Electro-osmosis flow rate

Electrically assisted transdermal dmg deflvery, ie, electrotransport or iontophoresis, involves the three key transport processes of passive diffusion, electromigration, and electro osmosis. In passive diffusion, which plays a relatively small role in the transport of ionic compounds, the permeation rate of a compound is deterrnined by its diffusion coefficient and the concentration gradient. Electromigration is the transport of electrically charged ions in an electrical field, that is, the movement of anions and cations toward the anode and cathode, respectively. Electro osmosis is the volume flow of solvent through an electrically charged membrane or tissue in the presence of an appHed electrical field. As the solvent moves, it carries dissolved solutes. 

Electro-osmosis in a capillary. In the local model of the previous section we assumed for the flow rate v the phenomenological generalized Darcy s law (6.3.3a) with constant coefficients. 

We can observe electro-osmosis directly with an optical microscope using liquids, which contain small, yet visible, particles as markers. Most measurements are made in capillaries. An electric field is tangentially applied and the quantity of liquid transported per unit time is measured (Fig. 5.13). Capillaries have typical diameters from 10 fim up to 1 mm. The diameter is thus much larger than the Debye length. Then the flow rate will change only close to a solid-liquid interface. Some Debye lengths away from the boundary, the flow rate is constant. Neglecting the thickness of the electric double layer, the liquid volume V transported per time is... 

The volume flow through the membrane per unit time per unit area (rate of electro-osmosis) is... 

Although some degree of advective flow is generated by electro-osmosis, the low solubilization of chlorinated pesticides in the aqueous phase and low desorption rates from the soils limit the movement of contaminants in soUs. As represented in Table 11.1, solubilities of the chlorinated pesticides are very low. Furthermore, the solubility of organic pesticides in most cases is rate limited, which causes even lower aqueous phase concentrations. 

Steady states, as we have seen in Part One, are obtained when fluxes in opposite directions are involved. In electro-osmosis, hydrodynamic flow is opposed by electro-osmotic flux. In thermo-osmosis, hydrodynamic flow is opposed by thermo-osmotic flux. In case of chemical reactions, such situations can arise when positive feedback is opposed by negative feedback. For example, when autocatalysis is opposed by inhibitory reaction, steady state can be attained. However, the reaction rates are non-linear and have only non-linear steady states in practice. We illustrate this point by the following example. 

In electro-osmosis, the volume flow rate (dV/df) is measured through a capillary or a porous plug which can be treated as a series of capillaries. Using the Smoluchowski equation (Eq. 3.15), this is related to the zeta potential. For flow in a capillary of cross-sectional area A, we obtain... 

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