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Natural Division of the Problem
The Mechanism of Combustion Collapse
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3x 3x X X acoustic timescale activation energy asymptotics adiabatic flame temperature assumed assumption boundary conditions T(l,t Buckmaster and Ludford changes chemical reaction coefficients compatibility condition compatibility equation constant continuity equation Damkbhler number DECAY OF DROPLET decay of temperature density depend derivatives diffusion flame drop surface droplet combustion energy balance energy equation equilibrium solution exponential decay exponential type extinction Damkohler number f oo fast time evolution fast time scale Fick's law Figure flame sheet fractions must sum frozen solution fuel drop gives governing equations heat capacity Hence influx initial data largest perturbation leading order length scale Mach number Mary Grace Williams mass balance mass fractions molecular masses nondimensionalization numerical results reactants reaction rate reaction sheet reaction term reaction zone reduce relaxation layer satisfies the compatability Schwab-Zeldovich relations simplified species equation steady solution stoicheometric sum substitution temperature profiles Tf 3Tf thesis vanish X X with boundary zero