Comparison with Helmholtz double layer theory

Comparison with Helmholtz double layer theory 

The electrophoretic velocity is given from double layer theory [2] as 

This shows that the kinetic theory is consistent with the thermodynamic theory. Experimental proof of Onsager relation would be obtained if the experiments on sedimentation potential and electrophoretic velocity are performed for the particles of same size and shape. 

There is some controversy regarding the numerical factor 4 in Eq. (6.16). According to rigorous theory of Debye and Huckel [3], it is 6, when the electrophoretic drag due to double layer is also considered. However, Henry [4] has shown that it lies between 4 and 6. Thus Eq. (6.16) should be written as 

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Comparison with Helmholtz double layer theory... 

FIGURE 3.17 Surface-ion distribution function for a 2 1 electrolyte with a = 0.30 nm and c = 1.0 M for (a) a fixed dimensionless potential at the Helmholtz plane P(a/2) = -0.15 (b) a fixed dimensionless surface charge = a a lq = 0.1685. Symbols MC simulations solid line, MPB5 dash-dotted fine, MPB6 dotted line, DPT dashed line, GCS (Bhuiyan and Outhwaite, 2004, Comparison of the modified Poisson-Boltzmann theory with recent density functional theory and simulation results in the planar electric double layer. Physical Chemistry Chemical Physics, 6, no. 13, 3467. Reproduced by permission of The Royal Society of Chemistry.)... 

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