Neumann state

To obtain a rough physical understanding of the mechanism of the instability, attention may be focused first on a planar detonation subjected to a one-dimensional, time-dependent perturbation. Since the instability depends on the wave structure, a model for the steady detonation structure is needed to proceed with a stability analysis. As the simplest structure model, assume that properties remain constant at their Neumann-spike values for an induction distance after which all of the heat of combustion is released instantaneously. If v is the gas velocity with respect to the shock at the Neumann condition, then may be expressed approximately in terms of the explosion time given by equation (B-57) as Z = vt. From normal-shock relations for an ideal gas with constant specific heats in the strong-shock limit, the Neumann-state conditions are expressible by v/vq = po/p —... 

According to the specified criterion, the detonation exists only if at the Neumann state, dT /T divided by the coefficient of dM/M on the left-hand side of equation (29) exceeds dA/A divided by the coefficient of dM/M on the left-hand side of equation (28). For sufficiently strong leading shocks, the value of M at the Neumann state is such that this criterion to reduce approximately to... 

Specific heat of com pmmds. In 1831 F. E. Neumann stated the following law The product of the specific heat and the molecular weight of substances which are similar in chemical character, is a constant. By similar in chemical character, Neumann means substances, such as metallic oxides of the formula MeO or MeOg, metallic sulphides MeS, chlorides MeCl, and so on. The following table illustrates this law for metallic oxides of the formula MeO ... 

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