Flux equality

Under conditions of sedimentation equilibrium, the sum of these two fluxes equals zero, or... 

Electroultrafiltration has been demonstrated on clay suspensions, electrophoretic paints, protein solutions, oil—water emulsions, and a variety of other materials. Flux improvement is proportional to the appHed electric field E up to some field strength E where particle movement away from the membrane is equal to the Hquid flow toward the membrane. There is no gel-polarization layer and (in theory) flux equals the theoretical permeate flux. It... 

Assuming an input flux equal to oceanic evaporation, this would give a turnover time of about 750 years. The turnover time analysis is not strictly correct since freshwater resides in a number of interconnected reservoirs however. 

Figure 9.23 Schematic representation of the various electrochemical and chemical reactions occurring in a membrane electrode assembly and the concentration gradients of O2, H2, and Pt ions. The location where the local O2 molar flux equals one-half of the local H2 molar flux is marked by 5pt. (Reproduced with permission from Zhang J et al. [2007a].)...

Local quality method Dryout occurs when the local nonuniform heat flux equals the uniform heat flux dryout value at the same local conditions (quality, etc.). 

Under steady-state conditions, the internalisation flux equals the rate of supply by diffusive transport and chemical reactions. As was shown earlier (cf. equations (12) and (13)), the maximum flux (rate) of solute internalisation by a microscopic cell under diffusion-limited conditions can be given by ... 

Butler- Volmer equation and, 1217 controlled reaction rates, 1213, 1218 -convective mechanism. 1229 flux-equality equation, 1213 heat flow and, similarities, 1215 interfacial response at constant current 1216, 1218... 

How the Transport Flux Is Linked to the Charge-Transfer Flux The Flux-Equality Condition... 

If diffusion is the transport mechanism, the flux equality condition becomes... 

The flux continuity or flux equality condition can be applied even when the current density i and the transport flux,/ are changing with time. One simply structures dr into small time intervals and says that the condition is valid within this infinitesimal time. 

Once this flux equality condition (7.173) is formulated, one simply works out transport as a Pure transport problem and equates it to 1 InF times the current density across the interface since n faradays per mole are required for the transported material to be electronated. If the transport process consists of pure diffusion (i.e., there is no contribution from either migration or hydrodynamic flow), then the flux is given by Fick s first law (see Section 4.2.2), i.e.,... 

In reality, the concentration gradient is constant for only a short distance from the interface and then becomes asymptotic to zero in the bulk. But one can resort to a linearization of the concentration profile, and then one can use the artifice of an imagined (i.e., simplified) diffusion layer in which the concentration is taken as if it changed in a linear fashion from the interfacial value to the bulk value c0. The effective thickness 8 of the diffusion layer, which can be taken as a constant independent of time only under steady-state conditions in which natural convection occurs, proved a useful quantity. With its aid, one can write out the flux-equality condition in the form... 

This is due to the large electron fluxes in modern accelerators. For a current of 10 mA we have an electron flux Je - 1017 s-1. The photon flux equals the product... 

The steady-state deelectronation current density id is related by the condition of flux equality (Section 4.2.7) to the flux J of hydrogen permeating through the metal (Fig. 12.70) ... 

As a special case, if the relative flux equals the vapor phase bulk composition y being in equilibrium with the liquid bulk phase composition xu then we speak of a nonreactive azeotrope. Thus, the azeotropic case can be seen as a limiting case of the arheotropic case. 

The diffusivity, a2, is subsequently determined under the condition that the intercepts of the linear fits for the thermally thick and thin conditions are equal. For the PA6 nanocomposite, when the diffusivity is equal to 0.9 x 10 7m2/s, the intercepts are almost the same at about 11.5kW/m2. These intercepts are equal to the 0.64 fraction of the critical heat flux (below which there is no ignition) for ignition [21], and thus the critical heat flux can be calculated equal to 11.5/0.64 = 17.9 kW/m2. The ignition temperature can then be calculated by considering the critical heat flux equal to surface reradiation and convection losses ... 

Then assuming that the mass-flux equality holds for the effect compartment, i.e., Vckc = Vyky, the drug concentration y (t) in the effect compartment can be described by the linear differential equation... 

This relationship is a consequence of the detailed balance condition that in equilibrium each of the reactions in this scheme is in equilibrium with its forward flux equal to reverse flux [127]. Similarly,... 

In the equations given in Table 5.2 the surface temperature is not known. The surface temperature is obtained by making the heat and mass transfer fluxes equal as given in equation (5.32). This is equivalent to equating the expressions for the values of t for heat and mass transfer... 

The second problem concerns an understanding of the sharing of transport duties (e.g., the carrying of current) in pure liquid electrolytes. In aqueous solutions, it was possible to comprehend the relative movements of ions in the sense that one ionic species could drift under an electric field with greater agility and therefore transport more electricity than the other until a concentration gradient was set up and the resulting diffusion flux equalized the movements when the electrodes were reached. In fused salts, this comprehension of the transport situation is less easy to acquire. At first, it is even difficult to see how one can retain the concept of transport numbers at all when there is no reference medium (such as the water in aqueous solutions) in which ions can drift. 

Superficially, the attenuation is related to the random projected areas of the particles. The relationship is more complex than this however, due to the breakdown in the laws of geometric optics so that complex diffraction, scattering, interference and absorption effects have to be considered. For small particles, an amount of light flux, equal in magnitude to that incident upon the particle, is diffracted away from the forward direction (Figure 7.10), making their effective obscuration area twice their projected... 

Then the boundary condition at a boundary is obtained by setting the specified heat flux equal to -k(3T/dx) at that boundary. The sign of the specified heat flux is determined by inspection positive if the heat flux is in the positive direction of the coordinate axis, and negative if it is in the opposite direction. Note that it is extremely important to have Ihe correct sign for the specified heat flux since the wrong sign will invert Ihe direction of heat transfer and cause the heat gain to be interpreted as heat loss (fig. 2-29),... 

It may be instructive to note that the system will come to equilibrium with respect to the solute when the flux equals zero. From the above equation it is evident that this happens when the electrochemical gradient of the solute is zero or, in other words, when its electrochemical potential is equal on the two sides of the membrane. 

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