Abstract
From the known statistics of fiber-fiber contacts in random fiber networks, an analytic estimate is obtained for the variance of local porosity in random fiber suspensions and evolving filtrate networks. The variance of local porosity, and hence the distribution of projected areal density, seem to depend on fiber geometry only through the cube of mean diameter. Also, the coefficient of variation of local flow rate perpendicular to the plane of the pad is, to a first approximation, independent of the mode of flow. Analytic estimates are obtained also for the effect of fiber clumping on the variance of local porosity of pads for small inspection zones.
This is a preview of subscription content, log in via an institution to check access.
REFERENCES
H. Corte and E. H. Lloyd, Fluid flow through paper and sheet structure, in Consolidation of the Paper Web, Transactions of the Fundamental Research Symposium, Cambridge 1965, F. Bolam, ed. (Technical Section of BPBMA, London 1966), pp. 981–1009. See also Discussion following, p. 1010.
C. T. J. Dodson and W. W. Sampson, The effect of paper formation and grammage on its pore size distribution, J. Pulp Pap. Sci. 22(5):J165–J169 (1996).
C. T. J. Dodson and W. W. Sampson, Modeling a class of stochastic porous media, Appl. Math. Lett. 10(2):87–89 (1997).
R. E. Miles, Random polygons determined by random lines in a plane, Proc. Nat. Acad. Sci. USA 52:901–907, 1157–1160 (1964).
J. Scharcanski and C. T. J. Dodson, A new simulator for paper forming using neural network methods, Appita J. 48(5):347–350 (1995).
C. T. J. Dodson, The statistical analysis of patterns of deformation in flat bonded fibrous networks, J. Phys. D: Appl. Phys. 3:269–276 (1970).
C. T. J. Dodson, Spatial variability and the theory of sampling in random fibrous networks, J. Roy. Statist. Soc. B 33(1):88–94 (1971).
R. R. Farnood, C. T. J. Dodson, and S. R. Loewen, Modeling flocculation. Part I: Random disk model, J. Pulp Pap. Sci. 21(10):J348–J356 (1995).
H. Corte, The porosity of paper, Chap 6, in Handbook of Paper Science, H. F. Rance, ed. (Elsevier Scientific Publishing, Amsterdam, 1982).
C. T. J. Dodson, Fibre crowding, fiber contacts and fiber flocculation, Tappi J. 79(9): 211–216 (1996).
R. R. Farnood, N. Yan, M. T. Kortschot, and C. T. J. Dodson, Modelling flocculation: A gallery of simulated flocculated papers, Nord. Pulp Pap. Res. J. 12(2):86–89 (1997).
A. Kiviranta and H. Paulapuro, The role of fourdrinier table activity in the manufacture of various paper grades, Tappi J. 75(4):172–185 (1992).
J. Gorres, R. Grant, T. Cresson, and P. Luner, The effect of drainage on randomly formed papers: a simulation study, Tappi J. 69(7):104–105 (1986).
W. W. Sampson, J. McAlpin, H. W. Kropholler, and C. T. J. Dodson, Hydrodynamic smoothing in the sheet forming process, J. Pulp Pap. Sci. 21(12):J422–J426 (1995).
B. Norman, U. Sjödin, B. Alm, K. Björklund, F. Nilsson, and J-L. Pfister, The effect of localised dewatering on paper formation, in Proc. TAPPI 1995 International Paper Physics Conference, Niagara-on-the-Lake, 1995 (Tappi Press, Atlanta, 1995), pp. 55–59.
O. Schultz-Eklund, C. Fellers, and P-A. Johansson, Method for the local determination of the thickness and density of paper, in Proc. Tappi International Paper Physics Conference, Kona, 1991 (Tappi Press, Atlanta, 1991), pp. 511–523.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dodson, C.T.J., Sampson, W.W. Spatial Statistics of Stochastic Fiber Networks. Journal of Statistical Physics 96, 447–458 (1999). https://doi.org/10.1023/A:1004597121797
Issue Date:
DOI: https://doi.org/10.1023/A:1004597121797