Imposed Gradients

The same stoichiometric gradients can also be generated by var5dng the gas composition in cell 1. Let us assume that two electrode chambers are isolated from each other and the oxygen partial pressure in one chamber (say at x= L) is suddenly changed. We also assume the electrode reactions and the surface exchange at the electrode contact to be very fast, while the uncontacted surfaces are sealed or inactive. The concentration profiles in the interior can then be calculated from Pick s second law with fixed concentrations on both sides as boundary conditions. The solutions are given in Appendix 3 (see also Ref ). The 

As the cell voltage is determined by the boundary values only, it is at all times given by the zero-current value of Eqs. (72) and (73). Using electronic probes the result is  

The heuristic equivalent to Eq. (77) can also be directly derived from the equivalent circuit Par(Ser(/ , if the 

Reprinted from J. Maier and G. Schwitzgebel, Mater. Res. Bull., 17 (1982) 1061-1069. Copyright 1982 with permission from Elsevier. 

The symmetrical reversal of the above chemical polarization experiment is the sudden replacement of the oxygen partial pressure on x = L by the original one Then the concentration profiles decay by chemical depolarization (allowing again for a measurement of Lf). If, however, the gas flow at that gas chamber is just stopped, the gas pressure equilibration takes more time in that it not only affects the sample volume but also the volume of the gas chamber. This directly connects with the permeation technique described in the next section. 

---

Chakraborty S (2006) Analytical solutions of Nusselt number for thermally fully developed flow in microtubes under a combined action of electroosmotic forces and imposed gradients. Int J Heat Mass Transfer 49 810-813... 

To study the nature of this rapid polymer transport in detail, this section will be concerned with a series of experimental measurements on one particular system, namely a solution of dextran T10 (N5W 10 ) with a uniform concentration of 135 kg m-3 and an imposed gradient of a linear, flexible polyvinylpyrrolidone) (NTn 3 x 10s) (PVP 360). This gradient initially extended from 5 kg m3 to zero concentration. The choice of using the polymers at this concentration was based upon our earlier work441 in which it was shown that nearly maximal transport rates of PVP 360 occur in such a system. This system will be referred to as the standard system. The phase diagram of this PVP 360/dextran T10 mixture clearly demonstrates that the transport experiments were performed within the one-phase region 47). 

In the case of rhodopsin membrane under calcium gradient, the technique shows a nonlinearity of fluxes with respect to imposed gradients. We also notice some permeability variations just after rhodopsin bleaching and at last a calcium adsorption consequent to lighting performed in situ. 

Hyperpolarizability does not imply that the system is completely at the control of the external gradients. Indeed, the response is very special--there is a strong tendency for the form of the response to be essentially that of the modes of the stability analysis which are most weakly stable and, beyond the point of instability, become the autonomous (imposed gradient free) pattern. 

Induction of New Phenomena by Imposed Gradients. Studies on the effects of imposed electric fields on chemical waves (see below on signal propagation) show that phenomena can be induced in the system by the imposed gradient that do not exist in the field free medium. For example, it was found (l l) that for a system wherein only one type of wave existed in the field free case, two stable types of waves exist in the system subject to the field. This "induction of multiplicity" implies that beyond a critical value of the applied field strength new phenomena may set in that are not simple distortions of field free patterns. Another strictly imposed field effect is found in the case of a new two dimensional crescent shaped wave that occurs when a circular wave is subjected to a supracritical field (15). 

The first term on the right-hand side of (110) is the gradient of the particle potential energy and the second term the force induced by the imposed gradient of the overall flow. 

McCoy, B. J. "Counteracting chromatographic electrophoresis and related imposed-gradient sejjaration processes" AIChE J. 1986,32, pp 1570-73. 

In contrast to the case discussed above, an imposed gradient in the interfacial tension causes a viscous flow in the adjoining bulk phase(s), as shown in Figure 17.15. For instance, if the interfacial tension is locally lowered by applying an amphiphilic compound the monolayer moves away from that place to annihilate the interfadal tension gradient. This phenomenon is called the Marangoni effect. The ensuing shear rate in the bulk phase is such that Equation 17.22 is satisfied. 

Lengyel, I, Kadar, S. Epstein, I. R. 1992a. Quasi-Two-Dimensional Turing Patterns in an Imposed Gradient, Phys. Rev. Lett. 69, 2729-2732. 

Experiments show that the position of the layer where the structures form depends on the boundary conditions. In Figure 6 we show how the position of the layer where the structures form depends on the malonic acid concentration. It is not simple to model these results, because in the experimental system there are three spatial dimensions. Two of these three dimensions, which are perpendicular to the gradients imposed by the fixed concentration at the boundaries, are equivalent. The extent of the system in these two dimensions is much greater than in the third direction where we have the imposed gradient. 

MPC transport coefficients have also been evaluated by calculating the linear response of the system to imposed gradients. This approach was introduced by Kikuchi et al. [26] for the shear viscosity and then extended and refined in [35] to determine the thermal diffnsivity and bulk viscosity. Here, we sununarize the derivation of the shear viscosity. 

---