Electroosmotic convective flow

SECM has been recently used by Bath et al. in the investigation of elec-troosmotic convective flow (10). Electroosmosis occurs in porous membranes employed in fuel cells, representing an important practical issue in the parasitic crossover of fuel (e.g., methanol) and in the flooding/drying of the fuel cell electrodes (29,30). Electroosmotic flow across skin, a naturally occurring ion-selective membrane, is also of interest in transdermal drug delivery, as discussed in Sec. III.B.2. 

Capillary electrophoresis is based on the same principle as gel electrophoresis. Charged analytes can be separated in an applied electric field according to their mobility. In contrast to gel electrophoresis, however, separations are carried out in a small diameter capillary containing a free solution of electrolyte rather than on a slab gel. Moreover, convective flows due to Joule heating occur more easily in a free solution than in the gel. In contrast to GE, electroosmotic flow is often part of the separation process. 

Figure 6. A schematic of the electroosmotic flow of the medium (e.g., an electrolyte) in a capillary caused by the flow of counter ions as a plug, under the influence of the applied electric field, E UL, is the convective liquid velocity from electroosmosis. Adapted from Everett.48...

Electrophoretic migrations are always superimposed on other displacements, which must either be eliminated or corrected to give accurate values for mobility. Examples of these other kinds of movement are Brownian motion, sedimentation, convection, and electroosmotic flow. Brownian motion, being random, is eliminated by averaging a series of individual observations. Sedimentation and convection, on the other hand, are systematic effects. Corrections for the former may be made by observing a particle with and without the electric field, and the latter may be minimized by effective thermostating and working at low current densities. 

Parasitic Flow How often assumes a destructive role, despite efforts to prevent it. Convective currents frequently lead to the remixing of separated components. Electroosmotic flow (see Section 4.9) is destructive in some (not all) electrophoretic systems and is difficult to eliminate because of the ubiquitous presence of surface charges. These unintended and generally unproductive forms of flow can be termed parasitic flow. The following discussion serves to distinguish parasitic flows from nonparasitic flow processes. 

The external electric field is in the direction of the pore axis. The particle is driven to move by the imposed electric field, the electroosmotic flow, and the Brownian force due to thermal fluctuation of the solvent molecules. Unlike the usual electroosmotic flow in an open slit, the fluid velocity profile is no longer uniform because a pressure gradient is built up due to the presence of the closed end. The probability of the particle position is obtained by solving the Fokker-Planck equation. The penetration depth is found to be dependent upon the Peclet number, which is a measure of significance of the convective electroosmotic flow relative to the Brownian diffusion, and the Damkohler number, which is a ratio of the characteristic diffusion-to-deposition times. 

Fig. 4 Imposing an electrical potential gradient across a charged membrane produces a convective solvent flow in the direction of counter-ion transport (i.e., from anode-to-cathode in the case of skin). This electroosmotic effect (EO) adds to electrorepulsion (ER) to enhance the transport of cationic compounds during iontophoresis (4a) while acting against the electromigration of anions (4b).

Although the low Reynolds number characteristic of most of these flows eliminates the challenges of nonlinearity in the convective term and the associated difficulty in modeling turbulent flows (which is actually not true in some gas-liquid devices), we are instead forced to face the nonlinearity of the source term in the Poisson-Boltzmann equation, the nonlinearity of the coupling of electrodynamics with fluid flow, aud the uncertainty in predicting electroosmotic boundary conditions. 

A convection current, 7conv> resulting from the electroosmotic flow... 

The electroosmotic flow, resulting in a convection current, Icom... 

Under electroosmotic flow the current in the channel is composed of three parts (1) the bulk conductivity current, lcond,bu]k, (2) the surface conduction current, lcond,surf, and (3) the convection current created by the fluid motiOTi, /cond,conv Typically, the convection current is several orders of magnitude smaller than the other currents and is neglected. Therefore, the total current is given as... 

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