Lorenz Model for Chaos in Electrokinetic Instability

We demonstrate that the Lorenz system of equations can approximate the nonlinear flow dynamics of the electrokinetic instability (EKI) in a microchannel driven by an electric field applied parallel to the diffusive interfaces separating the co-flowing centre and sheath streams with mismatched electrical conductivity. Using Galerkin projection, we show that the electrohydrodynamic flow equations can be approximated by the Lorenz equations in the limit of small conductivity difference between the flow streams. The derived dynamical model qualitatively captures the characteristics of EKI in both linear and nonlinear regimes, including the neutral stability criterion and alternating transitions between periodic and aperiodic states with increasing electric Rayleigh numbers. While not quantitatively precise, this simplified dynamical model provides valuable insights into the essential nonlinearities responsible for chaotic behaviour observed in EKI experiments.