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.
Keywords: Array of slats; Electroosmotic flow; Longitudinal electroosmotic pumping; Nano-scale channels; Transverse electroosmotic pumping.
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