13.5 Exercises [particle electrophoresis top]

1. The Smoluchowski limit (thin double layer limit) for electrophoresis of a cylinder aligned perpendicular to the electric field with thin double layers is

   (13.33)

   while the Hückel limit (thick double layer limit) for electrophoresis of a cylinder aligned perpendicular to the electric field with thick double layers is

   (13.34)

   Consider the solution for the electric field around an insulating cylinder (which is the superposition of a uniform field and a dipole), and evaluate the maximum electric field on the surface in this case as compared to the bulk electric field. In the case of thin double layers, this maximum electric field is applied to the ions in the double layer, and gives rise to the particle motion relative to the fluid. In the case of thick double layers, the field applied to the ions in the double layer is for the most part the bulk electric field. Draw a schematic of these two cases and explain why the electrophoretic velocities in these two cases differ by 1∕2.

2. Plot the exact and approximate relations for Henry’s functions for spheres and cylinders. Plot a^* on a log scale from 1×10^-2 to 1×10³. Estimate the maximum error of the approximate functions.
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