General Mobility Expression

Consider the forces acting on an arbitrary sphere S enclosing the soft sphere at its center. We take the radius of S tends to infinity. Since the net electric charge within S is zero, there is no net electric force acting on S and one needs consider only the hydrodynamic force Eh. The equation of motion for S is thus given by 

The dynamic electrophoretic mobility p(co) of a soft particle can be obtained by solving Eqs. (25.19) and (25.20) with the result that 

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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... 

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 ... 

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],... 

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... 

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... 

Equations (125) and (126) explicitly show that in the initial slope approximation the elements of the generalized mobility matrix can be expressed only in terms of integrals over the corresponding partial static structure factor. Both equations are valid as long as one assumes a Gaussian distance distribution of the distances r between the monomers i on arm a and monomers j on arm p. 

The e, f, g and h constants were determined so that the general empirical expression for the alkylbenzene retention factor with such microemulsion mobile phases could be expressed as ... 

Okada et al. found that the internal mobilities of LT in molten alkali nitrates are well expressed as a function of molar volume, independent of the kind of the second cation. This finding leads to a general empirical equation ... 

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. 

In a crystal, the electronic and ionic conductivities are generally tensor quantities relating the current density Iq to the applied electric field E in accordance with Ohm s law. The scalar expression for the mobile-ion current density in the different principal crystallographic directions has the form... 

This expression is the general Wagner factor which includes the influence of all the motion of the other species on the motion of species i by the effect of the internal electric fields. W may be larger than 1 which indicates an enhancement of the motion by the simultaneous motions of other species, or W may be smaller than 1 which means that the species are slowed down because of the immobility of other species which are therefore unable to compensate for the electrical charges. The first situation is desirable for electrodes whereas the second one is required for electrolytes in which mobile species should not move except when electrons are provided through the external circuit. Since the transference numbers in Eqn (8.27) include the partial and total conductivities (tj = OjlYjk or the products of the diffusivities (or mobilities) and the concentrations, Eqn (8.27) shows that W depends both on kinetic... 

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