Electro-osmotic flow through a two-dimensional screen-pump filter

The electro-osmotic flow driven by a screen pump, composed of a line array of evenly spaced identical rectangular solid blocks, is investigated under the Debye-Hückel approximation. The geometry of the screen pump is determined by the spacing and aspect ratio of the solid blocks. A constant surface zeta potential is assumed on the block surface. The method of eigenfunction series expansion is applied to solve analytically for the applied electric field, electric charge potential in the fluid, and flow field. Because of the low Reynolds number, Stokes equations are applied for the flow. The analytic result is first confirmed by comparing with the exact solution of the electro-osmotic flow in an infinite channel. Then different geometries of the screen pump and the effect of the electrokinetic width are computed for their influence on the flow rate. Recirculating eddies and reversing flow are found even though the applied electric driving field is unidirectional.

Figure 1

(a) The cross section of the two-dimensional screen pump where the electric-osmotic flow passes through. The half of the channel width is $H$, which is used to normalize lengths. The portion between the dash-dotted lines is the unit section of the screen pump. (b) The unit section of the pump. The lengths have been normalized, given the (half) channel length $a$ and the (half) width of the free-flow field $b$. Due to symmetry, we need only to solve for the domain in the first quadrant. The domain is decomposed into two regions such that Region I is inside the channel between the neighboring blocks and Region II is the semi-infinite free-flow strip.

Figure 2

The potential ${\phi }_p$ of the applied electric field. The screen filter geometry is $a=1.0$, $b=1.5$.

Figure 3

The EDL potential, ${\phi }_e$. The screen filter geometry is $a=1.0$, $b=1.5,$ and the Debye-Hückel parameter is $K=10$.

Figure 4

The asymptotic behavior (dashed lines with distinct symbols) approaching to the exact flux (solid lines) of infinitely long (continuous) channels for (a) $K=0.5$, (b) $K=2,$ and (c) $K=10$. The results of the screen pump approach to the theoretical values of the continuous channels when the channel length $a$ increases.

Figure 5

The volume flux versus the geometry of the screen pump and the Debye-Hückel parameter $K$. From top, (a) $K=0.1$, (b) $K=1$, and (c) $K=10$. The horizontal axes are the free-flow field width $b$. Three channel lengths $a=0.1,1,$ and 5 are depicted by lines in each panel.

Figure 6

The flow fields with the screen pump geometry $a=4$ and $b=1.5$. Four values of $K$ are plotted: (a) $K=1$, (b) $K=10$, (c) $K=100$, and (d) $K=200$.

Figure 7

The flow fields with the screen pump geometry $a=0.1$ and $b=1.5$. Four values of $K$ are plotted: (a) $K=1$, (b) $K=10$, (c) $K=100$, and (d) $K=200$.

Figure 8

The flow fields with the screen pump geometry $a=0.01$ and $b=1.5$. Four values of $K$ are plotted: (a) $K=1$, (b) $K=10$, (c) $K=100$, and (d) $K=200$. Note that in this thin screen pump, recirculating eddies appear, and they lead to reversing flow at large $K$, $K=200,$ for example.