Extraction of Material from a Porous Body into a Moving Liquid

  • A. I. MoshinskiiEmail author


In this paper, we study the nonstationary process of extracting material from a porous body simulated by a system of semi-infinite capillaries into a moving liquid in which the transfer rate of the material in the flow is a linear function of the cross-flow coordinate. The case where the liquid velocity at the interface becomes zero is considered. It is assumed that the diffusion in the flow is quasi-stationary. Analytical dependences at the interface between the porous material and the flow region are found for mass transfer characteristics of practical interest (concentration, diffusion flow, total diffusion flux, and the total yield of the target component extracted through the cross section of the porous body).


porous body mass transfer mass flux two-component extract 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Development of Research on the Theory of Filtration in the USSR (1917–1967), Ed. by P. Ya. Polubarinova-Kochina et al. (Nauka, Moscow, 1969) [in Russian].Google Scholar
  2. 2.
    G. A. Aksel’rud and V. M. Lysyanskii, Extraction (Solid-Liquid System) (Khimiya, Moscow, 1974) [in Russian].Google Scholar
  3. 3.
    G. A. Aksel’rud and M. A. Al’tshuller Introduction to Capillary-Porous Technology (Khimiya, Moscow, 1983) [in Russian].Google Scholar
  4. 4.
    Yu. A. Buevich and Yu. A. Korneev, “Heat and Mass Transfer in a Dispersive Medium,” Prikl. Mekh. Tekh. Fiz. 15 (4), 134–140 (1974) [J. Appl. Mech. Tech. Phys. 15 (4), 500–506 (1974)].Google Scholar
  5. 5.
    Yu. A. Buevich, Yu. A. Korneev, and I. N. Shchelchkova, “Heat and Mass Transfer in Dispersed Flow,” Inzh.-Phys. Zh. 30 (6), 979–985 (1976).Google Scholar
  6. 6.
    R. I. Nigmatulin, Fundamentals of the Mechanics of Heterogeneous Media (Nauka, Moscow, 1978) [in Russian].Google Scholar
  7. 7.
    L. G. Loitsyanskii, Mechanics of Liquids and Gases (Nauka, Moscow, 1973; Pergamon Press, Oxford-New York, 1966).zbMATHGoogle Scholar
  8. 8.
    Yu. I. Babenko and E. V. Ivanov, Extraction: Theory and Applications (Professional, St. Petersburg, 2009) [in Russian].Google Scholar
  9. 9.
    A. I. Moshinskii, “Effect of the Pulsating Motion of Liquid in a Bidisperse Porous Medium on the Distribution of Material in It,” Izv. Ross. Akad. Nauk, Mekh. Zhidk Gaza, No. 6, 109–121 (2010).Google Scholar
  10. 10.
    Yu. I. Babenko and E. V. Ivanov, “Extraction into a Moving Liquid with a Velocity Gradient,” Teor. Osn. Khim. Tekhnol. 42 (5), 504–508 (2008).Google Scholar
  11. 11.
    N. N. Lebedev, Special Functions and Their Applications (Fizmatgiz, Moscow, 1963) [in Russian].Google Scholar
  12. 12.
    S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives and Some of Their Applications (Nauka Tekhnika, Minsk, 1987) [in Russian].zbMATHGoogle Scholar
  13. 13.
    Yu. I. Babenko, Heat and Mass Transfer: A Method for Calculating Thermal and Diffusion Fluxes (Khimiya, Leningrad, 1986) [in Russian].Google Scholar
  14. 14.
    Ph. Clement, G. Gripenberg, and S. O. Londen, “Schauder Estimates for Equation with Fractional Derivatives,” Trans. Am. Math. Soc. 352 (5), 2239–2260 (2000).MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    A. V. Pskhu, “Solution of a Boundary-Value Problem for a Fractional Partial Differential Equation,” Differ. Urav. 39 (8), 1092–1099 (2003).MathSciNetGoogle Scholar
  16. 16.
    A. V. Pskhu, Fractional Partial Differential Equations (Nauka, Moscow, 2005) [in Russian].zbMATHGoogle Scholar
  17. 17.
    M. A. Lavrent’ev and B. V. Shabbat, Methods of the Theory of Functions of a Complex Variable (Nauka, Moscow, 1973) [in Russian].Google Scholar
  18. 18.
    I. M. Gel’fand and G. E. Shilov, Generalized Functions and Actions on Them (Fizmatgiz, Moscow, 1959) [in Russian].zbMATHGoogle Scholar
  19. 19.
    Yu. Luchko and R. Gorenflo, “Scale-Invariant Solution of a Partial Differential Equation of Fractional Order,” Fract. Calc. Appl. Anal. 1 (1), 63–78 (1998).MathSciNetzbMATHGoogle Scholar
  20. 20.
    I. V. Andrianov, R. G. Barantsev, and L. I. Manevich, Asymptotic Mathematics and Synergetics: A Way to Holistic Simplicity (Editorial URSS, Moscow, 2004) [in Russian].Google Scholar
  21. 21.
    G. Doetsch, Guide to the Practical Application of the Laplace and Z-transforms (Nauka, Moscow, 1971) [Russian translation].zbMATHGoogle Scholar
  22. 22.
    E. T. Whittaker and G. N. Watson, A Course of Modern Analysis: Part II. The Transcendental Functions (Cambridge University Press, 1927).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.St. Petersburg Chemical and Pharmaceutical UniversitySt. PetersburgRussia

Personalised recommendations