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Hydrodynamic stability of the spherical front of a reaction accompanied by a strong increase in viscosity

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Abstract

The hydrodynamic stability of the steady spherical front of a reaction accompanied by a strong increase in viscosity taking place in a radial, centrally symmetric flow of condensed reaction medium is considered. The flow is assumed to be bounded by two permeable concentric spherical surfaces. The stability is investigated in the linear approximation with respect to small perturbations. A relation is obtained for the dependence of the perturbation growth rate on the parameters of the problem: the viscosity ratio of the medium at the front, the ratio of the boundary surface radii to the radius of the front, and the dimensionless hydrodynamic resistances of the boundary surfaces. It is shown that the front is stable over almost the entire physical region of variation of the parameters and that instability occurs only in the case of a low hydrodynamic resistance of the outer boundary surface as the front approaches.

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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 46–53, May–June, 1988.

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Zhiznin, G.V., Segal, A.S. Hydrodynamic stability of the spherical front of a reaction accompanied by a strong increase in viscosity. Fluid Dyn 23, 361–367 (1988). https://doi.org/10.1007/BF01054741

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Keywords

  • Viscosity
  • Small Perturbation
  • Outer Boundary
  • Boundary Surface
  • Strong Increase