Analysis of Relationship between Porosity and Roughness of Surface Based on Fractal Model

Abstract:

Based on fractal geometry, this paper established an experimental model of ballistic deposition using the two-dimensional teflon surface composed of particles, in order to probe into the relationship that the roughness and porosity of the surface correspond to the friction and gravity forces in the cases of varying slopes. The experiment tested the nonlinear growing, roughening and dynamic scaling record of the surface deposition image. 4,000 M6 nuts in a line were slid on a 1m×1m Teflon board placed in an angle to the horizontal plane and a photograph was taken for every falling. Then, the photographs were analyzed with digital image processing and photo calibration in MATLAB. The photo calibration and object detection have tried polynomial algorithm and Hough transform method. Also, the exponents for self-affine interfaces were verified according to the digital photography analysis. To an extent, the experimental study might reveal the relationships between roughness and porosity of a physical surface, which provided a first basis to conduct the mechanical analysis of relationship.

• Periodical: Advanced Materials Research (Volume 683)
• Pages: 413-418
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.683.413
• Online since: April 2013
• Authors: Jin Qiang Chen, Xuan Zuo Liu, Luca Ridolfi, Bei Du, Hui Min Wang, Fei Zhang
• Keywords: Experiment, Friction, Image Processing, Porosity, Roughness

References

[1] Goodchild, M. F. and Kemp, K. K. (1982). NCGIA Core Curriculum in GIS. National Center for Geographic Information and Analysis, University of California, Santa Barbara CA.

[2] Mandelbrot, B.B. (1982). The Fractal Geometry of Nature. W.H. Freeman and Company. ISBN 0-7167-1186-9.

[3] Barabási, A. L. and Stanley, H. E. (1995). Fractal Concepts in Surface Growth. Cambridge University Press, ISBN: 0521483085.

[4] Mandelbrot, B. B. and Freeman, W. H. & Co (1982). The Fractal Geometry of Nature. ISBN 0716711869.

[5] A. -L. Barabási, H. E. Stanley (1995), Fractal Concepts in Surface Growth, Cambridge University Press, ISBN: 0521483085.

[6] Meakin P., Ramanlal, P., Sander, L. M. and Ball, R. C. (1986). Ballistic deposition on surfaces. The American Physical Society, Phys. Rev. A 34, 5091–5103.

DOI: 10.1103/physreva.34.5091

[7] Prolhac S. and Spohn H. (2011). The one-dimensional KPZ equation and the Airy process. [J] Stat. Mech, P03020.

DOI: 10.1088/1742-5468/2011/03/p03020

[8] Gonzalez Rafael C., Woods Richard E. and Eddins Steven (2003). Digital image processing using MATLAB. Pearson Prentice Hall, ISBN-10: 0130085197. ISBN-13: 978-0130085191.

[9] Faig W. (1975) Calibration of close-range photogram metric system: mathematical formulation. [J] Remote Sensing , 41(12): 1 479-1 486.