17. T. D. Butler, L. K. Cloutman, J. K. Dukowicz, and J. K. Ramshaw, Prog. Energy Combust. Sci., !, 293-315 (1981). 18. P. O. Witze, Sandia Report N81-8242, Livermore (1981). 19. F. H. Harlow and A. A. Amsden, J. Comp. Phys., 8, 197-213 (1971). 20. W. Rivard, T. Butler, and O. Farmer, Numerical Solution of Problems in Hydromechanics [Russian translation], Moscow (1977). 21. S. Khert, Numerical Methods in Fluid Mechanics [in Russian], Moscow (1973), pp. 156- 164. 22. B. D. Dali, Numerical Solution of Problems in Hydromechanics [in Russian], Moscow (1977), No. 14, pp. 143-156. 23. J. F. Thompson, F. C. Thames, and C. W. Mastin, J. Comput. Phys., 15, 299-319 (1974). 24. P. D. Thomas and J. F. Middlekoff, Raket. Tekh. Kosmonavt., 18, No. 7, 55-61 (1980). 25. N. N. Yanenko, N. T. Danaev, and D. V. Liseikin, Numerical Methods in the Mechanics of Continuous Media [in Russian], Novosibirsk (1977), Vol. 8, No. 4, pp. 157-163. 26. C. Arcoumanis, A. F. Bicen, and J. H. Whitelaw, Trans. ASME J. Fluids Eng., 105, i05-112 (1983). 27. C. Bassoli, G. Biaggini, G. Bodritti, and G. M. Cornetti, "Two-dimensional combustion chamber analysis of direct injection diesel," SAE Tech. Paper Ser. (1984). STRUCTURE OF INHOMOGENEOUS MEDIA WITHIN THE RANDOM FRACTAL MODEL R. R. Nigmatullin and N. N. Sutugin UDC 536.7 The porosity of inhomogeneous media is treated within the random fractal mod- el. Analytic expressions are obtained for the size distribution curves of bulk mesopores. The concepts of a fractal and fractal dimensionality [i] are extremely fruitful in de- scribing the geometry of heterogeneous systems, in the study of percolation effects, proper- ties of various self-similar objects and structures, generated in hydrodynamics, astrophys- ics, electrochemistry, and other disciplines. More detailed information can be found, for example, in the reviews [2, 3]. The extension of the concept of a regular fractal and the introduction of a set of inhomogeneous objects with distributed values of fractal dimen- sionality became possible due to the multifractal approach, a topic discussed in the stud- ies [4, 5]. Besides this extended class of regular fractals another is possible, which, as far as we are concerned, is a more natural method of introducing fractals, where the fractal scale, and not its dimensionality, occupies the role of the random fractal. The random fractal model (RFM) is proposed on the basis of the new concept of generalized fractal. The distri- bution function of various scales is found, and equations are obtained for the porosity of an inhomogeneous medium. The equations for two-phase system concentrations are generalized and interpreted if the distribution of one of the phases is fractal. A more detailed inter- pretation of experiments, related to measurements of porosity and the proof of their frac- tal occurrence in sandstones, is given within the RFM [6, 7]. Also analyzed was the size distribution function of bulk mesopores with the purpose of searching regions of fractal structure with its help. Comparison with experiment makes it possible to establish a number of new consequences and indicates internal consistencies of the model. Description of Heterogeneous Media by Generalized Fractals. By means of some figure we divide the given volume V into original or elementary "volumes" vf(A) = GfA d with character- V, I. Ul'yanov (Lenin) Kazan State University. Zhurnal, Vol. 57, No. 2, pp. 291-298, August, 1989. 1988. Translated from Inzhenerno Fizicheskii Original articlesubmitted January l, 958 0022-0841/89/5702-0958512.50 9 1990 Plenum Publishing Corporation