mobility and values for the other parameters, one can extract The electrophoretic mobilities of two spherical particles are anathe average zeta potential. A comprehensive theory of this lyzed for the case where the electrical double layer is no longer kind is not at present a reality, but approximations have been thin with respect to the particle sizes, but the zeta potentials on developed that apply to the regimes of most practical interest. the particles are low. Using a method of reflections, we obtain the As a first approximation, one can consider a suspension mobilities as a power series in 1/r 12 up to O(r 010 12 ) (where r 12 is
that is sufficiently dilute that the particles can be taken to the center-to-center separation of the spheres), with the proviso be noninteracting, so that the average mobility is just the that the double layers on the two particles do not overlap. Unlike average of the mobilities of the isolated particles. Here ''suf-
the case of thin double layers, there is now a nonzero interaction ficiently dilute'' generally means a volume fraction of less between identical particles. The first term in the interaction is O(r 03 12 ), but the coefficient becomes large for thick double layers. than 5%, although it shall become clear in this paper than An expression for the average mobility of a mildly polydisperse in some cases it may need to be less than 1%. However even suspension of spheres with thick double layers is then derived for isolated particles some further restrictions are required correct to first order in the volume fraction of the spheres. The to make the problem tractable. The simplest case that is results of the reflection calculation are then used to obtain an comprehensively understood (in terms of the standard elecapproximate evaluation of this expression. It is found that the first trokinetic equations) is that of a spherical particle of radius order effect for thick double layers is significantly larger than it a with a uniform surface potential z p . This has been treated is for thin double layers, and that the average effect of polydisperboth numerically (2) and in various analytic approximations.
sity in size or surface potential is weak unless the double layers Among the latter, one approach is to assume that the width are quite thick. For a monodisperse suspension, an expression is of the electrical double layer, characterized by the inverse obtained for the mean square deviation of the particle velocity Debye length k 01 , is small compared to the particle size (so from the mean velocity. An approximate evaluation of this expression using the reflection results shows that the magnitude of the that ka is large) while still allowing for significant conducmean square fluctuations in the direction of the applied field can tion in this surface layer (3-5). This is appropriate for be significantly larger than that in the transverse direction. α§ 1997 many colloidal systems where ka ΓΊ 30 and z p may be large.
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Another approach is to assume that the scaled surface poten-Key Words: electrophoresis; suspension; double layer; polydistial ez p /(k B T ) is small, where e is the elementary charge, perse.
k B is Boltzmann's constant, and T is the absolute temperature. This second approach is particularly appropriate to the electrophoresis of proteins, for which the system can be such