Maximum velocity steady state model

Cook (1958), 91 3 (Steady-state detonation head for solid unconfined and confined charges) 93-7 (Experimental detonation head in gases) 97-9 (Experimental detonation head in condensed explosives) 120-22 (Detonation head model proposed in 1943) and 128 (Detonation head in ideal detonation with maximum velocity transient)... 

Preceding discussions (in this chapter and Chapter 8) relate to problems attending the measurement of propagation rates in heavy-metal azides. The alternative of calculating the maximum, steady-state detonation rates in these azides from first principles is not well established. Nevertheless, a one-dimensional thermohydrodynamic model does exist which can yield reasonable values for detonation properties (velocity, pressure, product density and composition, particle velocity, etc.) [113-119]. 

The time required to reach steady-state potential reading is dependent on the enzyme layer thickness because of the diffusion parameter for the substrate to reach the active sites of the enzyme and of the electroactive species to diffuse through the membrane to the sensor. A mathematical model relating the thickness of the membrane, d, the diffusion coefficient, D, the Michaelis constant, K, and the maximum velocity of the enzyme reaction, Vmax, has been developed ... 

There is, however, a theory for the growth of crazes that is consistent with all the experimental evidence. Argon, Hannoosh and Salama [52] have proposed that the craze front advances by a meniscus instability mechanism in which craze tufts are produced by the repeated break-up of the concave air/polymer interface at the crack tip, as illustrated in Figure 12.15. A theoretical treatment of this model predicted that the steady-state craze velocity would relate to the five-sixths power of the maximum principal tensile stress, and support for this result was obtained from experimental results on polystyrene and PMMA [52]. 

As expected, a slightly earlier light-off occurs when there are channels with high gas velocity. Conversely, steady state conversions decrease when the velocity is not uniform. For non uniform velocity distributions, at steady state the maximum temperature difference between adjacent channels is about 25 K. Given that the model ignores heat conduction in the solid, the actual temperature difference is probably much smaller except at monolith boundary. 

---