We have developed an electrokinetic process to rapidly stir micro- and nanoliter volume solutions for microfluidic bioanalytical applications. We rapidly stir microflow streams by initiating a flow instability, which we have observed in sinusoidally oscillating, electroosmotic channel flows. As the effect occurs within an oscillating electroosmotic flow, we refer to it here as an electrokinetic instability (EKI). The rapid stretching and folding of material lines associated with this instability can be used to stir fluid streams with Reynolds numbers of order unity, based on channel depth and rms electroosmotic velocity. This paper presents a preliminary description of the EKI and the design and fabrication of two micromixing devices capable of rapidly stirring two fluid streams using this flow phenomenon. A high-resolution CCD camera is used to record the stirring and diffusion of fluorescein from an initially unmixed configuration. Integration of fluorescence intensity over measurement volumes (voxels) provides a measure of the degree to which two streams are mixed to within the length scales of the voxels. Ensemble-averaged probability density functions and power spectra of the instantaneous spatial intensity profiles are used to quantify the mixing processes. Two-dimensional spectral bandwidths of the mixing images are initially anisotropic for the unmixed configuration, broaden as the stirring associated with the EKI rapidly stretches and folds material lines (adding high spatial frequencies to the concentration field), and then narrow to a relatively isotropic spectrum at the well-mixed conditions.

Electrokinetic flow is leveraged in a variety of applications, and is a key enabler of on-chip electrophoresis systems. An important sub-class of electrokinetic devices aim to pump and control electrolyte working liquids with spatial gradients in conductivity. These high-gradient flows can become unstable under the application of a sufficiently strong electric field. In this work the instability physics is explored using theoretical and numerical analyses, as well as experimental observations. The flow in a long, rectangular-cross-section channel is considered. A conductivity gradient is assumed to be orthogonal to the main flow direction, and an electric field is applied in the streamwise direction. It is found that such a system exhibits a critical electric field above which the flow is highly unstable, resulting in fluctuating velocities and rapid stirring. Modeling results compare well with experimental observations. The model indicates that the fluid forces associated with the thin dimension of the channel ͑transverse to both the conductivity gradient and the main flow direction͒ tends to stabilize the flow. These results have application to the design and control of on-chip assays that require high conductivity gradients, and provides a rapid mixing mechanism for low Reynolds number flows in microchannels.

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In this paper we present a multiple-species electrokinetic instability ͑MSEKI͒ model. We consider a high aspect ratio flow geometry, a base state where the conductivity gradient is orthogonal to the applied electric field ͑i.e., a spanwise gradient configuration͒, and a four-species chemistry model. A linear stability analysis ͑LSA͒ of the depth-averaged governing equations is shown to have unstable eigenmodes for conductivity ratios as close to unity as 1.01. We present the experimental image data and full nonlinear simulations of the governing equations for a conductivity ratio of 1.05. Images of the disturbance dye field from the nonlinear simulations show good qualitative agreement with the experiment. Both the trend and absolute value of the temporal evolution of the critical wave number are captured by the MSEKI model. Growth rates extracted from the experimental data also compare favorably with those predicted by LSA. Species electromigration is shown to have a significant influence on the development of the conductivity field and instability dynamics in multi-ion configurations. We anticipate this model to be of practical interest to researchers developing electrokinetically driven, chip-based bioanalytical devices.

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