  This study presents a detailed investigation of how the rheological behaviour
of fluid could influence the electrokinetic instability (EKI) phenomenon in a
microfluidic T-junction. The non-Newtonian power-law model with different
values of the power-law index (n) is used to obtain fluids of different
rheological behaviours. We find that as the fluid rheological behaviour changes
from shear-thickening (n > 1) to shear-thinning (n < 1) via the Newtonian (n =
1) one, the EKI phenomenon is significantly influenced under the same
conditions. In particular, the intensity of this EKI phenomenon is found to be
significantly higher in shear-thinning fluids than in Newtonian and
shear-thickening fluids. As a result, the corresponding mixing phenomenon,
often achieved using this EKI phenomenon, is also notably enhanced in
shear-thinning fluids compared to that achieved in Newtonian and
shear-thickening fluids. A detailed analysis of both the flow dynamics and
mixing phenomena in terms of streamlines, velocity fluctuations, concentration
field, mixing efficiency, etc., is presented and discussed in this study. We
also employ the data-driven dynamic mode decomposition (DMD) technique to
analyze the flow field in more detail. In particular, the information on the
coherent flow structures obtained with different values of the power-law index
facilitates the understanding of both the EKI-induced chaotic convection and
mixing phenomena in a better way; for instance, why the mixing efficiency is
higher in shear-thinning fluids than that in Newtonian and shear-thickening
fluids. Moreover, we observe that the spatial expanse and intensity of these
coherent structures differ significantly as the power-law index changes,
thereby providing valuable insights into certain aspects of the underlying flow
dynamics that otherwise are not clearly apparent from other analyses.
