Mobility expression

The ion mobility coefficients pj are calculated similarly. First, the ion mobility of ion j in background neutral i is calculated using the low- -field Langevin mobility expression [219]. Then Blanc s law is used to calculate the ion mobility in... 

The esterases have also been classified according to p/ value, i.e., the isoelectric points assessed by electrophoretic mobility expressed in pH units. For many years, this was one of the major criteria used to distinguish esterases. The drawback of the classification based on pI values is that the isoelectric points can vary between species and even between strains of the same species. 

The effective mobility, expressed by Equation 6.16, can be directly calculated from the observed mobility by measuring the electroosmotic mobility using a neutral marker, not interacting with the capillary wall, which moves at the velocity of the EOF. Accordingly, the effective mobility p of cations in the presence of cathodic EOF is calculated from p ts by subtracting p gf ... 

Boundary effects on the electrophoretic migration of a particle with ion cloud of arbitrary thickness were also investigated by Zydney [46] for the case of a spherical particle of radius a in a concentric spherical cavity of radius d. Based on Henry s [19] method, a semi-analytic solution has been developed for the particle mobility, which is valid for all double layer thicknesses and all particle/pore sizes. Two integrals in the mobility expression must be evaluated numerically to obtain the particle velocity except for the case of infinite Ka. The first-order correction to the electrophoretic mobility is 0(A3) for thin double layer, whereas it becomes 0(A) for thick double layer. Here the parameter A is the ratio of the particle-to-cavity radii. The boundary effect becomes more significant because the fluid velocity decays as r l when the double layer spans the entire cavity. The stronger A dependence of the first order correction for thick double layer than that obtained by Ennis and Andersion [45] results from the fact that the double layers overlap in... 

In the present paper, pore level descriptions of bubble and bubble train displacement in simple constricted geometries are used in developing mobility expressions for foam flow in porous media. Such expressions provide a basis for understanding many of the previous core flood observations and for evaluating the importance of foam texture and interfacial mobility. Inclusion of the effects of pore constrictions represents an extension of the earlier efforts of Hirasaki and Lawson (1). 

Equation (21.63) covers a plate-like soft particle. Indeed, in the limiting case of oo, the general mobility expression (Eq. (21.41)) reduces to... 

Equation (21.51) consists of two terms the first term is a weighted average of the Dorman potential i/ don and the surface potential ij/o- It should be stressed that only the first term is subject to the shielding effects of electrolytes, tending zero as the electrolyte concentration n increases, while the second term does not depend on the electrolyte concentration. In the limit of high electrolyte concentrations, all the potentials vanish and only the second term of the mobility expression remains, namely. 

Equation (21.62) shows that as k co, p tends to a nonzero limiting value p°°. This is a characteristic of the electrokinetic behavior of soft particles, in contrast to the case of the electrophoretic mobility of hard particles, which should reduces to zero due to the shielding effects, since the mobility expressions for rigid particles (Chapter 3) do not have p°°. The term p°° can be interpreted as resulting from the balance between the electric force acting on the fixed charges ZeN)E and the frictional force yu, namely. 

In order to analyze the dependence of the mobility on the electrolyte concentration, it is convenient to rewrite the mobility expression (21.128) as the sum of the... 

This agrees with the mobility expression for a rigid particle with a radius b in concentrated suspensions obtained in previous papers [5, 12]. 

The field-dependent mobility expression is universal and applicable to a large class of materials including conjugated polymers, blends, and mixtures of polymers and dyes. 

Figure 4, Construction of plasmids harboring mobile expression elements containing structural genes for the conversion of toluene to p-cresol, and p-cresol to HBA. (a) pESMll and (b) pESM23. The structure of the mini-TnS transposons is emphasized in the figure for clarity. The DNA sequences coding antibiotic resistance markers aphA and tet, regulatory proteins lacfi and nahR, and promoters Ptrc and Psal are indicated. The mobile units are present in the delivery plasmid pUT as XbaTEcoRI restriction fragments (44).

As it is known [86], MWD cttrve in case of aggregation cluster-cluster depends on the diffusive characteristics of a system in many respects, namely on clusters mobility expressed by their rate fi, which can be estimated according to the Eq. (66) of Chapter 1. In its firm, the exponent of a value in this relation defines MWD curve maximum position according to the Eq. (67) of Chapter 1. One should expect that the clusters mobility will be the higher, the smaller initial monomers solution viscosity q is. This supposition is confirmed by the dependence 0 (p ), adduced in Fig. 49, which is linear and passes through coordinates origin. 

Therefore it appears that application of an alternating electric fleld to an electrolyte reveals an intrinsic property of its constituents ions, viz., their mechanical mobility expressed as their electrical mobilities. 

III. Mobility Expression Correct to Order (Henry s Formula). 28... 

The first attempt to derive the relation between fi and was made by Von Smoluchowski [10] and Hiickel [11], and later by Henry [12]. Full electrokinetic equations determining electrophoretic mobility fi of spherical particles with arbitrary values of Ka and were derived independently by Overbeek [13] and Booth [14]. Wiersema et al. [15] solved the equations numerically. The computer calculation of the electrophoretic mobility was considerably improved by O Brien and White [16]. Approximate analytic mobility expressions have been proposed by several authors [17-19]. 

Consider a spherical hard particle of radius a and zeta potential moving with a velocity U in a liquid containing a general electrolyte composed of N ionic species with valence z, and bulk concentration (number density) and drag coefficient A, (/ = 1,2,..., N). The origin of the spherical polar coordinate system (r, 0, ) is held fixed at the center of the particle. Ohshima et al. [19] derived the following general mobility expression ... 

III. MOBILITY EXPRESSION CORRECT TO ORDER f (HENRY S FORMULA)... 

Henry s equation (2.6) assumes that is low, in which case the double layer remains spherically symmetrical during electrophoresis. For high zeta potentials, the double layer is no longer spherically symmetrical. This effect is called the relaxation elfect. Henry s equation (2.6) does not take into account the relaxation effect, and thus this equation is correct to the first order of Ohshima et al. [19] derived an accurate analytic mobility expression correct to order 1/ka in a symmetrical electrolyte of valence z and bulk concentration (number density) n with the relative error less than 1% for 10 < Ka < 00, which is... 

Equation (2.16) is applicable for all for 10 < ka < oo. To obtain an approximate mobility expression applicable for ka < 10, it is convenient to express the mobility in powers of and make corrections to higher powers of in Henry s mobility equation (2.6), which is correct to the first power of Ohshima [25] derived a mobility formula for a spherical particle of radius a in a symmetrical electrolyte solution of valence z and bulk (number) concentration n under an applied electric field. The drag coefficient of cations, A+, and that of anions, A, may be different. The result is... 

The electrophoretic mobility of hquid drops is quite different from that of rigid particles since the flow velocity of the surrounding liquid is conveyed into the drop interior [28 -32]. The electrophoretic mobility of a drop thus depends on the viscosity rjd of the drop as well as on the liquid viscosity rj. Here we treat the case of mercury drops, in which case the drop surface is always equipotential. The general mobility expression for a mercury drop having a zeta-potential is derived by Ohshima et al. [30],... 

An approximate analytic mobility equation apphcable for arbitrary values of was daived by Levich [28], and Ohshima et al. [30] derived a more accurate mobility expression correct to order 1 /ka for the case of symmetrical electrolytes of valence z. The leading term of their expression is given by [30]... 

VIII. GENERAL MOBILITY EXPRESSION FOR SOFT PARTICLES... 

Ohshima [42-45] presented a theory for electrophoresis of a soft particle. The general mobility expression of a soft particle that consists of the hard particle core of radius a covered with a layer of polyelectrolytes of thickness d (=b — a) and moves in an electrolyte solution of viscosity tj is given... 

For cylindrical soft particles, Ohshima [49,50] derived the following mobility expressions ... 

The general mobility expression (2.76) is also applicable for the case where a hard particle of radius a carrying with zeta-potential is covered with an uncharged polymer layer. Ohshima [61] derived the following mobility expression applicable for arbitrary values of ku but for low zeta potentials Y... 

Friedman (1971) found a solution to this problem. He calculated the Hall mobility jjl using the random phase model which served also as the basis for the mobility expression Eq. (5.7). As in the case of hopping conduction of a small polaron (Holstein and Friedman (1968)) Friedman assumed that the applied magnetic field modifies the phase of the transfer integral between sites. A minimum of three sites, which are mutual nearest... 

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