Mixing-dynamics of a passive scalar in a three-dimensional microchannel

The mixing of a diffusive passive-scalar driven by electro-osmotic fluid motion in a micro-channel is studied numerically. Secondary time-dependent periodic or random electric fields, orthogonal to the main stream, are applied to generate cross-sectional mixing. This investigation focuses on the mixing dynamics and its dependence on the frequency (period) of the driving mechanism. For periodic flows, the probability density function (PDF) of the scaled concentration settles into a self-similar curve showing spatially repeating patterns. In contrast, for random flows there is a lack of self-similarity in the PDF for the time interval considered. An exponential decay of the variance of the concentration, and associated moments, is found to exist for both periodic and random velocity fields. The numerical results also indicate that measures of chaoticity (in a deterministic chaotic system) decay exponentially in the frequency – at large frequencies – in agreement with the theory.