Cylindrical Channel EO Flow

Analytical results for an ideal EO flow within the Debye-Hiickel approximation can also be derived for a cylindrical channel of circular cross section with radius a. Similar to equation (6.65) for flat plate, the Poisson-Boltzmann equation, (r), for cylindrical geometry in the Debye-Hiickel approximation is 

The fiilly developed velocity field v = v r)e, with boundary conditions 

The analysis can be carried out exactly as for the infinite parallel plate geometry (equations (6.80) and (6.81)), and we arrive at the result  

We note that v for a. Hence, the EO flow rate can be derived as 

Note (1) When the double layer thickness is very small compared to the characteristic length, say, a/Ap 100, the fluid moves as in plug flow. Thus, the velocity slips at the wall that is, it goes from 11 to zero discontinuously. 

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