The real challenge in porous media transport was the treatment of turbulent flow regimes or plainly - the development of governing equations for the Upper scale VAT turbulent description. Firstly the mathematical models and governing equations were developed and published in 1983 -- 89 having the air pollution modeling and chemical engineering as the fields of immediate application:
Shcherban, A.N., Primak, A.V., and Travkin, V.S., "Simulation of Mass- and Heat Transfer Under Atmospheric Air Pollution in Towns and Industrial Centers", Prom. Teplotekhnika, Vol.5, No.4, pp.96-104, (1983), (in Russian).
The first two correct mathematical and physics models on Turbulent transport in porous media were published in -
Scherban, A.N., Primak, A.V., and Travkin, V.S. "Mathematical Models of Flow and Mass Transfer in Urban Roughness Layer," Problemy Kontrolya i Zaschita Atmosfery ot Zagryazneniya, 1986, No. 12, pp. 3-10, (in Russian).
Primak, A.V., Shcherban, A.N. and Travkin, V.S., "Turbulent Transfer in Urban Agglomerations on the Basis of Experimental Statistical Models of Roughness Layer Morphological Properties," in Trans. World Meteorological Organization Conference on Air Pollution Modeling and its Application, Geneva, 1986, Vol. 2, pp.259-266.
which is uploaded into this website in -
See why these were the first correct publications in our analysis in section -
Primak, A.V. and Travkin, V.S., 1989, "Simulation of Turbulent Transfer of Meteoelements and Pollutants Under Conditions of Artificial Anthropogenic Action in Urban Roughness Layer as in Sorbing and Biporous Two-Phase Medium", in Trans. Intern. Symp. Interconnection Problems Hydrological Cycle and Atmospheric Processes Under Conditions of Anthropogenic Influences, Schopron.
Komkov, S.M., Primak, A.V., and Travkin, V.S., 1987, "Analysis of Processes and Calculation Methods of Gascleaners with Surface Condensation of Steam-gaseous Mixtures," in Trans. V U.S.S.R. Conference on "Aerosols and its Application to Economy, Latvia, Yurmala, Moscow, pp. 72-73.
Later on this approach has been spread to other physical disciplines (developments for many of those are offered for observation in the present Web site)
Few governing equations on turbulent transport in porous media can be found in published texts as, for example, in
POROUS MEDIUM TURBULENT VAT EQUATIONS (100K)
in the paper in "Fluids Engineering" (1995)
More or less short texts were published in the paper in "Advances in Colloid and Interface Science" (1998)
and in the beginning part of the general text on HSP-VAT concepts and few applications - in Advances in Heat Transfer, V.34, (2001)
It is still not any one conclusively complete manuscript on porous media Turbulent phenomena description has been published so
far. Still, more basics and substantiation can be found in our -
I am sorry telling this for many times, but great number of publications on Turbulent transport in porous media are just having incorrect models. Or incorrect basically mathematical concepts, rules, or too much simplified assumptions when there is no sense to talk about foundation.
Travkin, V. S. and Catton, I., "Porous Media Transport Descriptions - Non-Local, Linear and Non-linear Against Effective Thermal/Fluid Properties," Advances in Colloid and Interface Science, 1998, Vol. 76-77, pp. 389-443.
Travkin, V.S. and Catton, I., Transport phenomena in heterogeneous media based on volume averaging theory// Advances in Heat Transfer, New York, Academic Press, 2001, Vol. 34, pp. 1-144.
Travkin, V.S. and Catton, I., "A two temperature model for turbulent flow and heat transfer in a porous layer," Journal of Fluids Engineering, 1995, Vol. 117, pp. 181-188.
Travkin, V.S. and Catton, I., "Nonlinear Effects in Multiple Regime Transport of Momentum in Longitudinal Capillary Porous Medium Morphology", J. Porous Media, 1999, Vol. 2, No.3, pp. 277-294.