2002 - Volume 1 - JEFF. Journal of Engineered Fibers and Fabrics

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Figure 8 Linear relationship between the mean number of contacts per fiber and fiber crimp. For crimp increasing from k=1.0 to k=4. statistics for isotropic samples: random data are displayed as squares and flocculated data are displayed as x-marks; statistics for anisotropic samples: random data are displayed as hexagram, and flocculated data are displayed as points. In general, higher fiber crimp implies higher mean number of contacts per fiber. Figure 9 Linear relationship between the mean number of fiber per zone and fiber crimp. For crimp increasing from k=1.0 to k=4.0: statistics for isotropic samples: random data are displayed as squares and flocculated data are displayed as x-marks; statistics for anisotropic samples: random data are displayed as hexagram, and flocculated data are displayed as points. In general, higher fiber crimp implies in higher mean number of fibers per zone. Fiber crimp has a higher impact on isotropic structures, than on anisotropic structures. Also, isotropic structures tend to present higher mean number of fibers per zone, as crimp is increased. process control instruments could be devised to exploit our methods and results. We find that mean and standard deviation are positively correlated for some fiber network parameters, such as 28 INJ Spring 2002 2 Figure 10 Linear relationship between the mean void size and fiber crimp. For crimp increasing from k=1.0 to k=4.0: statistics for isotropic samples: random data are displayed as squares and flocculated data are displayed as x-marks; statistics for anisotropic samples: random data are displayed as hexagram, and flocculated data are displayed as points. In general, higher fiber crimp implies in smaller mean voids. Fiber crimp has a higher impact on isotropic structures, than on anisotropic structures. Also, isotropic structures tend to present the smaller mean void size as crimp is increased. mean void size, network density, and mean density of fiber contacts. Therefore, increasing (or decreasing) their mean also increases (or decreases) their variability. Fiber crimp seems to have a higher impact on isotropic structures; they tend to generate smaller mean voids, higher mean number of fibers per zone, and higher total number of bonds per fiber, than do anisotropic structures. It seems significant also that our simulations also suggest a relationship between mean number of fibers per zone and mean void size, independent of the nature of the stochastic fibrous structure. In other words, the shape of the transfer function curve will be the same, even if the structure contains crimped fibers or not, if it is random or flocculated, isotropic or anisotropic; this could be an important universal effect. These information provide valuable insight, that could help modeling the underlying distributions of these parameters in fiber networks. Future work, will probe the transport properties through the voids in nonwovens (isotropic or anisotropic), model structural elements such as constrictions (i.e. throats) and pore connectivity (i.e. tortuosity and coordination numbers), as well as comparing the results of our simulations to experimental data. Acknowledgements The authors wish to thank CNPq (Brazilian National Research Council) and The British Council for support during the progress of this work.
A B Figure 11 Relationship between the means of local mass (i.e. density) and mean void size in (a) For constant crimp k=1.35 statistics of random samples as density is increased are displayed as crosses; statistics of flocculated samples as fiber clumping is increasing are displayed as circles; statistics of anisotropic samples as anisotropy is increasing are displayed as triangles. For crimp increasing from k=1.0 to k=4.0 : statistics for isotropic samples: random data are displayed as squares and flocculated data are displayed as x-marks; statistics for anisotropic samples: random data are displayed as hexagram, and flocculated data are displayed as points; and (b) experimental data (Bliesner, 1964). References Bliesner, W.C. 1964. “A Study of the Porous Structure of fibrous Sheets Using Permeability Techniques.” TAPPI J., 47 (7): 392-400. Cox, D. R. and V. Isham. 1980. “Point Processes.” Monographs in Applied Probability and Statistics. Chapman & Hall, pp. 188. Cressie, N. A. C. 1993. Statistics for Spatial Data. John Wiley & Sons Inc. Deng, M. and Dodson, C. T. J. 1994. Paper: An Engineered Stochastic Structure. TAPPI Press, Atlanta. Dodson, C.T.J. and Sampson, W.W. 1997. “Modelling a Class of Stochastic Porous Media.” Applied Mathematics Letters 10, no. 2: 87-89. Dodson, C.T.J. and Sampson, W.W. 2000. “Flow Simulation in Stochastic Porous Media.” Simulation J., 74(6):351-358, 2000. Gong, R.H. and Newton, A. 1996. “Image-Analysis Techniques Part II: The Measurement of Fiber Orientation in Nonwoven Fabrics,” J. Textiles Institute 87, no. 2: 371-388. Kim, H.S. and Pourdeyhimi, B. 2000. “A Note on the Effect of Fiber Diameter, Fiber Crimp and Fiber Orientation on Pore Size in Thin Webs,” Intern. Nonwovens J. 9, no. 4: 15-19. Lewis, P. A. W. and G. S. Shedler. 1979. “Simulation of Non-Homogeneous Poisson Processes by Thinning.” Naval Research Logistics Quarterly, No. 26, pp. 403-13. Neyman, J. and E.L. Scott. 1958. “Statistical Approach to Problems in Cosmology.” Journal of the Royal Statistical Society B, 20, pp. 1-29. Ripley, B. D. 1983. “Computer Generation of Random Variables: a Tutorial.” International Statistical Review, No. 51, pp. 301-319. Scharcanski, J.; Dodson, C.T.J. 1996. “Texture Analysis for Estimating Spatial Variability and Anisotropy in Planar Stochastic Structures.” Optical Engineering Journal, Vol. 35, No. 8, pp. 2302-2309. Stoyan, D.; Kendall, W.S. and Mecke, J. 1995. Stochastic Geometry and its Applications. John Wiley & Sons, New York. — INJ INJ Spring 2002 29
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