Limiting flux ratios

The bioaffinity parameter a basically reflects the free metal ion concentration, whereas the limiting flux ratio b reflects the total labile metal species concentration. Due to the complexation, the ratio a/b thus changes by a factor (1 +sKcl) in spherical geometry, while the factor (1 I sKc ) (l I Kc ) is required for planar geometry [26]. 

Fig. 13.1. Evolution of the relative flux ratios before and after siliconization of carbon, oxygen and silicon measured on the ALT toroidal limiter as a function of shot number. The data are for a density of 3 x 1013/cm3 with 1.3 MW nuclear beam heating (co-injection)...

Fig. 13.2. Development of the C+ and CD flux ratio as function of the discharge number for a graphite test limiter inserted in a freshly siliconized TEXTOR environment...

Fig. 13.3. Evolution of the relative flux ratios of carbon (a), methane (b) and silicon (c) measured from pure graphite and Si-doped CFC limiters as a function...

For a particular diffusion layer thickness S the thermodynamic availability, as measured with an ISE or calculated from a speciation model, and the electrochemical availability, as measured by ASV, represent limiting cases of a continuum of trace metal availability. The nature of this continuum is most simply defined by considering the flux of the free metal ion across the diffusion layer to a surface which senses the metal availability. The ratio of the observed flux (J) to the limiting flux (J] ) is unity for ASV measurements under current limiting conditions and zero for ISE measurements. 

The first term in Eq. (42) describes the diffusion-limited flux, while the second term l/ l + a) is a correction factor for slow reaction kinetics. Because a is defined as the ratio D /k h, the value of is known and of Djn can be determined independently, the value of k can be determined using Eq. (42). Direct determination offe and from flux measurements as a function of the membrane thickness may be obtained varying the membrane thickness. As a result a is obtained also. If a < 1, the transport is mainly limited by diffusion of the complex while the transport is primarily controlled by the reaction rate in the case that a > 1. 

Fig. 42. Etching yield of silicon bombarded by a Cl atom beam simultaneously with a C1+ ion beam of controlled energy. At low values of the flux ratio, etching is limited by Cl atom supply. At the other extreme, etching is limited by the ion flux. Dashed lines are the result of a Langmuir-Hinshelwood model of the surface reaction. After [70].

The difiusivity is thus dependent upon concentration and flux ratio, and strictly speaking we should not see a theory of catalyst effectiveness based on constant diflfusivity. Efowever, this is more detail than it is worth a good approximation is obtained from the limit of equation (7-72) for constant pressure conditions and Ab = —Na- Then... 

The flux at the surface of the sun ( 63 W/mm ) falls off inversely with the square of the distance to a value 1.37 mW/mm above the earth s atmosphere, or typically 0.8 to 1 mW/mm on the ground. The Second Law of Thermodynamics permits an optical device (in principle) to concentrate the dilute solar flux at earth in order to attain temperatures up to but not exceeding that of the sun s surface. This places an upper limit on the solar flux density achievable on earth and correspondingly on the concentration ratio of any optical device. From simple geometry, this limiting concentration ratio is related to the sun s angular size 20) by... 

As we have previously noted, the relative sizes of Dsbo and DsKSo depend on the transport-limited fluxes of electrons or substrate across the layer. These in turn depend on conductivity and morphology of the film. Let us define the following ratio ... 

Keywords Elementary flux mode Evolution of metabolism Nutrient limitation Resource-ratio theory Stoichiogenomics... 

When the transport is limited by diffusion, the initial transport selectivity is predicted from the results of single-ion transport experiments (27). The flux ratio can be expressed by Equation 29. 

Answer by author The experimental heat flux is definitely dependent upon the air humidity. Within the limits of the environments investigated however we were not able to find a dependence between the air humidity and the heat flux ratio. 

Most prompt methods of analysis depend upon the measurement of thermal neutron capture radiation using reactor sources of neutrons. In spite of the large potential increase in sensitivity, relative to conventional reactor activation, practical application of the prompt method is limited by the low neutron fluxes available in neutron beams. It is seldom possible to exceed a thermal neutron flux of 10 cm s". Henkelmann, in his assessment of prompt y-ray analysis, concludes that (assuming a neutron flux ratio of 10 between decay and prompt methods) prompt methods only offer increased sensitivity... 

For a given monitored variable (e.g. primary circuit pressure, containment pressure) or calculated variable (e.g. reactor power, critical heat flux ratio), a safety limit is established on the basis of safety criteria. This limit should be that value of the variable beyond which unacceptable safety consequences are expected to occur (see Fig. 2). 

It may seem curious that Knudsen diffusion coefficients still appear in equations (5.18) and (5.19), which supposedly give the flux relations at the limit of bulk diffusion control. However, inspection reveals that only ratios of these coefficients are effectively present, and from equation (2,11) it follows that... 

In ulttafUttation, the flux,/ through the membrane is large and the diffusion coefficient, D, is small, so the ratio cjcan teach a value of 10—100 or mote. The concentration of retained solute at the membrane surface, may then exceed the solubility limit of the solute, and a precipitated semisohd gel forms on the surface of the membrane. This gel layer is an additional battier to flow through the membrane. 

In thermoelectric cooling appHcations, extensive use has been made of cascaded systems to attain very low temperatures, but because the final stage is so small compared to the others, the thermal flux is limited (Eig. 3). The relative sizes of the stages ate adjusted to obtain the maximum AT. Thus, for higher cooling capacity, the size of each stage is increased while the area ratios ate maintained. 

With lower heat-flux ratings and higher ratios of internal water volume to heating surface than is the norm today, complex external treatment was not always necessary where deemed necessary, it was often limited to basic sedimentaion or filtration techniques employing inorganic coagulants and flocculants, typically followed by the use of natural zeolites (see sections 9.2.3.1 and 9.2.5 for additional information). 

It is shown that an increase in the heat flux is accompanied by an increase in the liquid and vapor velocities, the meniscus displacement towards the outlet cross-section, as well as growth of vapor to liquid forces ratio and heat losses. When is large enough, the difference between the intensity of heat transfer and heat losses are limited by some final value, which determines the maximum rate of vaporization. Accordingly, when is large all characteristic parameters are practically invariable. 

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