ANALYSIS OF THE ELECTRIC DOUBLE LAYER EFFECT ON MICROCHANNEL FLOW STABILITY

Sedat Tardu

doi:10.1080/10893950490516938

Abstract

It is shown that the microchannel flow under the electric double layer (EDL) effect is inviscidly unstable. A classical Orr–Sommerfeld analysis revealed that the critical Reynolds number of the primary (linear) instability may decrease by a decade, provided that the liquid contains a very small amount of ions and is associated with large enough zeta potential and low conductivity/viscosity. When the EDL layer is thick, the inflexion point moves away from the viscous near wall region, and the inviscid instability mechanism becomes more dominant. The EDL modes are slower than the Poiseuille ones and the spectrum of the eigenvalues shows its strong destabilizing effect. There are some strong arguments suggesting that the nonlinear stability mechanism under the EDL effect is also more severe compared with the macroscale flow. The present investigation suggests that early transition in microchannel flows is plausible and can be checked through well-controlled experiments.

Highlights

The “macro effects” should not be confused with real “micro effects” when explaining the deviations from the classical Navier–Stokes approach observed in microchannel flows
Tardu [2] used the universal relation of slip length as a function of the shear rate given by Thompson and Troian [3] to estimate the critical width of microchannels to have slip liquid flows
The main goal of this study is to directly investigate the electric double layer (EDL) effect on the linear stability of planar channel flow and estimate indirectly the resulting transitional Reynolds numbers

Summary

Introduction

The “macro effects” should not be confused with real “micro effects” when explaining the deviations from the classical Navier–Stokes approach observed in microchannel flows. The slip length and the temperature jump can be related to the Knudsen number through the momentum and temperature accommodation coefficients and first- or secondorder models in the rarefied regime of gas flows. Tardu [2] used the universal relation of slip length as a function of the shear rate given by Thompson and Troian [3] to estimate the critical width of microchannels to have slip liquid flows. He concluded that the hydraulic diameters of such devices have to be smaller than 0.52 μm. The slip velocity is only 0.04% of the centerline velocity at the transitional Reynolds number

Objectives

Results

Conclusion