Abstract
Electrokinetic instability refers to unstable electric field-driven disturbance to fluid flows, which can be harnessed to promote mixing for various electrokinetic microfluidic applications. This work presents a combined numerical and experimental study of electrokinetic ferrofluid/water co-flows in microchannels of various depths. Instability waves are observed at the ferrofluid and water interface when the applied DC electric field is beyond a threshold value. They are generated by the electric body force that acts on the free charge induced by the mismatch of ferrofluid and water electric conductivities. A nonlinear depth-averaged numerical model is developed to understand and simulate the interfacial electrokinetic behaviors. It considers the top and bottom channel walls’ stabilizing effects on electrokinetic flow through the depth averaging of three-dimensional transport equations in a second-order asymptotic analysis. This model is found accurate to predict both the observed electrokinetic instability patterns and the measured threshold electric fields for ferrofluids of different concentrations in shallow microchannels.
Highlights
We have extended our earlier work[47] and developed a depth-averaged model for better understanding and predicting the electrokinetic instability in microchannel ferrofluid/water co-flows
Its validity and accuracy have been tested by comparing the predictions with both the experimental measurements and the predictions of a regular 2D model
We demonstrate that the depth-averaged model is able to capture the experimentally observed dynamic behaviors at the ferrofluid/water interface under different electric fields. It can predict with a close agreement the measured threshold electric fields for ferrofluids of different concentrations in shallow microchannels
Summary
The regular 2D model predicts the occurrence of chaotic waves at an electric field (110.7 V/cm) that is even smaller than the experimental threshold electric field; see Fig. 1(c) (top) This indicates the strong stabilizing effects on electrokinetic flow from the top and bottom channel walls. The numerical threshold electric fields from the regular 2D model are included, which, though predicting correctly the decreasing trend of threshold electric field with increasing ferrofluid concentration, are all substantially lower than the experimental values. Their dependence on ferrofluid concentration is much weaker than the experimental observation. This is again, as explained above, because the top/bottom wall stabilizing effects on electrokinetic flow have been ignored in the regular 2D model
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