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An effectiveness factor of electro-osmotic flow is often used

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An effectiveness factor of electro-osmotic flow is often used. This factor is defined as the volumetric flow rate due to electo-osmosis divided by that due to an applied pressure gradient. Derive an expression for this.

Derive expressions for the velocity profile and the volumetric flow rate for a circular channel. Examine the limiting cases of this equation for small R and large R (in comparison with the Debye length).