One-dimensional gas

In chemical process applications, one-dimensional gas flows through nozzles or orifices and in pipelines are the most important apphcations of compressible flow. Multidimensional external flows are of interest mainly in aerodynamic applications. 

Consider a one-dimensional gas-solid pipe flow where the electrostatic effect is negligible. The momentum equation of the particle phase can be expressed as [Klinzing, 1981]... 

For a crystal in contact with a supersaturated solution, the kink site density is expected to be larger than at equilibrium. Since the movement of kinks along a step is energetically neutral, the kinks may be regarded as analogous to a one-dimensional gas. Hence, the density of kinks along a step is... 

We now define new operators Oa(q), which are the Fourier components of operators characterizing the various ordered states of the interacting one-dimensional gas, namely a = CDW, SDW, or singlet, triplet superconductivity SS and TS, for example ... 

Almost two decades ago theoreticians predicted that in a quasi-one-dimensional metal, characterized as having a one-dimensional gas of weakly interacting electrons, instabilities could arise leading to transitions to various ground states, such as charge density wave (CDW), spin density wave (SDW), or superconducting (61). Previously, it had been predicted that electron-phonon coupling in a one-dimensional... 

A data aquisition system based on a one dimensional, gas filled detector is shown in Fig. 31. The general philosophy of the system is to be as independant as possible from a central computer as the enormous amount of data demand an on line data analysis during the experiment. 

Models for turbulent fluidized bed reactors are normally based on one dimensional gas flow, despite the significant radial density gradients observed experimentally [56, 57],... 

In this connection let us consider the FrShlieh-type Hamiltonian. As it is well known sueh a one-dimensional gas has no stability with Tsspect to the transition to the Peierls dielectric or to the superconductor state. If we use the self-consistent method the gap in the electronic spectrum of Fermi excitations will be of order of g- for Peierls distorted phase and for superconducting one. where ... 

High-resolution analysis of the entire suite of C2-C12 NMHCs by conventional one-dimensional gas chromatography is typically performed with various siloxane-coated fused-silica capillaries or PLOT columns. Designing a single GC analysis which will adequately separate the entire complex mixture is very difficult to achieve, because ethene, acetylene, and ethane are difficult to separate, even with a 100 m siloxane-coated column. Furthermore, separations with a column of this length take approximately 70 min. The PLOT columns can completely resolve the C2-C3 NMHCs, but resolution of the Cg-Ci2 NMHCs is poor. If the sample is analyzed separately in a 60 m siloxane column, mounted in one GC and a PLOT column mounted in another, the analyses can be completed in approximately 45 min. The preconcentrated sample is transferred to a 60 m X 0.32 mm i.d. fused-silica capillary column coated with a 1 /rm-thick film of poly-dimethylsiloxane (PDMS) and a 30 m X 0.53 mm i.d., PLOT column coated with alumina to resolve the C4-C12 and C2-C3 NMHCs, respectively. The oven temperature for the PDMS column is held at — 50°C for 2 min, then increased to 210°C at 8°Cmin and thereafter to 250°C at... 

In further studies of the TSP on a randomly diluted lattice [49] the expression for Icip), the average length of the shortest path per occupied site was derived. For a triangular lattice, Icip) is unity and has a correction of order of (1-p) . In the case of a square lattice, retaining only first order terms, the optimal paths can be derived from the dynamics of a model of a one-dimensional gas of kinks and anti-kinks. With the Cartesian metric, it was found that Icip) < 1 + O ((1 — p) ) a constructive upper bound valid for all p... 

The internal couplings between the two translational mechanical subvarieties are ruled by the coupling relationships already seen for the one-dimensional gas ... 

We expect to find a dilute regime, with coils that behave very much like a one-dimensional gas of hard rods, each of length /. If the average concentration is c, the number of chains per unit length is (ir/4) (c/iV)... 

Figure 8.3 In the dimer state the two particles of a one-dimensional gas are adjacent. 

Using the calculation methods of one dimensional gas dynamic shows how different motive media behave during the expansion in the motive nozzle. Depending on the expansion ratio ( = motive vapour pressure/suction pressure), the Mach number at the motive nozzle outlet for some vapours is charted in Figure 4.18. It can be seen, that the velocity is in the supersonic range and therefore the corresponding effects (expansion, compression and shock waves) have to be considered. 

The mathematical model describing the gas flow distribution in one crossing cell can be summarized follows. For steady state, one dimensional gas flow, the mass balance is... 

This shows that the cdl-duster model gives indeed the correct entropy for a one-dimensional gas. In the case of the 2 or 3 dimensional perfect gas, no exact treatment is yet possible, but it has been shown that the first approxunation after the Lennard-Jones and Devondiire cell modd already gives a large part of the communal entropy (Cohen, De Boer and Salsburg [1955]). 

In a study of natural flux of trichloroethylene (TCE) from the subsurface reported by Tillman et al. (2003), surface flux measurements made by a flux chamber were compared with flux simulations using a transient, one-dimensional gas-flow and transport model incorporating the effects of gas phase diffusion,... 

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