Free contact model

These conclusions hold only for a free contact model. Contact in shock tubes or with external triggers are excluded. 

Henry and Fauske (1975, 1976) have proposed a model to describe the events leading to a large-scale vapor explosion in a free contact mode. Their initial, necessary conditions are that the two liquids, one hot and the other cold, must come into intimate contact, and the interfacial temperature [Eq. (1)] must be greater than the homogeneous nucleation temperature of the colder liquid. Assuming the properties of both liquids are not strong functions of temperature, the interface temperature is then invariant with time. Temperature profiles within the cold liquid may then be computed (Eckert and Drake, 1972) as... 

Fig. 4 Contact model used Contact point indicators torsion indicators r], and normal vector indicating the center-to-center direction n, for the stress-free state (a) and stressed state (b). Reprinted from [46] with kind permission from Springer...

To predict the real interactions of the particles in the FB, their material properties were obtained experimentally and used as parameters of DEM contact model. The deformation and breakage behavior of pellets were obtained with the help of single particle compression tests. The energy loss during the collisions was obtained by means of free-fall impact tests. 

We have to stress that the analysed problems prove to be free boundary problems. Mathematically, the existence of free boundaries for the models concerned, as a rule, is due to the available inequality restrictions imposed on a solution. As to all contact problems, this is a nonpenetration condition of two bodies. The given condition is of a geometric nature and should be met for any constitutive law. The second class of restrictions is defined by the constitutive law and has a physical nature. Such restrictions are typical for elastoplastic models. Some problems of the elasticity theory discussed in the book have generally allowable variational formulation... 

The above measurements all rely on force and displacement data to evaluate adhesion and mechanical properties. As mentioned in the introduction, a very useful piece of information to have about a nanoscale contact would be its area (or radius). Since the scale of the contacts is below the optical limit, the techniques available are somewhat limited. Electrical resistance has been used in early contact studies on clean metal surfaces [62], but is limited to conducting interfaces. Recently, Enachescu et al. [63] used conductance measurements to examine adhesion in an ideally hard contact (diamond vs. tungsten carbide). In the limit of contact size below the electronic mean free path, but above that of quantized conductance, the contact area scales linearly with contact conductance. They used these measurements to demonstrate that friction was proportional to contact area, and the area vs. load data were best-fit to a DMT model. 

The dominant mechanism of purification for column crystallization of solid-solution systems is recrystallization. The rate of mass transfer resulting from recrystallization is related to the concentrations of the solid phase and free liquid which are in intimate contact. A model based on height-of-transfer-unit (HTU) concepts representing the composition profile in the purification section for the high-melting component of a binary solid-solution system has been reported by Powers et al. (in Zief and Wilcox, op. cit., p. 363) for total-reflux operation. Typical data for the purification of a solid-solution system, azobenzene-stilbene, are shown in Fig. 20-10. The column crystallizer was operated at total reflux. The solid line through the data was com-putecfby Powers et al. (op. cit., p. 364) by using an experimental HTU value of 3.3 cm. 

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