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INTERFACE DYNAMICS IN FLUID FLOW IN POROUS MEDIA We have experimentally studied [22] the evolution of the interface in quasi-twodimensional displacement of viscous fluids in inhomogeneous media in order to test the dynamic scaling idea and to determine the exponents. The experimental setup [22] was a linear Hele-Shaw cell made of parallel plexiglass plates of size 24 cm x 100 cm. lm diameter glass beads between the plates. The beads were spread randomly and homogeneously in one layer and glued to the lower plate.

In addition, the range over which self-affine scaling could be observed was limited. It is expected, however, that the appropriate modifications of the existing simple models will account for the observed discrepancies. 35 Acknowledgements: The author thanks A. Jak6 and D. E. Wolffor their help in carrying out different parts of this study. Inspiring discussions with S. Buldyrev, S. Havlin and H. E. Stanley during the author's visit to Boston University are also acknowledged. The present research was financially supported by the Hungarian Scientific Research Foundation Grant No.

According to the scaling approach, if a growing surface is a self-affine fractal in the steady-state its saturation width has a power law dependence on L: w(L) '" L Oi (3) where a is the so-called roughness exponent. 28. 8 . , . - - - - - - - - - - - - - - , , . . 0 . 2 Fig. 4. 1 [r(nm)] (a) Plot of the interface width as a function of L for the STM image in fig. 3. 29. (b) Correlation function for the same image. 55. A direct determination of a was done by using equation (3) and (6) on the data of fig.

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