Mobilities difference

One of the major differences in fluid flow behaviour for gas fields compared to oil fields is the mobility difference between gas and oil or water. Recall the that mobility is an indicator of how fast fluid will flow through the reservoir, and is defined as... 

In the ideal case, the ionic conductivity is given by the product z,Ft/ . Because of the electrophoretic effect, the real ionic mobility differs from the ideal by A[/, and equals U° + At/,. Further, in real systems the electric field is not given by the external field E alone, but also by the relaxation field AE, and thus equals E + AE. Thus the conductivity (related to the unit external field E) is increased by the factor E + AE)/E. Consideration of both these effects leads to the following expressions for the equivalent ionic conductivity (cf. Eq. 2.4.9) ... 

The selectivity of separation is mainly affected by parameters of the bulk electrolyte in the capillary. These include type of anion and cation, pH, ionic strength, concentration, addition of modifiers such as com-plexing agents, organic solvents, surfactants, etc. It is expressed in terms of mobility differences (A/i) or the mobility ratio s (a) ... 

Hydroxylic solvents are capable of solvating anions through hydrogen bonding, and so halide mobilities are relatively low in alcohols, with chloride the least mobile. The mobility decreases observed for all the halides upon going up the homologous series of aliphatic alcohols may be the result of the increased size and mass of the alkyl group. A similar mass effect may be seen in the lowered mobility of the halides in dimethylacetamide compared to dimethylformamide. Here, as in the alcohol series, dipole moments and viscosities of the two solvents do not appear to be sufficiently different to explain the mobility differences. 

Continuous systems use the same buffer, at constant pH, in the gel, sample, and electrode reservoirs. With continuous systems, the sample is loaded directly on the gel in which separation will occur. The sample application buffer is the same as the gel and electrode buffer, but at about half the concentration. The localized voltage drop that results from decreased conductivity in the sample solution helps drive sample proteins into the gel and sharpens protein bands. Once inside a gel, proteins are separated on the basis of their individual (gel-mediated) mobility differences. Bandwidths are highly dependent on the height of the applied sample... 

In general, the differences in expression and structure of HI variants strongly suggests that variants of linker histones have important roles in chromatin architecture, and might be essential players in the epigenetic control of developmental gene expression. Future studies will be necessary to identify factors that target, modify, and mobilize different linker histones. 

With capillary electrophoresis (CE), another modern primarily analytically oriented separation methodology has recently found its way into routine and research laboratories of the pharmaceutical industries. As the most beneficial characteristics over HPLC separations the extremely high efficiency leading to enhanced peak capacities and often better detectability of minor impurities, complementary selectivity profiles to HPLC due to a different separation mechanism as well as the capability to perform separations faster than by HPLC are frequently encountered as the most prominent advantages. On the negative side, there have to be mentioned detection sensitivity limitations due to the short path length of on-capillary UV detection, less robust methods, and occasionally problems with run-to-run repeatability. Nevertheless, CE assays have now been adopted by industrial labs as well and this holds in particular for enantiomer separations of chiral pharmaceuticals. While native cyclodextrins and their derivatives, respectively, are commonly employed as chiral additives to the BGEs to create mobility differences for the distinct enantiomers in the electric field, it could be demonstrated that cinchona alkaloids [128-130] and in particular their derivatives are applicable selectors for CE enantiomer separation of chiral acids [19,66,119,131-136]. 

In general, charged CDs have shown superior discrimination abilities, especially the highly-sulfated (HS-CDs) ones. Furthermore, the separation mechanism is altered by the introduction of electrostatic interactions. Finally, the use of chiral selectors carrying a charge opposite to that of the analytes can greatly improve the mobility difference between the two enantiomers. The use of mixtures of CDs in chiral separation is also possible. ... 

The concentration of additive that results in maximal electrophoretic mobility differences is not automatically the concentration that gives maximum resolution, since other aspects such as viscosity or ionic strength play a role as well. ... 

The use of a charged chiral selector is probably the best solution to improve the classical PET when CE is hyphenated with MS. Better solubility, additional electrostatic interactions, and improvement of the stereoselective separation power afforded by the self-mobility of the chiral additives into the BGE are among the numerous advantages of these charged selectors. When electromigration of the chiral species and the analytes are opposite (PFT-countercurrent approach), the mobility difference between free and complexed analytes is increased, leading to a higher resolution than with a neutral chiral selector. In optimized countercurrent... 

In order to find the concentration at which the mobility difference between two enantiomers reaches a maximum, one must differentiate Eq. (17) according to the concentration, i.e., to find a partial differential 3 AijlrsI d[C], After differentiating Eq. (17) and simplification of the obtained result, one may obtain the equation that relates the maximal mobility difference between the enantiomers to the concentration of a chiral selector as follows ... 

Thus, based on Eq. (18) it becomes possible to determine the concentration of the chiral selector resulting in a maximal mobility difference between the enantiomers, assuming that the binding constants of both enantiomers with chiral selector are known. This method for determination of the optimal CD concentration has been used by several groups. 

Fig-1 Measured and predicted enantiomeric mobility difference of tioconazole as a function of free-/3-CD concentration. (Reproduced with permission from Ref. 11.)... 

Sanger-van de Griend et al. (29) determined the binding constants of several local anaesthetics with DM-/3-CD. These data showed that the achiral separation of analogues is a result of their mobility difference, whereas the resolution of enantiomers results from the difference in their binding constants with CDs. 

Chemical effects also occur in crystalline oxides that is, impurity atoms diffuse at varying rates through oxides. In all cases, cation diffusion is much faster than oxygen diffusion, but similar cations, such as Ca and Mg, can behave very differently in different oxides. This is due to differences in chemical potential and activity, and mobility differences. 

In CZE, separations are controlled by differences in the relative electrophoretic mobilities of the individual components in the sample or test solution. The mobility differences are functions of analyte charge and size under specific method conditions. They are optimized by appropriate control of the composition of the buffer, its pH, and its ionic strength. 

This is the well-known Hall factor or r factor, which, in the low magnetic field limit, makes the Hall mobility different from the conductivity mobility. To see this relationship, consider the limit (or B- 0). Then... 

We have known by examining the room temperature spectrum of the bulk-crystals that the phase structure depends strongly on the molecular weight but it is generally composed of the crystalline, interfacial, and interzonal regions, of which molecular mobilities differ with each other. The temperature dependency of the phase struc-... 

In the second case, if the species mobilities differ greatly, the dimensionality of the system of kinetic equations decreases [103], Let all the components be divided into two groups of species a slow (5) and a rapid (r) one. This yields three types of pair functions. For the rapid species the condition of the equilibrium distribution can be considered as satisfied. Then, for the pair functions of types sr and rr instead of the kinetic Eqs. (32) algebraic relations in Appendix A apply, whose dimensionality can be lowered using the method of substitution variables according to Appendix B. In this case the kinetic Eqs (31) for the local concentrations and Eq. (32) for the pair functions type ss do not change. A similar situation remains in passing to the one-dimensional discrete and point-like models. 

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