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Towards understanding the non-Gaussian pore size distributions of nonwoven fabrics

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  • Qin, Xianan
  • Song, Congwei

Abstract

Due to the central limit theorem, experimental data usually follows the Gaussian distribution. However, the pore size of nonwoven fabrics, which is a type of quasi two-dimensional structure formed by curved filaments, has been found to deviate from Gaussian but shows Gamma shaped distributions with shape parameters larger than one. Namely, they show right skewness, have the only zero point at the origin, and show long tail that converges at the horizon. Most of existing literatures model the non-Gaussian distributed pore size based on integrate geometry theories, which neglect the curvature in filaments and are too mathematically complicated. In this paper, we provide a new theory based on the maximum-entropy principle for the non-Gaussian distributed pore size of nonwoven fabrics. We first derive the expression of the Shannon entropy and then set constraints based on the structural properties of nonwoven fabrics. By maximizing the Shannon entropy, we obtain a general expression for the pore-size distribution. The physical meanings of the constraints are discussed. Our theory has shed light on the underlying mechanisms of the non-Gaussian pore size distribution of nonwoven fabrics, and can be listed as a theoretic basis for related lab or industrial applications.

Suggested Citation

  • Qin, Xianan & Song, Congwei, 2021. "Towards understanding the non-Gaussian pore size distributions of nonwoven fabrics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    • Handle: RePEc:eee:phsmap:v:581:y:2021:i:c:s0378437121004891
    DOI: 10.1016/j.physa.2021.126216
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    References listed on IDEAS

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    1. Itto, Yuichi, 2016. "Deviation of the statistical fluctuation in heterogeneous anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 522-526.
    2. G. Kaniadakis, 2009. "Maximum entropy principle and power-law tailed distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 3-13, July.
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