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On the Irreducible Tensors Method in the Theory of Diffusive Interaction between Particles

  • Sergey D. Traytak

Abstract

In the papers by Elperin and Krasovitov 1–3 the authors claim that they have suggested a new method called “modified method of irreducible multipoles” in order to solve the quasi steady state heat and mass transfer equations for systems with many interacting burning particles. “A method of solution of the Laplace equation in a region exterior to N arbitrarily located spheres of different radii is suggested. The method is based on the expansion of the solution into irreducible multipoles.” (p. 79) 1. “The present study extends the modified method of irreducible multipoles expansion, suggested by Elperin and Krasovitov (1994) to combustion of random char/carbon particles of different radii.” (p. 167) 2. “The method of expansion into irreducible multipoles which was developed in our previous works (Elperin and Krasovitov, 1994a, 1994b) is applicable to more realistic problems and is particularly suitable for dense random clusters of droplets (particles).” (p. 288) 3. It is important to note here that mathematically the irreducible tensors approach gives the possibility of finding the solution of linear boundary-value problems (BVP) for the Laplace equation in a three-dimensional multi-connected domain.

Keywords

Laplace Equation Hydrodynamic Interaction Addition Theorem Total Heat Flux Burning Particle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    T. Elperin, and B. Krasovitov, Analysis of evaporation and combustion of random clusters of droplets or particles by the modified method of irreducible multipoles expansion, Atomization and Sprays, 4, 79–97 (1994).Google Scholar
  2. 2.
    T. Elperin, and B. Krasovitov, Combustion of cylindrical and spherical random clusters of char/carbon particles, Combust. Sci. and Tech., 102, 165–180 (1994).CrossRefGoogle Scholar
  3. 3.
    T. Elperin, and B. Krasovitov, Evaporation and growth of multicomponent droplets in random dense clusters, Trans. ASME, 119, 288–297 (1997).CrossRefGoogle Scholar
  4. 4.
    S.D. Traytak, Theory of quasi steady state recondensation of N drops, Book of abstracts of the XV conference on actual problems on physics of aerosol systems, Odessa 1, 30 (1989) (in Russian).Google Scholar
  5. 5.
    S.D. Traytak, Theory of recondensation of N drops, Theor. Osnovy. Khim. Tekh.,24 473–482 (1990); (English translation Theor. Found. Chem. Eng.,24 320–328 (1991)).Google Scholar
  6. 6.
    K. Annamalai and W. Ryan, Interactive processes in gasification and combustion. Part 1: Liquid drop arrays and clouds, Prog. Energy Combust. Sci., 18, 221–295 (1992).CrossRefGoogle Scholar
  7. 7.
    J.H. Jeans, The mathematical theory of electricity and magnetism (Cambridge, 1925 ).Google Scholar
  8. 8.
    P.M. Morse and H. Feshbach, Methods of theoretical physics. ( McGraw-Hill, New York, 1953 ).MATHGoogle Scholar
  9. 9.
    S. Hess and W. Kohler, Formeln zur Tensor-Rechnung. ( Palm and Enke, Erlangen, 1980 ).Google Scholar
  10. 10.
    S.D. Traytak, The diffusive interaction in diffusion-limited reactions: the steady-state case, Chem. Phys. Letters, 197, 247–254 (1992).CrossRefGoogle Scholar
  11. 11.
    E.W. Hobson, The theory of spherical and ellipsoidal harmonics. (Chelsea Publ. Comp. New York, 1965 )Google Scholar
  12. 12.
    B.Z. Vulikh, Introduction to functional analysis for scientists and technologists. (Pergamon Press, 1963 ).Google Scholar
  13. 13.
    S.D. Traytak, Solution of some problems of the potential theory in multiconnected domains (in preparation).Google Scholar
  14. T, Elperin and B. Krasovitov, Reply to Comment “On the irreducible tensors method in the theory of interaction between burning particles” by S. Traitak (Submitted to Combust. Sci. and Tech.,2001).Google Scholar
  15. 15.
    B. Krasovitov, Evaporation and condensation of large size and moderate size droplets in gaseous media with arbitrary temperature gradients,Ph. D. Thesis, Moscow (in Russian).Google Scholar
  16. 16.
    E.R. Schukin, B. Krasovitov and Yu.l. Yalamov, Evaporation and condensation of large size and moderate size droplets in gaseous media with arbitrary temperature gradients, Deposited in VINITI No. 3706-B91, Moscow, 1991 (in Russian).Google Scholar
  17. 17.
    S. Hess, Birefringence caused by the diffusion of macromolecules or colloidal particles, Physica 74A, 277 (1974).MathSciNetCrossRefGoogle Scholar
  18. 18.
    P. Brunn, The effect of Brownian motion for a suspension of spheres, Rheol. Acta 15, 104–119 (1976).MATHGoogle Scholar
  19. 19.
    P. Brunn, The behavior of a sphere in non-homogeneous flow of a viscoelastic fluid, Rheol. Acta 15, 589611 (1976).Google Scholar
  20. 20.
    W.E. Kohler, Current induced Kerr effect in weakly ionized gases in the presence of a magnetic field, Physica 86A, 159–168 (1977).CrossRefGoogle Scholar
  21. I. Pardowitz and S. Hess, On the theory of irreducible processes in molecular liquids and liquid crystals, Nonequilibrium phenomena associated with the second and fourth rank alignment tensors, Physica 100A, 540–562 (1980).CrossRefGoogle Scholar
  22. 22.
    P. Mazur and W. Van Saarlos, Many-sphere hydrodynamic interactions and mobilities in a suspension, Physica 115A, 21–57 (1982).MathSciNetCrossRefGoogle Scholar
  23. Y.N. Kulbitsky and V.V. Struminsky, General solution of the problem of motion N dispersed particles using Stokes Approximation, Dept. Of Mechanics of Inhomogeneous Media, Preprint No. 17 (1988) (in Russian).Google Scholar
  24. 24.
    V.A. Belozertsev and A.V. Terzian, Calculation of the average velocity of gravitational settling of cluster of droplets with hydrodynamic interactions in nonisothermal fluid, Deposited in VINITI No. 7132-B88, 90105, Moscow (1988) (in Russian).Google Scholar
  25. 25.
    M.N. Gaydukov and V.A. Belozertsev, Gravitational setting of cluster of droplets with hydrodynamic interactions in nonisothermal fluid, Deposited in VINITI No. 7132-B88, 106–120, Moscow (1988)(in Russian). 26. B.L. Silver, Irreducible tensor methods (Academic press New-York, 1976 ).Google Scholar
  26. 27.
    S.D. Traytak, Heat and mass exchange in a spatially ordered array of drops, Teplofiz. Vys. Temp., 27, 969–975 (1989).Google Scholar
  27. 28.
    S.S. Kutateladze and V.M. Borishansky, Handbook on heat transfer ( Dayton, Ohio, 1963 ).Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Sergey D. Traytak
    • 1
  1. 1.Department of Mathematical Analysis of Moscow Pedagogical UniversityMoscowRussia

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