J]. Heat and Mass Transfer,1995,31(l):49-55.
[7]蒋林华,朱卫华,夏颂佑.粉煤灰水泥浆体的分形结构研究[J].河海大学学报,1999,1(1)：58-62.
[8]刘小君.表面形貌的分形特征研究[J].合肥工业大学学报,2000,23(2)：236-239.
[9]Mandelbrot B B. The fractal geometry of nature [M]. San Francisco:Freeman,1982:23-57.
[10]许祥在,翟秋兰.多孔材料的孔径分布与渗透性测定[J].分析仪器,1999,(4)：48-52.
[11]施斌,李生林.粘性土微观结构SEM图象的定量研究[J].中国科学(A辑),1995,25(6)：666-672.
[12]熊承仁,唐辉明,刘宝琛,张家生利用SEM照片获取土的孔隙结构参数[J].地球科学-中国地质大学学报,2007,32(3)：415-419.
[13]浦红,杨峥,陈斌.用计算机图像处理软件定量分析SEM图像[J].物理测量,2004,(1)：30-32.
[14]Zhang J R, Liu Y Z, Liu Z D. Quantitative Analysis of Micro-porosity of Eco-material by Using SEM Technique [J]. Journal of Wuhan University of Technology——Mater Sci Ed, 2004,19(2):35-37.
[15]张季如,祝杰,黄丽,黄文竞.土壤微观结构定量分析的IPP图像技术研究.武汉理工大学学报,2008,30(4)：80-83.
[16]Chang J, Yortsos YC. Pressure Transient Analysis of Fractal Reservoirs[J]. SPEFE,1990,5(1):31-38.
[17]Katz A J, Thompson A H. Fractal sandstone pores:Implications for conductivity and pore formation[J]. Phys. Rev. Lett,1985,""(54):1325-1328.
[18]Acuna J A, Ershagghi I, Yortsos Y C. Practical Application of Fractal Pressure Transient Analysis of Naturally Fractured Reservoirl. soc. Pet EngForm Eval,1995,10(3):173-179.
[19]孔祥言,李道伦,卢德唐.分形渗流基本公式及分形油藏样板曲线[J].西安石油大学学报(自然科学版),2007,22(2)：1-3.
[20]郁伯铭.多孔介质输运性质的分形分析研究进展[J],力学进展,2003,33(3)：333-346.
[21]刘晓丽,梁冰,薛强.多孔介质渗流率的分形描述[J],水科学进展,2003,14(6)：769-772.
[22]刘俊亮,田长安,曾燕伟,董彪.分形多孔介质孔隙微结构参数与渗透率的分维关系[J].水科学进展,2006,17(6)：812-817.
[23]陈永平,施明恒.基于分形理论的多孔介质渗透率研究[J].清华大学学报,2001,40(12)：94-97.
[24]Pitchumani R, Yao S C. Correlation of thermal conductivities of unidirectional fibrous composites using local fractal technique. ASME J. Heat Transfer,1991,113(4):788-796.
[25]Shi Y, Xiao J S, Pan M, Yuan R Z. A fractal permeability model for gas diffusion layer of PEM fuel cells[J]. Journal of Power Sources,2006,""(160):277-283.
[26]熊承仁,唐辉明,刘宝琛,张家生.利用SEM照片获取土的孔隙结构参数[J].地球科学——中国地质大学学报,2007,32(3)：415-419.
[27]毛灵涛,薛茹,安里千.MATLAB在微观结构SEM图像定量分析中的应用[J].电子显微学报,2004,23(05)：579-583.
[28]秦宣云,崔彩虹,谷成玲,郑洲顺.双重分形多孔介质孔隙率的研究[J].佳木斯大学学报,2008,26(05)：680-682.
[29]李小川,施明恒.多孔介质热导率的数值计算[J].工程热物理学报,2008,29(02)：291-293.
[30]章毓晋.图像处理和分析[M].北京：清华大学出版社,1998：19-21.
[31]Mandelbrot B B. The Fractal Geometry of Nature[M]. New York:Freeman,1982:23-57.
[32]张济忠.分形[M].北京：清华大学山版社,1995：41-65.
[33]K.法尔科内著.分形几何-数学基础及其应用[M].沈阳：东北大学出版社,1991：147-183.
[34]Zhang J R, Liu Y Z, Liu Z D. Quantitative Analysis of Micro-porosity of Eco-material by Using SEM Technique [J]. Journal of Wuhan University of Technology——Mater Sci Ed, 2004,19(2):35-37.
[35]朱名江.递归算法[J].中文信息,2002,(08)：36-39.
[36]俞杰,许化溪.一种易于实现的适于细胞图像连通区域的标记算法[J].江苏大学学报医学版,2005,15(2)：152-155.
[37]严蔚敏,陈文博编著.数据结构及应用算法教程[M].北京：清华大学出版社,2001：158-161.
[38]赵玲.回溯在多孔介质孔径测量中的应用研究[J].武汉理工大学学报信息与管理工程版,2010,32(2)：280-283.
[39]董远.图像分形维数计算技术[J].计算机应用与软件,2001,18(6)：208-212.
[40]胡可乐,李平.Logistic映射中奇怪吸引子的盒维数计算[J].江苏理工大学学报,1998,19(5)：62-65.
[41]Thompson A H, Katz A J, Kroch C E. The Micro geometry and Transport Properties of Sandstones [J]. Advances in Physics,1987,36(5):625-694.
[42]Yu B M, Cheng P. A fractal permeability model for bi-dispersed porous media[J]. Int. J. Heat Mass Transfer,2002,45(1):2983-2993.
[43]Yu B M, Li J H. Some fractal characters of porous media[J]. Fractals,2001,9(3):365-372.
[44]Keller J M, Chen S, Crownover R M. Texture Description and Segmentation through Fractal Geometry[J]. Computer Vision, Graphics, and Image Processing,1989,""(45):150-166.
[45]汪富泉,李后强.分形几何与动力系统[M].哈尔滨：黑龙江教育出版社,1993：125-181.
[46]雷树业,王利群,贾兰庆等.颗粒床孔隙率与渗透率的关系[J].清华大学学报,1998,38(5)：20-28.
[47]Adler P M, Thovert J F. Real porous media:local geometry and macroscopic properties[J]. Appl. Mech. Rev,1998,51(9):537-585.
[48]B M Yu, L J Lee, H Q Cao, A fractal in-plane permeability model for fabrics[J]. Polymer Composites,2002,22(2):201-221.
[49]A.E.薛定愕.多孔介质中的渗流物理[M].北京：石油工业出版社,1982：43-45.
[50]何斌,马天予,朱红莲.Visual C++数字图像处理[M].北京：人民邮电出版社,2004：445-447.
[51]刘培生,马晓明.多孔材料检测方法[M].北京：冶金工业出版社,2006：1-56.
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