Steady state theory

Leslie C. Edie, Car-following and Steady-state Theory for Noil-congested Traffic, Operations Research, 9, No. I, 66-76 (1961). 

Let us compare these results with the predictions of the theory formulated by Lampe etal. (24) in terms of a steady-state concentration of collision complexes. This is a classical macroscopic treatment insofar as it makes no assumptions about the collision dynamics, but its postulate of collision complexes implies that v8 = vp/2 for the system treated above. Thus, its predictions might be expected to coincide with those of the collision-complex model. Figure 3 shows that this is not so the points calculated from the steady-state theory (Ref. 25, Equation 10) coincide exactly with the curve for which v8 = vv. The reason for this is that the steady-state treatment assumes a constant time available for reaction irrespective oC the number of reactions occurring in any one reaction... 

No steady-state theory for kinetically controlled heterogeneous IT has been developed for micropipettes. However, for a thin-wall pipette (e.g., RG < 2) the micro-ITIES is essentially uniformly accessible. When CT occurs via a one-step first-order heterogeneous reaction governed by Butler-Volmer equation, the steady-state voltammetric response can be calculated as [8a]... 

Bungay PM, Morrison PF, Dedrick RL. 1990. Steady-state theory for quantitative microdialysis of solutes and water in vivo and in vitro. Life Sci 46(2) 105-119. 

Assuming that Reaction 5 is not reversible and that it is the ratedetermining step in the proposed termination mechanism, the rate of oxidation predicted on application of the steady-state theory is given by Equation A. 

Assuming that Reactions 5 and 14 are irreversible, combining Schemes 1 and 3 and applying the steady-state theory leads to a theoretical rate of oxygen absorption given by Equation D ... 

The hydrodynamic theory of the penetration of targets by lined cavity jets was developed, according to Cook (Ref 7, p 252), independently by Pugh (Birkhoff s et al Ref 2) and by Hill et al (Ref 1). Pack Evans (Refs 3 4) discussed the steady-state theory of penetration in which the jet-velocity. distribution was ignored and the penetration velocity was assumed constant. Pugh, 8t Eichelberger (Refs 5 6) discussed the nonsteady-state of jet penetration in which, the actual velocity distribution in the jet was taken into account as well as the variation of the velocity of penetration with.depth These theories are discussed by Cook (Ref 7) Refs 1) R. Hill, N.F. Mott D.C. Pack, Unpublished "Ministry of Supply Report, January 1944 2) G. Birkhoff, D.P. Mac-... 

The quasi-steady-state theory has been applied particularly where a condensed phase exists whose volume changes slowly with time. This is true, for example, in the sublimation of ice or the condensation of water vapor from air on liquid droplets (M3, M4). In the condensation of water vapor onto a spherical drop of radius R(t), the concentration of water vapor in the surrounding atmosphere may be approximated by the well-known spherically symmetric solution of the Laplace equation ... 

The theme of the conference was divided into three parts the first one concerned General Statements of Cosmological Theory. It was introduced by speeches by Lemaitre, on the Primaeval Atom Hypothesis and the Problem of Clusters of Galaxies, by Oscar Klein who developed Some Considerations Regarding the Earlier Development of the System of Galaxies, and by Hoyle on The Steady-State Theory. This was followed by a talk by Gold, on the Arrow of Time and another by Wheeler on Some Implications of General Relativity for the Structure and Evolution of the Universe. ... 

The solution of the above problem applies to both transient and steady-state feedback experiments. Since transient SECM measurements are somewhat less accurate and harder to perform, most quantitative studies were carried out under steady-state conditions. The non-steady-state SECM response depends on too many parameters to allow presentation of a complete set of working curves, which would cover all experimental possibilities. The steady-state theory is simpler and often can be expressed in the form of dimensionless working curves or analytical approximations. 

Chains, Stokes law with, 68-70 Chan, T., 120 Chapman, S. J., 168-169 Characteristic charge, 187 Characteristic length and diffusion, 155 Charging mechanisms, 179 collisions with ions, 185 contact electrification, 182-183 corona discharge, 195-198 diffusion, 185-189,195 electric, 179-183 equilibrium with, 200-201 steady-state theory of, 201-207 transient approach to, 207-208 field charging, 185,189-195 flame ionization, 184-185 and force, 179-180 frictional, 184... 

Steady state theory The cosmological theory that the universe had no beginning. This theory has been largely replaced by the big bang theory. 

Leuning, R. 1987. Leaf temperatures during radiation frost part II. A steady state theory. Agric. Forest Meteorol. 42 135-155. 

In the same year that the a y paper was published, another cosmological scheme was proposed to account for the presently observed universe. The architects of this theory were Fred Hoyle, Hermann Bondi, and Thomas Gmld from Cambridge University, who developed it in two papers pubfished in 1948. This theory, called the steady state theory, was the polar opposite of the big bang." Whereas the big bang posited a definite beginning and ongoing evolution, the steady state theory was based on what can be... 

H. Bondi and T. Gold, The Steady-state Theory of the Expanding Universe, Monthly Notices of the Royal Astronomical Society 108, 2S2-27Q (1948) and F. Hoyle, A New Model for the Expanding Universe, Monthly Notices of the Royal Astronomical Society 108, 373-382 (1948). 

The film theory was originally proposed by Whitman,195 who obtained his idea from the Nernst117 concept of the diffusion layer. It was first applied to the analysis of gas absorption accompanied by a chemical reaction by Hatta.85,86 It is a steady-state theory and assumes that mass-transfer resistances across the interface are restricted to thin films in each phase near the interface. If more than one species is involved in a multiphase reaction process, this theory assumes that the thickness of the film near any interface (gas-liquid or liquid-solid) is the same for all reactants and products. Although the theory gives a rather simplified description of the multiphase reaction process, it gives a good answer for the global reaction rates, in many instances, particularly when the diffusivities of all reactants and products are identical. It is simple to use, particularly when the... 

Any form of convection, of course, increases the value of Ks. In slurry operation with no liquid flow, gas flow induces convection. In an agitated slurry reactor, stirring causes convection. In a pulsating slurry reactor, pulsation of the slurry induces convection and in a three-phase fluidized bed, the movements of both gas and liquid phases cause convection. Any one or more modes of convection will increase the value of the solid-liquid mass-transfer coefficient. In broad terms, the convective liquid-solid mass-transfer coefficient is correlated by-two steady state theories. Here we briefly review and compare them. 

Thus, a relation of the type (9-58) may be valid because of the fact that the specific power group leads to nearly equal particle Reynolds number based on the relative velocity. Kuboi et al.67 also showed that, as long as an approximate relative velocity is used, the steady-state theories predict almost as good a mass-transfer coefficient as the more complex unsteady-state theories, a view not supported by some other workers.75,125 They claimed that the velocity of a particle relative to the surrounding liquid may correspond closely to the effective relative velocity for particle-to-liquid mass transfer. 

As outlined above, steady-state theories for the liquid-solid mass transfer are largely classified into two categories i.e., those based on Kolmogoroff s theory and those based on the terminal velocity-slip velocity approach. 

---