Exact Expression for Cylindrical Channel EO Flow

we calculate the EO flow and potential change in a long capillary for different A /a (Debye length to radius ratios). Let us assume that the mean velocity and tube radius are sufficiently small and inertia effects can be neglected. The dilute electrolyte solution in the capillary is assumed to be binary. The momentum equation is 

Let us assume the electrolyte solution is of Mly dissociated symmetrical salt with z+ = -z = z and the capillary is circular. We adopt cylindrical coordinate system (x, f) with x positive in the direction of flow and r the radial coordinate with origin at the axis of the symmetry. We have the momentum equation (6.94) in cylindrical coordinate as 

To define the interaction between the electric field and ion concentration, let us invoke the Poisson equation V 0 = For a capillary of length, L, larger compared with its radius, a, 

The above equation means that at any small segment of the capillary, the ion concentrations are in a local quasiequilibrium determined solely by the radial variation in 0. Because of the above behavior, it is convenient to divide the potential into two parts as 

Substituting the potential distribution from equation (6.97) in equation (6.96), we have 

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