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Exact nonlinear solution for constant-rate expression from material of finite thickness

  • P. Broadbridge (a1) (a2) and P. J. Banksa (a3)

Abstract

We present new exact solutions for the flow of liquid during constant-rate expression from a finite thickness of liquid-saturated porous material with nonlinear properties. By varying a single nonlinearity parameter and a dimensionless expression rate, we systematically investigate the effect of nonlinearity and of an impermeable barrier (e.g. a piston). We illustrate the water profile shape and the water ratio deficit at the expression surface (e.g. a filter membrane) as a function of time.

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References

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[1] Banks, P. J., “Theory of constant-rate expression and subsequent relaxation”, in Drying '85 (eds. Toei, R. and Mujumdar, A. S.), (Hemisphere, Washington, DC, 1985) 102108.
[2] Banks, P. J. and Burton, D. R., “Press dewatering of brown coal: Part 1- Exploratory studies”, Drying Technol. (N.Y.) 7 (1989) 443475.
[3] Broadbridge, P., “Integrable flow equations that incorporate spatial heterogeneity”, Transp. Porous Media 2 (1987) 129144.
[4] Broadbridge, P., “Infiltration in saturated swelling soils and slurries: exact solutions for constant supply rate”, Soil Sci. 149 (1990) 1322.
[5] Broadbridge, P., Knight, J. H. and Rogers, C., “Constant rate rainfall infiltration in a bounded profile: solutions of a nonlinear model”, Soil Sci. Soc. Am. J. 52 (1988) 15261533.
[6] Broadbridge, P. and White, I., “Constant rate rainfall infiltration: A versatile nonlinear model: 1. Analytic solution”, Water Resour. Res. 24 (1988) 145154.
[7] Cannon, J. R., The one-dimensional heat equation, (Addison-Wesley, Reading, Mass., 1984).
[8] Cole, J. D., “On a quasi-linear parabolic equation occurring in aerodynamics”, Q. Appl. Math. 9 (1951) 225236.
[9] Fujita, H., “The exact pattern of a concentration-dependent diffusion in a semi-infinite medium: 2”, Textile Res. J. 22 (1952) 823827.
[10] Gautschi, W., “Error function and Fresnel integrals”, in Pocketbook of Mathematical Functions (eds. Abramowitz, M. and Stegun, I. A.), (Verlag Hani Deutsch, Frankfurt, West Germany, 1964).
[11] Hopf, E., “The partial differential equation ut + uux = μuxxCommun. Pure Appl. Math. 3 (1950) 201230.
[12] King, M. J., “Immiscible two-phase flow in a porous medium: utilization of a Laplace transform boost”, J. Math. Phys. 26 (1985) 870877.
[13] Kirchhoff, G., Vorlesungen über die Theorie der Warme (Barth, Leipzig, 1894).
[14] Knight, J. H. and Philip, J. R., “Exact solutions in nonlinear diffusion”, J. Eng. Math. 8 (1974) 219227.
[15] Landman, K. A., “Some moving boundary problems in solid/liquid separation”, in Proceedings of the Mini-Conference on Free and Moving Boundary and Diffusion Problems (eds. Hill, J. and Anderssen, R.), (Centre for Mathematical Analysis, Australian National University, Canberra, 1990) to appear.
[16] Milne-Thomson, L. M., The calculus of finite differences (Macmillan, London, 1933).
[17] Murase, T., Iwata, M., Banks, P. J., Kato, I., Hayashi, N. and Shirato, M., “Press dewatering of brown coal: Part 2-Batch and continuous-screw operations”, Drying Technol. (N. Y.) 7 (1989) 697721.
[18] Oberhettinger, F. and Badii, L., Tables of Laplace transforms (Springer, Berlin, 1973).
[19] Philip, J. R., “The theory of infiltration: 4. Sorptivity and algebraic infiltration equations”, Soil Sci. 84 (1957) 257264.
[20] Smiles, D. E., “Constant rate filtration of bentonite”, Chem. Eng. Sci. 33 (1978) 13551361.
[21] Storm, M. L., “Heat conduction in simple metals”, J. Appl. Phys. 22 (1951) 940951.
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Exact nonlinear solution for constant-rate expression from material of finite thickness

  • P. Broadbridge (a1) (a2) and P. J. Banksa (a3)

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