TY - JOUR

T1 - Self-Compaction or Expansion in Combustion Synthesis of Porous Materials

AU - Shkadinsky, K. G.

AU - Shkadinskaya, G. V.

AU - Matkowsky, B. J.

AU - Volpert, V. A.

N1 - Funding Information:
We are pleased to thank Prof. A. G. Merzhanov and Dr. W. G. Grosshandler for helping to arrange the collaboration between the authors, under the auspices of the U.S.-USSR Program of Cooperation in Basic Scientific Research jointly sponsored by the NSF and the USSR Academy of Science. This research was supported in part by D.O.E. Grand DE-FG02-87ER25027 and N.S.F. Grant CTS 9008624. Permanent Address for KGS and VAV: Institute of Structural Macrokinetics, USSR Academy of Sciences. 142432 Chernoholovka, Moscow Region, USSR. Permanent Address for GVS: Institute of Chemical Physics, USSR Academy of Sciences, 142432 Chernoholovka, Moscow Region, USSR.

PY - 1993/2/1

Y1 - 1993/2/1

N2 - We propose a mathematical model for the combustion of porous deformable condensed materials, which we use to describe the deformation of the high temperature products, induced by the pressure difference of the gas outside and inside the sample, in the absence of any external forces. The deformation occurs as a result of pore compaction (expansion), resulting in a more (less) dense product material. To describe the evolution of porosity we derive an equation which allows us to define a characteristic time of deformation td. If tdis sufficiently smaller than the characteristic time of combustion tn the deformation process is sufficiently fast to compensate for pressure gradients, so that pressure is equalized almost instantaneously, and filtration is suppressed. If td tr, deformation occurs solely in the product, and does not affect the propagation velocity. We determine various characteristics of a uniformly propagating combustion wave, and the materials produced by it, such as the propagation velocity, combustion temperature, final depth of conversion and final porosity of the product, as a function of the thermophysical parameters of the system. We also identify a regime of pulsating propagation, in which case the final porosity of the products is periodic in space. We show that both the uniformly propagating wave and the pulsating propagating wave solutions are stable, each corresponding to its own parameter regime. We also find that the deformation process can affect stability. In particular, the effect of viscosity is found to be stabilizing.

AB - We propose a mathematical model for the combustion of porous deformable condensed materials, which we use to describe the deformation of the high temperature products, induced by the pressure difference of the gas outside and inside the sample, in the absence of any external forces. The deformation occurs as a result of pore compaction (expansion), resulting in a more (less) dense product material. To describe the evolution of porosity we derive an equation which allows us to define a characteristic time of deformation td. If tdis sufficiently smaller than the characteristic time of combustion tn the deformation process is sufficiently fast to compensate for pressure gradients, so that pressure is equalized almost instantaneously, and filtration is suppressed. If td tr, deformation occurs solely in the product, and does not affect the propagation velocity. We determine various characteristics of a uniformly propagating combustion wave, and the materials produced by it, such as the propagation velocity, combustion temperature, final depth of conversion and final porosity of the product, as a function of the thermophysical parameters of the system. We also identify a regime of pulsating propagation, in which case the final porosity of the products is periodic in space. We show that both the uniformly propagating wave and the pulsating propagating wave solutions are stable, each corresponding to its own parameter regime. We also find that the deformation process can affect stability. In particular, the effect of viscosity is found to be stabilizing.

KW - deformation

KW - densification

KW - filtration combustion

KW - self-propagating high-temperature synthesis

KW - traveling waves

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U2 - 10.1080/00102209308947240

DO - 10.1080/00102209308947240

M3 - Article

AN - SCOPUS:0027202864

SN - 0010-2202

VL - 88

SP - 271

EP - 292

JO - Combustion science and technology

JF - Combustion science and technology

IS - 3-4

ER -