Lorenz Model for Chaos in Electrokinetic Instability

Area of Science:

• Fluid Dynamics
• Nonlinear Dynamics
• Microfluidics

Background:

• Electrokinetic instability (EKI) arises in microchannels due to electric fields and conductivity mismatches.
• Understanding the nonlinear dynamics of EKI is crucial for microfluidic applications.

Purpose of the Study:

• To approximate the nonlinear flow dynamics of EKI using the Lorenz system.
• To develop a simplified dynamical model for EKI in microchannels.

Main Methods:

• Galerkin projection was used to derive the dynamical model.
• The electrohydrodynamic flow equations were approximated by the Lorenz equations.

Main Results:

• The Lorenz system qualitatively captures EKI characteristics in linear and nonlinear regimes.
• The model predicts neutral stability criteria and transitions between periodic and aperiodic states.
• A small conductivity difference allows Lorenz equations to approximate EKI dynamics.

Conclusions:

• The simplified Lorenz model provides valuable insights into EKI nonlinearities and chaotic behavior.
• While not quantitatively precise, the model aids in understanding fundamental EKI dynamics.