Analytical solution of electro-osmotic flow in a semicircular microchannel

The electro-osmotic flow through a microchannel with a semicircular cross section is studied under the Debye–Huckel approximation. Analytical series solutions are found for two basic cases. The solutions for the two basic cases considered can be superposed to yield solutions for any combination of constant zeta potentials on the flat or curved wall boundaries. Moreover, in the limit of a thin electric double layer (small Debye length compared to the nominal dimension), a method of solution is shown for variable zeta potentials by using the Smoluchowski slip approximation.