Eelectrokinetic turbulence and chaos in ionic migration and in microfluidic convection

Turbulence in the ionic migration and in the microfluidic electro-hydrodynamic convection (mixing) under constant and low-frequency external electric field has been studied using distributed chaos approach and notion of effective (turbulent) diffusivity. Results of corresponding laboratory experiments have been also used for this purpose. It is shown that for the migration and convection (mixing) under constant and low-frequency external electric field the turbulent power spectra have stretched exponential form $E(k) \propto \exp-(k/k_{\beta})^{2/3}$. In the case of the microfluidic convection the distributed chaos is tuned to the large-scale coherent structures generated by the low-frequency oscillating external electric field ( $k_{\beta}$ is proportional to the forcing frequency).