Under steady-state conditions

The mathematical description of the echo intensity as a fiinction of T2 and for a repeated spin-echo measurement has been calculated on the basis that the signal before one measurement cycle is exactly that at the end of the previous cycle. Under steady state conditions of repeated cycles, this must therefore equal the signal at the end of the measurement cycle itself For a spin-echo pulse sequence such as that depicted in Figure B 1.14.1 the echo magnetization is given by [17]... 

The high rate of mass transfer in SECM enables the study of fast reactions under steady-state conditions and allows the mechanism and physical localization of the interfacial reaction to be probed. It combines the usefid... 

Dir, whereas for small distances d < r), /r Did. The large effective obtainable enables fast heterogeneous reaction rates to be measured under steady-state conditions. Zhou and Bard measured a rate constant of 6 x 10 Ms for the electro-hydrodimerization of acrylonitrile (AN) and observed the short-lived intennediate AN for this process [65]. 

New radicals are introduced by thermolysis of the hydroperoxide by chain-branching decomposition (eq. 4). Radicals are removed from the system by chain-termination reaction(s) (eq. 5). Under steady-state conditions, the production of new radicals is in balance with the rate of radical removal by termination reactions and equation 8 appHes for the scheme of equations 1—5 where r. = rate of new radical introduction (eq. 4). 

SJng Je Rod-Fed Electron Beam Source. The disadvantages of multiple sources for alloy deposition can be avoided by using a single wire-fed or rod-fed source (Fig. 3) (3). A molten pool of limited depth is above the soHd rod. If the equiUbrium vapor pressures of the components of an alloy A B are in the ratio of 10 1 and the composition of the molten pool is A qB, under steady-state conditions, the composition of the vapor is the same as that of the soHd being fed into the molten pool. The procedure can be started with a pellet of appropriate composition A qB on top of a rod A B to form the molten pool initially, or with a rod of alloy A B to evaporate the molten pool until it reaches composition A qB. The temperature and volume of... 

Fig. 3. AHoy evaporation from a single rod-fed source under steady-state conditions p° = 10p° AB feed rod, A B molten pool, A qB and vapor and deposit, A B, where p° = the equilibrium vapor pressure of component B B, and p° = the equilibrium vapor pressure of component A A. Part (a) shows...

Rotational viscometers often were not considered for highly accurate measurements because of problems with gap and end effects. However, corrections can be made, and very accurate measurements are possible. Operating under steady-state conditions, they can closely approximate industrial process conditions such as stirring, dispersing, pumping, and metering. They are widely used for routine evaluations and quahty control measurements. The commercial instmments are effective over a wide range of viscosities and shear rates (Table 7). 

Thus when an electric field is appHed to a soHd material the mobile charge carriers are accelerated to an average drift velocity v, which, under steady-state conditions, is proportional to the field strength. The proportionality factor is defined as the mobility, = v/E. An absolute mobility defined as the velocity pet unit driving force acting on the particle, is given as ... 

Most theories of droplet combustion assume a spherical, symmetrical droplet surrounded by a spherical flame, for which the radii of the droplet and the flame are denoted by and respectively. The flame is supported by the fuel diffusing from the droplet surface and the oxidant from the outside. The heat produced in the combustion zone ensures evaporation of the droplet and consequently the fuel supply. Other assumptions that further restrict the model include (/) the rate of chemical reaction is much higher than the rate of diffusion and hence the reaction is completed in a flame front of infinitesimal thickness (2) the droplet is made up of pure Hquid fuel (J) the composition of the ambient atmosphere far away from the droplet is constant and does not depend on the combustion process (4) combustion occurs under steady-state conditions (5) the surface temperature of the droplet is close or equal to the boiling point of the Hquid and (6) the effects of radiation, thermodiffusion, and radial pressure changes are negligible. 

Determination of Crystallization Kinetics. Under steady-state conditions, the total number production rate of crystals in a perfectly mixed crystallizer is identical to the nucleation rate, B. Accordingly,... 

Under steady-state conditions the temperature of the evaporating surface increases until the rate of sensible heat transfer to the surface equals the rate of heat removed by evaporation from the surface. To calculate this temperature, it is convenient to modify Eq. (12-26) in terms of humidity rather than partial-pressure difference, as follows ... 

As the oxygen transfer rate under steady-state conditions must equal oxygen uptake, K a may be calculated ... 

With the above as an introduction, we now consider the important operational case of filtration performed under constant pressure. In practice, all the parameters defined above are nearly constant under steady state conditions except V and r, which are varied by the operator. We may therefore integrate the working expression for filtration over the limits of volume from 0 to V, and for residence time over the limits of 0 to x ... 

I FIGURE 11.27 Heat conduction through an external wall. The temperature distribution over die wall thickness is linear only under steady-state conditions. 

Under steady-state conditions, the temperature distribution in the wall is only spatial and not time dependent. This is the case, e.g., if the boundary conditions on both sides of the wall are kept constant over a longer time period. The time to achieve such a steady-state condition is dependent on the thickness, conductivity, and specific heat of the material. If this time is much shorter than the change in time of the boundary conditions on the wall surface, then this is termed a quasi-steady-state condition. On the contrary, if this time is longer, the temperature distribution and the heat fluxes in the wall are not constant in time, and therefore the dynamic heat transfer must be analyzed (Fig. 11.32). 

Thermal transmittance (t/-value) defines the ability to an element of structure to transmit heat under steady-state conditions. It is a measure of the quantity of heat that will flow through unit area in unit time per unit difference in temperature of the individual environments between which the structure intervenes. It is calculated as the reciprocal of the sum of the resistance of each component part of the structure, including the resistance of any air space or cavity and of the inner and outer surfaces. It is expressed as W/m K. 

Conduction of heat through plain surfaces under steady-state conditions is given by the product of the area, temperature difference, and overall conductance of the surface (see Section 1.8) ... 

The intracellular pH can also regulate the exchanger. [H+] strongly inhibits NCX activity under steady-state conditions, in fact, reduction in [pH] values, as little as 0.4, can induce a 90% inhibition of NCX activity. Such inhibitory action depends on the presence of intracellular Na+ ions, hence, the action exerted by H+ ions is pathophysiologically relevant with regards to brain and heart ischemia. 

Certain hydrodynamical problems, as well as mass-transfer problems in the presence of surface-active agents, have been investigated theoretically under steady-state conditions (L3, L4, L10, R9). However, if we take into account the fact that in gas-liquid dispersions, the nonstationary term must appear in the equation of mass- or heat-transfer, it becomes apparent that an exact analysis is possible if a mixing-contacting mechanism is adopted instead of a theoretical streamline flow around a single bubble sphere. 

Moving Bubbles with Clean Interfaces under Steady-State Conditions... 

Under steady-state conditions, as in the Couette flow, the strain rate is constant over the reaction volume for a long period of time (several hours) and the system of Eq. (87) could be solved exactly with the matrix technique developed by Basedow et al. [153], Transient elongational flow, on the other hand, has two distinctive features, i.e. a short residence time (a few ps) and a non-uniform flow field, which must be incorporated into the kinetics equations. In transient elongational flow, each rate constant is a strongfunction of the strain-rate which varies with time in the Lagrangian frame moving with the center of mass of the macromolecule the local value of the strain rate for each spatial coordinate must be known before Eq. (87) can be solved. 

A more rigorous treatment takes into account the hydrodynamic characteristics of the flowing solution. Expressions for the limiting currents (under steady-state conditions) have been derived for various electrodes geometries by solving the three-dimensional convective diffusion equation ... 

One should note that this happens without the occurrence of reactions between pairs of intermediates that have inherently lower rates under steady-state conditions. 

If two vessels each containing completely mixed gas, one at temperature T, and the other at a temperature T2, are connected by a lagged non-conducting pipe in which there are no turbulent eddies (such as a capillary tube), then under steady state conditions, the rate of transfer of A by thermal diffusion and molecular diffusion must be equal and opposite, or. 

The treatment here is restricted to first-order irreversible reactions under steady-state conditions. Higher order reactions are considered by ARJS(30). 

Liquid flows under steady-state conditions along an open channel of fixed inclination to the horizontal. On what factors will the depth of liquid in the channel depend Oblain a relationship between the variables using dimensional analysis. 

Solve the above equation for a first-order reaction under steady-state conditions, and obtain an expression for the mass transfer rate per unit area at the surface of a catalyst particle which is in the form of a thin platelet of thickness 2L. 

Models and theories have been developed by scientists that allow a good description of the double layers at each side of the surface either at equilibrium, under steady-state conditions, or under transition conditions. Only the surface has remained out of reach of the science developed, which cannot provide a quantitative model that describes the surface and surface variations during electrochemical reactions. For this reason electrochemistry, in the form of heterogeneous catalysis or heterogeneous catalysis has remained an empirical part of physical chemistry. However, advances in experimental methods during the past decade, which allow the observation... 

The above values of kz may be compared with that required to explain Green s results (20) (obtained from measurements on an atmospheric pressure H2/02/Ar flame at 2180°K. to which had been added 2.8% by volume of CoH2) in terms of Reaction 3. Under steady-state conditions the rates of production and loss of negative ions are equal. (Steady-state conditions are those under which ion concentrations maxi-... 

In a smooth muscle cell under steady state conditions, the reactions described by the set of Equations 2-6 are probably very close to equilibrium in the sense that they are not continuously held far away from equilibrium by ongoing metabolic reactions, e.g., ATP hydrolysis. The resting concentrations of the reactants of these... 

Reactions 2 and 3 regulate the balance of O and O3, but do not materially affect the O3 concentration. Any ozone destroyed in the photolysis step (3) is quickly reformed in reaction 2. The amount of ozone present results from a balance between reaction 1, which generates the O atoms that rapidly form ozone, and reaction 4, which eliminates an oxygen atom and an ozone molecule. Under conditions of constant sunlight, which implies constant /i and /s, the concentrations of O and O3 remain constant with time and are said to correspond to the steady state. Under steady-state conditions the concentrations of O and O3 are defined by the equations d[0]/df = 0 and d[03]/df = 0. Deriving the rate expressions for reactions 1-i and applying the steady-state condition results in the equations given below that can be solved for [O] and [O3]. 

Simandi and Nagy studied the kinetics of the catalyzed hydrogenation of cinnamic acid (S) to dihydrocinnamic acid (SHj) under steady-state conditions 166). They concluded that the kinetically important reactions were the two successive transfers of hydrogen atoms, viz.. 

S] + K )] for the hexokinase-catalyzed phosphorylation reactions of 2DG and D-glucose, respectively [S (substrate) + E (enzyme) — ES— -I- P (product)]. This constant (LC) accounts for the ratio of the arteriovenous extraction fraction (by transport and phosphorylation) of 2DG to that of D-glucose (LC= 1) under steady-state conditions. This concept can be directly applied to the case of 2DFG by employing the LC (-0.5) for 2DFG. 

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