Discontinuous potential profile

We observe then that no more than two species may be imperfectly separated when ( h) is zero, and that only one pure species may be obtained with a poor recovery. To determine what will happen in the other solvent in the region z > Z, it is better to start imagining what will happen if the initial solute mixture pulse were introduced at z = Z (Figure 3.2.5B). If we can assume that a different sequence of profiies of species will be observed in each solvent vessel, then one can get at the most two pure species, one in each vessei from the furthest region from the solute introduction point. It is clear that this type of discontinuous potential profile can at the most separate two pure species and thus inherently lacks multicomponent separation capability. When the diffosion proi ess ceases in such a system after an adequate time has elapsed, the species are going to distribute themselves between the two solvents in a... 

In comparing separation techniques, we generally find a striking difference in methods based on continuous (c) chemical potential profiles and those involving discontinuous (d or cd) profiles. There is, for example, a glaring contrast in instrumentation, applications, experimental techniques, and the capability for multicomponent separations between the two basic static systems, Sc (e.g., electrophoresis) and Sd (e.g., extraction). Similarly, there... 

In the following section we will focus on reactive interfaces. Here again, thermodynamic equilibrium corresponds to particular potential profiles in the interfacial zone. Although double layer phenomena do indeed also come into play for these reactive interfaces, here our analysis will be carried out on a much broader scale than merely the double layer alone. Therefore the potential profile appears simply as flat in both extreme phases, showing discontinuity when crossing the interface. This discontinuity, this potential difference between the two phases, is what thermodynamics connects up to the system s composition, as explained below. 

Refer to section 2.2.3 and to figures 2.15 and 2.16 in section 1.2.4.2 for the qualitative description of potential profiles in an electrochemical cell, including the different contributions to the voltage across an electrochemical system with a current flowing. In addition, remember that the description of the concentration or potential profiles is on the spatial scale of the diffusion layers and not on the double-layers scale (see section 3.3.1). In particular, while the potential profile is continuous on the scale of the double-layer dimensions, it shows discontinuities on the scale of the diffusion layers at the interfaces. 

Consider, in addition, the nature of the force beli used in separation. Since there is adsorption and/or desorption of solutes between the mobile fluid and the stationary solid phases, the potential profile under consideration for each solute is discontinuous, a simple step function (see Figure 3.2.2) there are no external forces. According to Section 3.2, such a system in a closed vessel without any flow does not have any multicomponent separation capability. Multicomponent separation capability is, however, achieved in elution chromatography by having bulk flow perpendicular to the direction of the discontinuous chemical potential profile. The velocity here functions exactly like the quantity (- ) in equation (3.2.37). 

At very high soil resistivities, a groimd bed design with a continuous anode running parallel to a pipeline may be required. In such environments discrete anodes will result in a poor current distribution, and the potential profile of the pipeline will be unsatisfactory. The pipe-to-soil potential may only reach satisfactory levels in close proximity to the anodes if discontinuous anodes are employed in high-resistivity soil. 

Electrotransport technology offers a number of benefits for therapeutic appHcations, including systemic or local adininistration of a wide variety of therapeutic agents with the potential adininistration of peptides and proteins long-term noninvasive administration, improving convenience and compliance controlled release, providing a desired deflvery profile over an extended period with rapid onset of efficacious plasma dmg levels and in some cases reduced side effects and a transport rate relatively independent of skin type or site. Additional benefits include easy inception and discontinuation of treatment, patterned and feedback-controlled deflvery, and avoidance of first-pass hepatic metaboHsm. 

Note that potential control profile discontinuities are allowed at each element location with error restrictions directly enforced for each element. For a sufficient number of elements (which can be determined by the algorithm in the previous section), the element can be as large as allowed by an active error constraint, or it can act as a degree of freedom for the control profile discontinuity, with its corresponding error constraint inactive. Otherwise, (35) is based on the implicit Runge-Kutta (IRK) or collocation... 

Lactation It is not known whether sirolimus is excreted in human breast milk. The pharmacokinetic and safety profiles of sirolimus in infants are not known. Because of the potential for adverse reactions in nursing infants from sirolimus, decide whether to discontinue nursing or to discontinue the drug, taking into account the importance of the drug to the mother. 

When A = k0 1, the kinetic term in Eq. (224) tends to be extremely large. On the other hand, 9/ /9t cannot be infinite, for obvious physical reasons (except at possible discontinuities in the potential variations). Thus the diffusion term 9 p/9y must compensate for the kinetic term in order that 9p/9r remain finite. In other words, a quasi-steady state is reached by mutual compensation of kinetics and diffusion. As a result, 9p/9r 9"p/9y and Ap. Equation (224) thus becomes equivalent to Eq. (225), at least as concerns the derivation of the concentration profile of P. 

Figure 6.9 Velocity profile in and above a submerged canopy. In the upper portion of the canopy flow is predominantly driven by turbulent stress, which penetrates downward into the canopy over attenuation scale (aCD) l. Below this flow is driven by potential gradients due to bed- or pressure gradients. At the top of the canopy the discontinuity in drag generates a mixing-layer. Above this the profile transitions to a logarithmic boundary layer profile.

Table I. Transmission probabilities at energies Er and Er 4 means that all four discontinuities of the potential are taken into account. In the procedure D 2 only the most external discontinuities produce a change in the amplitudes of the multichannel wave-function. Finally in Di, only the first discontinuity is introduced, "bkg in Di stands for background no structure in the profile is observed at this energy. The results show the similarity of Dt and D2 In Di a single peak collects the transmission probabilities dispersed among several channels in the other two procedures.

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