Stability analysis of time-periodic electrokinetic flow with slip effects

Abstract

We investigate the stability analysis of time-dependent electroosmotic flow with charged species concentration in a symmetric microchannel, taking into account the influence of slip velocity. The electroosmotic flow is governed by a time-dependent spatially harmonic electric field and is applied between two infinitely long parallel plates containing a dilute electrolytic solution. The base state solutions are calculated pertaining to the Debye–Hückle approximation in the Poisson–Boltzmann equation. Our study highlights two stability issues: electrokinetic and Stokes layer phenomena. The linear stability analysis is conducted by employing the Floquet theory of the dynamical systems obtained from the Galerkin expansion of the disturbance quantities, considering suitable basis functions. The stability of the time-periodic system is determined by the eigenvalues of the monodromy matrix obtained from the time-dependent matrix (or Floquet matrix) by numerical integration. The analysis reveals that both systems are linearly stable over the range of parameters relevant to microfluidic systems under the influence of slip velocity. It is demonstrated that despite the Stokes layer being more stable than the electrokinetic layer, the presence of slip further increases the stability of the system, even though it exhibits a complex behavior. These results have been supported by a full-scale numerical simulation showing that the velocity slip condition stabilizes the flow.