A periodic array of nano‐scale parallel slats for high‐efficiency electroosmotic pumping

Abstract

It is known that the eletroosmotic (EO) flow rate through a nano-scale channel is extremely small. A channel made of a periodic array of slats is proposed to effectively promote the EO pumping, and thus greatly improve the EO flow rate. The geometrically simple array is complicated enough that four length scales are involved: the vertical period 2L, lateral period 2aL, width of the slat 2cL as well as the Debye length λD. The EO pumping rate is determined by the normalized lengths: a, c, or the perforation fraction of slats η=1-(c/a) and the dimensionless electrokinetic width K=L/λD. In a nano-scale channel, K is of order unity or less. EO pumping in both longitudinal and transverse directions (denoted as longitudinal EO pumping (LEOP) and transverse EO pumping (TEOP), respectively) is investigated by solving the Debye-Hückel approximation and viscous electro-kinetic equation. The main findings include that (i) the EO pumping rates of LEOP for small K are remarkably improved (by one order of magnitude) when we have longer slats (a≫1) and a large perforation fraction of slats (η > 0.7); (ii) the EO pumping rates of TEOP for small K can also be much improved but less significantly with longer slats and a large perforation fraction of slats. Nevertheless, it must be noted that in practice K cannot be made arbitrarily small as the criterion of φc≈0 for the reference potential at the channel center put lower bounds on K; in other words, there are geometrical limits for the use of the Poisson-Boltzmann equation.

Transition of electrostatic potential from the inside of an open channel to the reservoir

“…The rst term of (9), which satises the boundary condition is also the solution to eqn (6) for an innite channel. The second term of (9), the complete Fourier series solution to eqn (6), which must be identically zero on the side walls, is included to account for the open edge effect.…”

“…Keh et al 7 presented the analytical solutions in closed forms obtained with a cylindrical cell model. For all the other cross-sections, semianalytical methods with boundary collocations 9 or even fully numerical methods, such as nite elements, 8 must be used.…”