Interdisciplinary Applied Mathematics

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where F is the electrophoretic conductance of the fluidic channel.

Consider an example, where two species A and B are present in the separation channel shown in Figure 18.6. Assume that species A is unit-positively charged and species B is unit-negatively charged, while the surface of the channel has a negative fixed charge. Therefore, the electroosmotic flow through the channel would be from left to right (i.e., from the anode side to the cathode side) as shown in Figure 18.6. The electrophoretic flow for A would be from left to right, but that for B would be in the opposite direction. This is due to the difference in the electrophoretic velocities of these two species. Thus, the ratio of the rate of molar increment at the outlet of the separation channel for the two species is given by the expression

Separation Ratio

(Q + sign(zA)x | Qph |A)c% (Q + sign(zB)x | Qph |b)cb

(Q+ I QphUtf

(Q— I Qph|b)C‘b

where c™ is the concentration of species A at the inlet, and cB is the concentration of species B at the inlet. Considering that the bulk flow is due to electrical potential gradient only (i.e., pressure-driven flow is absent), the separation ratio of the species can be expressed in terms of the electrophoretic conductance, electrohydraulic conductance, and the inlet concentration of the species, i.e.,

Separation Ratio = -———d A .    (18.12)

(H + Fb )cB

Thus, the knowledge of the electrophoretic conductance and the electrohydraulic conductance can be used to compute the separation ratio using equation (18.12), which can be considered as the device model for the separation module.

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