Expander, Collins

Fig. 5.33. Schematic drawing of a Collins expander with Micarta sleeves on all wearing surfaces.

The reader who is not well acquainted with the extensive and controversial literature of deamination mechanisms of the last five decades may have the impression from our relatively detailed review of White et al. s recent paper and of the related work of Collins group that the dominant role of ion pairing in deaminations was not clearly recognized earlier. This is by no means the case. The paper of White s group (1992b) was chosen for this discussion because it combines and expands previous partial results with 1-phenylethylamine derivatives for which mechanistic conclusions are not disguised by a multitude of products as they are illustrated in the introductory Scheme 7-1. 

Ahlfeld, S. K., Larson R. L., and Collins, H. R. (1987), Anterior cruciate reconstruction in the chronically unstable knee using an expanded polytetrafluoroethylene (PTFE) prosthetic ligament. Am. J. Sports Med. 15(4) 326-330. 

Experimental studies of voidage in the vicinity of bubbles rising in a fluidized bed have shown that these bubbles are surrounded by an expanded shell where the void fraction is considerably in excess of that in the remote bulk of the bed [61,62]. Such voidage variations had been reported in earlier experiments conducted using two-dimensional model beds [63,64]. Because these observations are at variance with the available theories of steady bubble motion in fluidized beds [65], they have been used by a number of researchers to reexamine these theories. Thus, Collins [66] fits an equation to the results of reference [63],... 

For the monoatomic chain both problems have been overcome by the QCA of CoUins [17] for solitary waves and periodic modes. Here the difference operator is inverted instead of expanded. Rosenau [21] developed a still more general approximation scheme which reduces to the result of Collins in the case of solitary waves. 

For hijh values of Z, it becomes advantageous to expand in powers of Z as well as 0tZ. gEarly calculations o gthis type ere done Dalgarno and Stewart, Layzer and Bahcall, Collin ... 

Using mass and energy balances, derive suitable equations for the liquid yield and work per unit mass compressed for a Collins helium liquefier utilizing two expanders. Assume all of the components of the system except the expansion valve are ideal and that the work from the expanders is utilized in the compression process. Derive similar equations for a Collins helium liquefier that uses a nitrogen bath to precool the compressed helium gas before entering the first expander. 

Helium gas in a Collins liquefier is compressed isothermally and reversibly from 0.101 MPa and 300 K to 1.41 MPa. After cooling this compressed gas to 60 K, 25% of the gas is expanded in the first expander to 0.101 MPa. The remaining gas is further cooled to 15 K where 50% of the original compressed gas is expanded in a second expander to 0.101 MPa. If both expanders operate adiabatically and reversibly, determine the liquid yield, work required per unit mass of helium compressed, work required per unit mass of helium liquefied, and the figure of merit, assuming that the expander work is dissipated externally. Determine these same quantities when the expanders have a thermodynamic efficiency of 70% and the compressor has an overall efficiency of 75%. 

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