The Role of Fuel Particle Size on Flame Propagation Velocity in Thermites with a Nanoscale Oxidizer

The effect of aluminum size on confined flame propagation velocities in thermite composites was investigated between 108 mm and 80 nm, and in all cases using nanometric copper oxide as the oxidizer. It was found that the velocity exhibited two distinct regimes; between 108 and 3.5 mu m the velocity scaled as the particle diameter to the -0.56 power, and becomes invariant of size below this. One explanation for the invariance is that the pressure-driven flow reaches some peak velocity, controlled by the pressure gradient, pore size, and fluid viscosity. Another explanation is that the system becomes limited by the internal gas heating rate, defined by the intrinsic kinetic time scale, and which can significantly impact the effective particle heating time. The particle heating time was calculated as a function of particle size, and as a function of gas heating rates ranging from 10(5)Ks(-1) to infinity. It was found that at any finite gas heating rate, there exists a critical particle diameter below which all sizes take the same amount of time to heat. This is a direct artifact of the characteristic thermal relaxation time scale; if the heating rate is not sufficiently fast, then the particle will rapidly equilibrate with the gas at each time step. The inverse of thermal relaxation time was used to calculate a critical heating rate defining a transition point, and which exhibits a dp2 scaling. This scaling sets a constraint on the kinetics, which must at least scale with dp(2) to remain in the size-dependent regime.