Article Fractal Geometry: Surface Characterization of Printing Paper
Yong Ju Lee , Geon-Woo Kim, Tai-Ju Lee and Hyoung Jin Kim *
Department of Forest Products and Biotechnology, Kookmin University, 77 Jeongneung-ro, Seongbuk-gu, Seoul 02707, Republic of Korea; song0588@kookmin.ac.kr (Y.J.L.); geonu@kookmin.ac.kr (G.-W.K.); leetj@kookmin.ac.kr (T.-J.L.) * Correspondence: hyjikim@kookmin.ac.kr Abstract: This study investigates the surface characteristics of printing papers using fractal geometry, focusing on surface roughness and surface friction as independent properties. The fractal dimension (FD) was analyzed using the power spectral density method, which provided a more distinct characterization of paper surfaces compared to the variogram method. Surface roughness and friction were measured using a stylus-based contact profilometer, and mean absolute deviation (MAD) parameters, such as the mean absolute deviation of surface roughness ( RMAD ) and friction, were calculated to capture surface variability. The results revealed that while conventional parameters, such as roughness average ( Ra ) and the average coefficient of friction, are highly sensitive to measurement conditions, MAD-based parameters demonstrate greater robustness and stability. For instance, the regression equation for RMAD vs. Ra showed a strong correlation, with an R² value close to 1.0. However, the slopes were significantly less than one. Furthermore, FD exhibited weak correlations with surface roughness and friction, with R² values of 0.342 and 0.016, respectively, highlighting its unique ability to characterize autocorrelation or complexity of surface. Additionally, the effects of coating on paper surfaces were evaluated, revealing reduced flocculation of surface profiles but a 5% increase in FD, indicating enhanced surface complexity. These findings underscore the complementary role of FD in providing a comprehensive understanding of surface properties, with potential applications in quality control and the design of paper products.
Keywords: roughness; friction; power spectral density (PSD); profilometry; mean absolute deviation (MAD)
Academic Editor: Carlo Cattani
Received: 17 December 2024 Revised: 2 February 2025 Accepted: 8 February 2025 Published: 17 February 2025
1. Introduction In the papermaking industry, the principles of fractal geometry have been applied to analyze the flowability of powders [1] and the properties of porous media [2,3]. Among these applications, fractal dimension (FD) analysis of the surface roughness of paper products has emerged as a promising approach for evaluating their physical properties [4]. Paper is produced via a filtration process in which pulp stock is deposited onto a forming fabric [5,6]. During this process, fibers, being significantly longer than their thickness, predominantly orient themselves within the plane of the paper, thereby creating a layered structure. The uniform distribution of fibers within the paper is influenced by several factors, including the forming consistency, hydrodynamic conditions during the forming stage, and the dimensions and properties of the fibers. This distribution is commonly described by the term “formation”, which encompasses key attributes such as appearance, printability, and strength [7]. Consequently, achieving precise control over formation is a critical focus for papermakers to ensure high-quality paper production [8].
Citation: Lee, Y.J.; Kim, G.-W.; Lee, T.-J.; Kim, H.J. Fractal Geometry: Surface Characterization of Printing Paper. Fractal Fract. 2025 , 9 , 123. https://doi.org/10.3390/ fractalfract9020123 Copyright: © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/).
Fractal Fract. 2025 , 9 , 123
https://doi.org/10.3390/fractalfract9020123
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