A family of gamma distributions can be used to model the pore size distributions in a range of stochastic porous media. Our simu lator generates distributional and net flow data for different fluid flow regimes through such networks. The outputs from the simu lation show strong relationships between mean flow and the variance of pore radii for turbulent, laminar, molecular and capillary flow. We observe also affine relationships between the coefficient of variation of local flow rate and the variance of pore radii for each of the above flow modes.
Miles, R.E. "Random Polygons Determined by Random Lines in a Plane." Proceedings of the National Academy of Science, Vol. 52, pp 901-907, 1157-1160, 1964.
2.
Corte, H. and Lloyd, E.H. "Fluid Flow through Paper and Sheet Structure." In Consolidation of the Paper Web, Transactions of the Fundamental Research Symposium , F. Bolam (ed.), Cambridge , 1965. Technical Section of BPBMA, London , 1966, pp 981-1009. See also "Discussion," following, pg 1010.
3.
Deng, M. and Dodson, C.T.J.Paper: An Engineered Stochastic Structure. Tappi Press , Atlanta, 1994.
4.
Dodson, C.T.J. and Sampson, W.W. "Spatial Statistics of Stochastic Fibre Networks." Journal of Statist. Phys., Vol. 96, No. 1-2, pp 447-458, 1999.
5.
Dodson, C.T.J. and Sampson, W.W. "Modeling a Class of Stochastic Porous Media ." Applied Math. Lett., Vol. 10, No. 2, pp 87-89, 1997.
6.
Dodson, C.T.J. and Sampson, W.W. "The Effect of Paper Formation and Grammage on its Pore Size Distribution." Journal of Pulp and Paper Science, Vol. 22, No. 5, pp J165-J169, 1996.
7.
Johnston, P.R. "The Most Probable Pore Size Distribution in Fluid Filter Media." Journal of Testing and Evaluation , Vol. 11, No. 2, pp 117-121, 1983.
8.
Johnston, P.R. "Revisiting the Most Probable Pore Size Distribution in Filter Media. The Gamma Distribution." Filtrn. and Sepn., Vol. 35, No. 3, pp 287-292, 1998.
9.
Corte, H. "The Porosity of Paper." Chapter 6 in Handbook of Paper Science, H.F. Rance (ed), Elsevier Scientific Publishing , Amsterdam, 1982.
10.
Corte, H. "Bestimmung der Porengröβenverteilung in Papier." Das Papier, Vol. 19, No. 7, pp 346-351, 1965.
11.
ASTM Method F316. "Pore Size Characteristics of Membrane Filters by Bubble Point and Mean (Middle) Flow Pore Test."
12.
Foscolo, P.U., Gibilaro, L.G. and Waldram, S.P. "A Unified Model for Particulate Expansion of Fluidised Beds and Flow in Fixed Porous Media." Chem. Eng. Sci., Vol. 38, No. 8, pp 1251-1260, 1983.
13.
Ng, W.K. , Sampson, W.W., Dodson, C.T.J. "The Evolution of a Pore Size Distribution in Paper." In Proceedings of Progress in Paper Physics - A Seminar, Stockholm, pp5-7, June 1996.
14.
Sampson, W.W. , McAlpin, J., Kropholler , H.W. and Dodson, C.T.J. "Hydrodynamic Smoothing in the Sheet Forming Process." Journal of Pulp and Paper Science, Vol. 21, No. 12, pp J422-J426, 1995.
15.
Norman, B., Sjödin, U., Alm, B., Björklund, K., Nilsson, F. and Pfister, J.-L. "The Effect of Localised Dewatering on Paper Formation." In Proceedings of the TAPPI 1995 International Paper Physics Conference , Niagara-on-the-Lake, pp 55-59, Tappi Press, Atlanta, 1995.
16.
Dodson, C.T.J. and Scharcanski, J. "Simulating Colloidal Thickening: Virtual Papermaking." SIMULATION, Vol. 74, No. 4, pp 200-206, April 2000.