TY - JOUR
T1 - Thermal explosion in a hot gas mixture with organic gel fuel droplets
AU - Goldfarb, Igor
AU - Gol'dshtein, Vladimir
AU - Greenberg, J. Barry
AU - Zinoviev, Ann
N1 - Funding Information:
Acknowledgments These studies were supported in part (I.G., V.G.) by the German-Israeli Foundation under Grant G-695-15.10/2001. J.B.G. gratefully acknowledges the partial support of the Lady Davis Chair in Aerospace Engineering and the Technion Fund for the Promotion of Research.
PY - 2006/10/1
Y1 - 2006/10/1
N2 - Recent experimental evidence has uncovered the peculiar behavior of certain gel droplets which, under appropriate ambient thermal conditions, evaporate and burn in an oscillatory fashion. In this work a preliminary foray is made into the theoretical analysis of the nature of the evolution of a hot gas mixture containing organic gel fuel droplets with oscillatory evaporation within the context of thermal-explosion theory. The problem is modeled as a system of highly nonlinear singularly perturbed ordinary differential equations. Non-dimensionalization of the equations enables identification of the parameters that play a major role in determining the dynamical regimes of the system of equations. The method of integral manifolds is exploited for the analysis and it is found, that for certain parametric regions, the system exhibits new dynamical behavior that is quite different from that found for conventional liquid droplets.
AB - Recent experimental evidence has uncovered the peculiar behavior of certain gel droplets which, under appropriate ambient thermal conditions, evaporate and burn in an oscillatory fashion. In this work a preliminary foray is made into the theoretical analysis of the nature of the evolution of a hot gas mixture containing organic gel fuel droplets with oscillatory evaporation within the context of thermal-explosion theory. The problem is modeled as a system of highly nonlinear singularly perturbed ordinary differential equations. Non-dimensionalization of the equations enables identification of the parameters that play a major role in determining the dynamical regimes of the system of equations. The method of integral manifolds is exploited for the analysis and it is found, that for certain parametric regions, the system exhibits new dynamical behavior that is quite different from that found for conventional liquid droplets.
KW - Gel fuel droplets
KW - Singularly perturbed system of equations
KW - Theory of integral manifolds
KW - Thermal explosion
UR - http://www.scopus.com/inward/record.url?scp=33845429467&partnerID=8YFLogxK
U2 - 10.1007/s10665-006-9068-8
DO - 10.1007/s10665-006-9068-8
M3 - Article
AN - SCOPUS:33845429467
SN - 0022-0833
VL - 56
SP - 129
EP - 142
JO - Journal of Engineering Mathematics
JF - Journal of Engineering Mathematics
IS - 2
ER -