M2P 2023

Membrane Characterization via Fractal Dimension Analysis

  • Jahangiri, Ali Reza (Lund University)
  • Mohammadi Amin, Meisam (DTU)

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Membranes are essential components in many industrial and biological processes, including water treatment, desalination, and biotechnology. The performance of these membranes is determined by their structural properties, including the size and shape of the pores, the tortuosity of the channels, and the roughness of the surface. In recent years, there has been a growing interest in using fractal dimension analysis to predict the performance of membranes, including in the domain of solid state physics. We can make use of this knowledge and bring it to the field of membrane technology. Fractal dimension is a mathematical concept that describes the degree of irregularity or complexity of a geometric shape. It can be used to quantify the roughness of a surface, the branching of a network, or the self-similarity of a pattern. The fractal dimension of a membrane can be estimated from its SEM (scanning electron microscopy) image, which provides a high-resolution visual representation of the surface. Via image processing, we can distill the 2D matrix into a representative number that is then linked to the performance characteristics. This will allow us to identify trends, narrow down the fabrication parameters. To perform fractal dimension analysis on SEM images of membranes, the following steps can be taken: 1) Acquire SEM images of the membrane at different magnification, 2) Pre-process the images to remove noise, improve contrast, and enhance the edges, 3) Use image analysis software to segment the image into regions of interest, such as the pores or the channels, 4) Compute the fractal dimension of each segmented region using a fractal dimension estimation algorithm, such as the box-counting method or the power-law method, 5) Compare the fractal dimension of the segments with the performance characteristics of the membrane, such as the permeability or the rejection rate. The fractal dimension of the segments should be positively correlated with the performance characteristics of the membrane. A higher fractal dimension indicates a higher degree of irregularity or complexity, which should result in a higher permeability or a lower rejection rate. The fractal dimension can also be used to classify the membrane into different types or grades, based on their structural properties. It is concluded that fractal dimension analysis of SEM images is a powerful tool for predicting the performance of membranes.