多孔结构分形分析及其在材料性能预报中的应用

Fractal Analysis of Pore Structure and Its Application for Prediction of Permeability and Porosity

摘要:

采用分形理论表征孔隙的结构特征，通过对烧结不锈钢纤维多孔材料的扫描电镜（SEM）照片进行图像处理和分形分析，详细研究图像分辨率、获取图像时的放大倍数、灰度图转化为二值图时阈值的大小等因素对孔结构分形分析结果的影响，并研究它们与分形维数的定性关系。结果表明，采用的烧结纤维多孔材料具有明显的分形特征，图像分辨率、放大倍数、阈值等因素对分形维数计算结果影响显著：与SEM图像的原始分辨率相比，分辨率变化越大则分形维数越大；分形维数随着放大倍数的增大而减小；灰度图转化为二值图时的阈值存在最佳值，且随着阈值的增大，分形维数先增大后减小。通过理论推导，建立了多孔材料孔隙度和渗透性能与孔结构分形维数之间的数学关系。可通过孔结构分形维数、面孔隙度、孔径等参数合理预测多孔材料的体孔隙度、渗透性能，预测结果与实测结果吻合良好。

Abstract:

Fractal theory was applied to characterize pore structure. By image processing and fractal analysis for SEM images of sintered stainless steel fiber porous materials, the influence of image resolution, magnification, and the threshold value from grayscale image to binary image on fractal analysis results of pore structure is investigated and their qualitative relationship with fractal dimension was also studied. The results indicate that sintered porous fiber materials have typical fractal nature; the image resolution, magnification and threshold value obviously impact fractal dimension: the larger the difference between original and applied resolution is, or the smaller the magnification is, the larger the fractal dimension becomes; there is a best threshold value for SEM image conversion from grayscale image to binary image, and with the threshold value increasing, the fractal dimension increases and then decreased. The mathematical relations between fractal dimension of pore structure and porosity as well as permeability of porous materials are also discussed. It is feasible to predict the porosity and permeability through the fractal dimension, surface porosity, pore size and other parameters reasonably and the predicted results are in good agreement with the measured results.