Electro-hydrodynamic flow through channels with micro-patterned walls

Abstract

This is an analytical study on electrohydrodynamic flow through a microchannel, of which the wall is micropatterned with a periodic array of longitudinal or transverse slip-stick stripes with different wall potentials. The flow is driven by steady or time-oscillating hydrodynamic and electric forcings. Four models are presented to study flow in a parallel-plate channel or in a circular channel, where, in each case, the forcings can be steady or oscillating with time of the same frequency. Using the methods of eigenfunction expansion and point collocation, the electric potential and velocity fields are determined by solving the linearized Poisson-Boltzmann equation and the Stokes equation subject to the mixed no-slip or partial-slip boundary conditions. The Onsager reciprocity relations for the fluid and current fluxes are deduced. Attention is paid to some particular kinds of stripe patterns, with a view to revisit and to generalize the theoretical limits made in previous studies on electrokinetic flow over an inhomogeneously slipping surface.

In the first part of this thesis, electrohydrodynamic flow through a micropatterned parallel-plate channel is considered. We present a formal proof of the symmetry of the Onsager relations as well as more general results for arbitrary channel height, electric double layer (EDL) thickness, oscillation frequency and also partial-slip length. In the steady-flow regime, when a surface is not 100% uniformly slipping but has a small fraction of area being covered by no-slip slots, the electroosmotic flow (EOF) enhancement can be appreciable reduced. When the EDL is not very thin or the uncharged regions are partial-slipping, there will be a finite inhibition effect on the EOF. Further in the oscillatory-flow regime, we show that, for uniformly charged walls, the effective slip length obtained from the hydrodynamic problem can still be used directly in the EOF as if the wall were uniformly slipping. The presence of uncharged perfectly-slipping stripes will always have a decreasing effect on the EOF, unlike the steady case where it gives no enhancement to the EOF in the thin EDL limit. Furthermore, we confirm the presence of a threshold frequency beyond which the flow will experience significant reduction in magnitude of the tidal volume. Slipping area fraction of the wall and wall potential are shown to have distinct effects on this threshold frequency and the flow response.

In the second part, electrohydrodynamic flow through a micropatterned circular channel is considered. Some remarks for EOF in a parallel-plate channel are also applicable to the present problem. Our focus is placed on the effects of the pattern pitch on the flow. When the wall is uniformly charged, the adverse effect on the EOF enhancement due to a small area fraction of no-slip slots can be amplified if the pitch decreases. When the slipping regions are uncharged, reducing the pitch will lead to a greater deviation from the Helmholtz-Smoluchowski limit in the steady-flow regime, yet this effect will be reversed for oscillatory flow. With oppositely charged slipping regions, a net reversed flow is possible, even when the wall is on the average electro-positive. The flow morphology is found to be subject to the combined influence of the geometry of the channel and the electrohydrodynamic properties of the wall.