# Interdisciplinary Applied Mathematics

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uek = MekE,    (7.16)

and it depends on the physical and chemical properties of the particle or surface and the suspending fluid.

The electroosmotic mobility for infinitesimally thin EDL is given by the Helmholtz-Smoluchowski relation (Hunter, 1981)

Meo

—C£

(7.17)

where Z is the zeta potential. Using the electroosmotic mobility, we obtain the Helmholtz-Smoluchowski electroosmotic velocity (also indicated as uHS in equation (7.24))

uEO = M eoE =-E.    (7-18)

M

The negative    sign is    due    to    the    use    of    surface    zeta    potential.    For    example, for    a negatively    charged    surface    (Z    < 0),    the    EDL    will    be positively

charged, and the resulting electroosmotic motion will be toward the cathode, as shown schematically in Figure 7.4. To give an idea of the typical mobility magnitudes, we present in Figure 7.5 the electroosmotic mobility of sodium tetraborate buffer as a function of the buffer concentration (Sadr et al., 2004). The experiments were performed in fused silica and quartz microchannels, with heights ranging from 5 Mm to 25 Mm, under electric fields E < 4.8 kV/m and buffer concentration (C) of 0.19 < C < 36 mM. The experimental results indicate significant variations in the electroosmotic mobility as a function of the buffer concentration, consistent with the theoretical predictions in (Conlisk et al., 2002).

The electrophoretic mobility for spherical colloidal particles with uniform zeta potential is (Hunter, 1981)

(7.19)

2Z£

3m ’

where the 2/3 coefficient is appropriate for infinitesimally thin EDL conditions. The reader is referred to (O’Brien and White, 1978), for further

Electric Field Direction

С

c>