Dense media

Schroeder J and Troe J 1985 Solvent shift and transport contributions in reactions in dense media Chem. Phys. Lett. 116 453... 

T. L P. JespOH/ M S / Min Proc / Metallurgical Engineer, Basic, Inc., Gabb.s, NV. (Dense Media Separation)... 

Dense-media separation may be used to produce either a finished concentrate or an upgraded feed for subsequent processing. In the latter case, it provides a low-cost means to reject a significant amount of essentially barren waste at a coarse size. 

Feed Preparation and Feed Size The ability to achieve a separation of different solid particles on the basis of density, as in all physical separation, depends on the degree to which the particles are liberated (detached) from each other. Liberation can be achieved by breaking the material in a manner that causes it to fracfure and free the individual grains of the constituents to be recovered. The degree of separation that can be realized by the dense-media process will depend on the degree of hberation of the individual grains. 

FIG. 19-32 Revolving-drum-type dense-media separatory vessel. (Coutiesy of Vesie7n Machinery Co.)... 

FIG. 19-33 Typical dense-media flow sheet for a coal-cleaning plant. Couiiesy of Frocess Machineiy Division, AtihurG. McKee Co.)... 

Dense-media cyclones are generally operated in the (0.7-1.0) X lO -Pa (10-15-lbf in ) range. It is not advisable to go below (0.4-0.56) X 10 Pa because the recoveiy of low-specific-gravity material and the rejection of impurity are improved at higher pressures. 

FIG. 19-35 Dense-media cone-vessel arrangements, (a) Single-gravity two-product system with pump sink removal, (b) Single-gravity two-product system with compressed-air sink removal. (Coutiesy of Process Machinefy Division, Afihur G, McKee Co.)... 

Because of the simplicity of the dense-media process, these can readily be maintained. 

Hoover, W.G., in Behavior of Dense Media Under High Dynamic Pressure (edited by Berger, J.), Gordon and Breach, New York, 1968, pp. 397-406. 

In the impact approximation (tc = 0) this equation is identical to Eq. (1.21), angular momentum relaxation is exponential at any times and t = tj. In the non-Markovian approach there is always a difference between asymptotic decay time t and angular momentum correlation time tj defined in Eq. (1.74). In integral (memory function) theory Rotc is equal to 1/t j whereas in differential theory it is 1/t. We shall see that the difference between non-Markovian theories is not only in times but also in long-time relaxation kinetics, especially in dense media. 

This means that the theory may be applied only to dense media where rotational relaxation proceeds at a higher rate than does orientational relaxation. 

Relations (2.46) and (2.47) are equivalent formulations of the fact that, in a dense medium, increase in frequency of collisions retards molecular reorientation. As this fact was established by Hubbard within Langevin phenomenology [30] it is compatible with any sort of molecule-neighbourhood interaction (binary or collective) that results in diffusion of angular momentum. In the gas phase it is related to weak collisions only. On the other hand, the perturbation theory derivation of the Hubbard relation shows that it is valid for dense media but only for collisions of arbitrary strength. Hence the Hubbard relation has a more general and universal character than that originally accredited to it. 

One may hope that the results presented in Eq. (3.23) and Eq. (3.24) remain valid beyond the framework of impact theory. As is seen from Chapter 1, linear in density Eq. (3.21) and Eq. (1.124) become invalid in highly dense media. However, it is unlikely that their relative efficiency will be considerably changed. Thus the direct proportion (3.24) may be retained even in the case where 1/xj increases nonlinearly with increase in density (see Fig. 1.23). Since it is easier to measure xj in the liquid than xe, it is of some importance to express the isotropic spectrum width as a function of xj. 

Debye s theory, considered in Chapter 2, applies only to dense media, whereas spectroscopic investigations of orientational relaxation are possible for both gas and liquid. These data provide a clear presentation of the transformation of spectra during condensation of the medium (see Fig. 0.1 and Fig. 0.2). In order to describe this phenomenon, at least qualitatively, one should employ impact theory. The first reason for this is that it is able to describe correctly the shape of static spectra, corresponding to free rotation, and their impact broadening at low pressures. The second (and main) reason is that impact theory can reproduce spectral collapse and subsequent pressure narrowing while proceeding to the Debye limit. 

The behaviour of te,2 (tj) is qualitatively different. In the dense media this dependence also satisfies the Hubbard relation (6.64), and in logarithmic coordinates of Fig. 6.6 it is rectilinear. As t increases, it passes through the minimum and becomes linear again when results (6.25) and (6.34) hold, correspondingly, for weak and strong collisions ... 

It was demonstrated in Chapter 6 that impact theory is able to describe qualitatively the main features of the drastic transformations of gas-phase spectra into liquid ones for the case of a linear molecule. The corresponding NMR projection of spectral collapse is also reproduced qualitatively. Does this reflect any pronounced physical mechanism of molecular dynamics In particular, can molecular rotation in dense media be thought of as free during short time intervals, interrupted by much shorter collisions ... 

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