Compressible regime

HEM for Two-Phase Pipe Discharge With a pipe present, the backpressure experienced by the orifice is no longer qg, but rather an intermediate pressure ratio qi. Thus qi replaces T o iri ihe orifice solution for mass flux G. ri Eq. (26-95). Correspondingly, the momentum balance is integrated between qi and T o lo give the pipe flow solution for G,p. The solutions for orifice and pipe now must be solved simultaneously to make G. ri = G,p and to find qi and T o- This can be done explicitly for the simple case of incompressible single-phase (hquid) inclined or horizontal pipe flow The solution is implicit for compressible regimes. 

Fig. 8. Dependence of non-trivial knot formation probability, p, on swelling parameter, a, in globular state. Points-data from Ref. [29] dashed ttne - approximation in weak compression regime solid line - approximation based on concept of crumpled globule (Eq. (S3))...

Figure 1. Molecular dynamics snapshot of a 2-dimensional Lennard-Jones SCF in the compressible regime at T = 0.55 in Lennard-Jones reduced units (Tr = T/Tc = 1.15) and p = 0.30 dl] (pr = pIpc = 0.79). Reprinted with permission from Ref. [12]. Copyright 1999 American Institute of Physics.

Energy transfer between the solute and solvent is a necessary component of solute reaction, because it enables the reacting solute to surmount its activation barrier and also to become trapped in the product potential well. At low to intermediate densities, where solute-solvent interactions may be infrequent and/or weak, energy transfer may be slow enough to become rate limiting. As such, it is critical to know how solvent compressibility, which arises in intermediate density SCFs in the compressible regime, affects solute-solvent energy transfer rates. We thus discuss a very simple process which... 

A possible, relatively ubiquitous source of error in the standard extraction analysis used above is the neglect of the very broad distributions of local densities which exist in the compressible regime (Fig. 2). Specifically, the extraction analysis assumes that the observable of interest, A, is a function of the mean local density, i.e. A((p )). However, the ensemble average of the observable, and thus the measured value, is really... 

Supercritical fluids in the highly compressible regime are of particular interest, because it is in this regime that one can easily access the intermediate solvent densities, and thus the associated intermediate solvent properties, which are obscured in subcritical fluids by the liquid-vapor coexistence curve. However, a large macroscopic compressibility arises from a balance of energetic and entropic forces which, concomitantly, give rise to interesting microscopic behaviors. These microscopic consequences must be accounted for if one is to accurately predict reaction rates in compressible SCFs. 

Goodyear, G., M. Maddox, and S. C. Tucker, Density inhomogeneities in the compressible regime of a supercritical Lennard-Jones fluid ., submitted. 

Note that in 2-dimensional systems the correlation length remains long further from the critical point than in 3-dimensional systems,[106,27] and this is why compressible regime behavior is already observed on the Tr = 1.15 isotherm of the 2-dimensional Lennard-Jones SCF. This is in contrast to the experimental isotherms considered the near-critical isotherm was at Tr = 1.01, while the high temperature isotherm was at Tr = 1.06. 

Chapter 16. Solute reaction dynamics in the compressible regime... 

Thickener Basin Depth. In the hindered settling conditions, the pulp depth is unimportant in the determination of thickening rate and can be omitted. As the pulp enters into the compression regime, the pulp depth and the agitation affect the thickening rate. In this case, the compression zone unit volume may be calculated from the equation (Perry et al., 1997)... 

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