DNA electrophoresis in a sparse ordered post array

We present a study of the electrophoresis of long DNA in a strong electric field through a hexagonal array of cylindrical microscale posts spaced such that the pore size is commensurate with equilibrium coil size of the DNA. Experimental mobility, dispersivity, and videomicroscopy data indicate that the DNA frequently collide with the posts, contradicting previous Brownian dynamics studies using a uniform electric field. We demonstrate via simulations that the frequent collisions, which are essential to separations in these devices, are due to the nonuniform electric field, highlighting the importance of accounting for electric-field gradients when modeling DNA transport in microfluidic devices.

Figure 1

(Color online) (a) Schematic illustration of a hexagonal array of cylindrical posts of diameter $d$ and center-to-center spacing $a$. Several field lines created by the insulating posts are depicted in the figure. The equilibrium coil size of the DNA is commensurate with the spacing between the posts. The DNA move from left to right, in the direction opposite the electric field. (b) Image of a portion of a $50\mu \text{m}\times 15\text{mm}$ PDMS hexagonal array of $1.2\mu \text{m}$ diameter microposts with a $3\mu \text{m}$ pitch. The electric field is applied from right to left. (c) To measure the mobility and dispersivity, the DNA are injected in a shifted-$T$ geometry and the fluorescence intensity vs time is collected at $i$ positions located $P_i=2.5i\text{mm}$ downstream from the injection point. The microchannel is $50\mu \text{m}$ wide and $1.97\mu \text{m}$ deep.

Figure 2

Plot of the experimentally measured dispersivity, $D^{\ast }$, made dimensionless with the molecular diffusivity $D$, as a function of the Péclet number defined in Eq. (2). The squares correspond to measurements in the post array; the triangles correspond to measurements in an empty channel. The size of the error bars is one standard deviation; the error in the empty channel is smaller than the size of the symbol. The inset shows an image of the DNA dynamics at $\text{Pe}=230$.

Figure 3

(Color online) Comparison of the electrophoretic mobility, $\mu$, made dimensionless with the free-solution mobility, ${\mu }_0$, and the number of collisions as a function of the Péclet number between the experimental data (◼), (ii) simulations with a nonuniform field (red, —○—), simulations with a uniform field (blue, -◻-), and Eq. (3) (black, - - -). The size of the error bars for the mobility is one standard deviation; the error in the simulations is smaller than the size of the symbols. The simulation lines are only to guide the eye.