Neumann theory

J. Von Neumann, Theory of Detonation Waves, Pergamon Press, 1963. 

Spike (or peak) pressure ahead of the detonation front was determined accdg to von Neumann theory. For this a linear extrapolation of the Us—Up data was conducted and assumption made that Us up relations represent nonreactive Hugoniots to the detonation velocities of expls... 

A similar presentation of von Neumann theory is given by Penney in Ref 24a, pp 6-7, where his Fig 2 is similar to Fig 4 shown here... 

G.B. Kistiakowsky E.B. Wilson, Jr1. "Final Report on die Hydrodynamic Theory of Detonation and Shock Waves OSRD 114(1941) 6) J. von Neumann "Theory... 

I. von Neumann, Theory of Self-Replicating Automata, A. Burks, Ed., University of Illinois... 

Figure 3.16 Validation of the Neumann theory for interfacial tensions. Reprinted from Kwok and Neumann (1999), with permission from Elsevier...

Good and co-workers have frequently pointed out (e.g. van Oss et al., 1987) that the inability of Neumann theory to predict negative liquid-liquid interfacial tensions results in often poor agreement for liquid-liquid interfaces and for predicting misci-bUity (miscibUity is equivalent to zero or negative interfacial tensions). 

It is worth mentioning that Professor Good has not always been so critical. In his 1977 review (Good, 1977) he sees much promise in the - then - recently appeared Neumann theory, while he mentioned several reasons why the surface tension component theory could break down, among others the importance of entropic effects (incidentally discussed by others later, e.g. Douillard, 1997). Nevertheless, Professor Good and Professor Fowkes clearly converged to the notion that the surface tension component theories constitute the most successful approach, with special emphasis on the explicit treatment of the very important acid-base interactions. 

Delia Volpe and Siboni are, despite the problems and limitations which they themselves point out, much more confident about the van Oss-Good theory than for the Neumann theory. They have considered the latter theory in several publications and their conclusion is, in agreement with others, that the Neumann theory is of semi-empirical nature and should be applied only to apolar surfaces. 

It appears, among several researchers, to be a consensus that the Neumann theory is best apphed to non-polar liquids and solids (Correia et al., 1989 Drelich and Miller, 1994) and that, all things being equal, the van Oss-Good theory performs best overall for the analysis of sohd surfaces. 

J,5 What do we believe about the van Oss-Good and Neumann theories ... 

The discussion of the van Oss-Good and Neumann theories is compheated by many factors, e.g. the validity range of the Young equation, the role of spreading pressure, the accuracy of experimental contact angle data and others. 

The Fowkes, Owens-Wendt and the Girifalco-Good theories are those most often presented in textbooks on colloids and interfaces but they would not be the ones we recommend using today. The more modem theories of Neumann and the acid-base by van Oss-Good are better choices. Strangely they are not presented in textbooks but they are the ones most widely accepted in engineering practice. The consensus today is that the Neumann theory has a rather weak theoretical justification but can be reliably used to estimate surface tensions of rather non-polar or slightly... 

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