Interdisciplinary Applied Mathematics

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FIGURE 7.4. A schematic view of electroosmotic and electrophoretic transport processes.

FIGURE 7.5. Electroosmotic mobility variation as a function of molar concentration (C)    for    sodium tetraborate    buffer    (Sadr    et    al.,    2004).    Experimental    results

are shown by squares, while the theoretical predictions are indicated by x. (Courtesy of A.T. Conlisk.)

details about the electrophoretic mobility and its relation to the zeta potential and the particle charge. For most practical applications, the electrophoretic mobility is determined experimentally, and for a given electric field, it results in an electrophoretic migration velocity of

uep = MepE.    (7.20)

Based on this, a positively charged particle (Z > 0) that is free to move will migrate towards the cathode, as schematically shown in Figure 7.4.

7.4 Electroosmotic Flows

Electroosmotic flow is generated due to the interactions of ions in the EDL with an externally applied electric field (E). Nonzero ion density within the EDL results in net ion migration toward the oppositely charged electrode, dragging the viscous fluid with it. This effect is characterized by the electroosmotic body force term in the Navier-Stokes equation (7.12). The externally applied electric field can be represented as

E = -Уф,

where ф is the electrostatic potential. Assuming the laws of electrostatics, the potential obeys

V • (оУф) = 0,    (7.21)

where о is the electric conductivity. The right-hand side of the equation is zero, since the electric charge density (pe) contained in the EDL is already included in equation (7.2). The external electric field is subject to the insulating boundary conditions (Уф • n = 0) on the walls. The zeta potential is assumed to be uniform for all surfaces.

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