Electric-Field-Induced Pattern Formation in Layers of DNA Molecules at the Interface between Two Immiscible Liquids

The concentration patterns of DNA molecules attached to the interface between two immiscible aqueous phases forming under an electric field are studied. The pattern formation is driven by hydrodynamic interactions between the molecules originating from the electro-osmotic flow due to the Debye layer around a molecule. A nonlinear integrodifferential equation is derived describing the time evolution of the concentration field at the liquid-liquid interface. A linear stability analysis of this equation shows that a mode of given wavelength is initially stable, but destabilizes after a critical time which is inversely proportional to the wavelength. The scaling behavior of the critical time with electric field strength and viscosity found in the experiments agrees with the predictions by the theoretical model.

Figure 1

Schematic of the experimental setup used to study DNA concentration patterns at the liquid-liquid interface in an ATPS. The patterns are imaged through the glass slide at the bottom.

Figure 2

Fluorescence microscopy images of patterns in the DNA concentration field at the liquid-liquid interface. (a) ($t=t_0$, $U=30\text{V}$) and (b) ($t=2.2t_0$, $U=30\mathrm{V}$) show the variation of the patterns with time. $t$ is the time that has passed after applying the voltage, and $t_0$ indicates the experimentally determined time of pattern formation (see Sec. 1.4 in Ref. [19]). (b),(c) ($t=2.2t_0$, $U=10\text{V}$) and (d) ($t=2.2t_0$, $U=20\mathrm{V}$) demonstrate the variation of the patterns with applied voltage. The gray scale map of the original fluorescence micrographs was inverted for better visibility.

Figure 3

(a) Schematic of an alternative experimental setup used to visualize the recirculating flow field around DNA clusters. The viewing direction is perpendicular to the electric field. (b) Traces of DNA molecules in a recirculating flow field around two clusters close to the liquid-liquid-solid contact line. The gray scale map of the original fluorescence micrographs was inverted for better visibility. (c) Schematic representation of the flow field around a DNA molecule attached to the interface.

Figure 4

Main diagram: Time of pattern formation $t_0$ as a function of the applied voltage $U$ for a fixed dextran phase viscosity of 22.5 mPa s. Inset: The same, but as a function of $\eta$, for a fixed applied voltage of 20 V. The symbols represent the experimental data, the curves the scaling relations obtained from the theoretical model. The error bars represent the standard error of the mean.