Energy efficiency analysis of mass transport enhancement in time-periodic oscillatory electroosmosis

Abstract

The streamwise mass transport of passive, neutral non-reacting solutes in oscillatory electroosmotic microchannel flows is theoretically investigated from an energy consumption and efficiency perspective for general asymmetric wall zeta potentials and slip velocities. Analytical solutions to the averaged mass transport and total power input (consisting of Joule heating, viscous dissipation, and sliding friction) are obtained and expressed in terms of the relevant parameters governing the system. Particularly, we define a “χg-parameter” to quantify the mass transport gained (excluding pure diffusion) per total power input in our analysis and discussions. While the no-slip, symmetric potential χg-performances agree with the mass transport results reported in previous literature, a “resonance like” behavior in the χg-performances is identified for large enough Womersley numbers and symmetric slip lengths despite the extra sliding friction, viscous dissipation, and Joule heating consumptions in the symmetric zeta potential configuration. When favorable asymmetries in the wall potentials and slip lengths are introduced, the χg-performances are not only considerably improved, but also highly correlated with the magnitudes of the velocity gradients in the oscillatory velocity profiles, hence reinforcing the physical picture of Taylor–Aris dispersion. Geometric symmetry can be identified among distinct velocity profiles which yield the same χg-performance. These profiles are generally associated with particular families of wall potential and/or slip length combinations also exhibiting symmetry among one another. Finally, the aspect ratio of the slit microchannel (width divided by length) is found to play a crucial role in significantly improving the χg-energy efficiency of mass transport in time-periodic electroosmosis.