Curvature-induced dispersion in electro-osmotic serpentine flows

Flow and transport phenomena occurring within serpentine microchannels are analyzed for both two- and three-dimensional curvilinear configurations. The microfluidic conduit is modeled as a spatially periodic "thin" channel, enabling asymptotic expansions of the pertinent transport fields in terms of a small parameter epsilon, representing the ratio of channel (half-) width to curvilinear channel length per serpentine period. The electric potential distribution, as well as the attendant electro-osmotic flow field, is calculated for the limiting case where the Debye layer thickness is small relative to the channel width. Generalized Taylor-Aris dispersion theory is employed to calculate the serpentine-scale velocity and dispersivity of a charged point-size colloidal Brownian particle ("molecule") entrained in the solvent Stokes flow engendered by the electrokinetic forces. These respective macrotransport coefficients are expressed, inter alia, in terms of quadratures of the local curvature within a unit cell of the serpentine device.