Electro-osmotic flow in rectangular microchannels: geometry optimization

Abstract

Abstract. Micro-flow devices have turned over the years from the subject of fundamental research to fully-fledged industrial applications. Although for some cases the transport phenomena in micro-devices can be handled satisfactorily by using the same approach as for their larger-size counterparts, micro-effects such as electro-osmotic flow (EOF) are typical of small scales and can be employed to circulate coolant through heat sinks by means of electro-osmotic pumping. In order to obey the constraints that different engineering applications impose, design criteria must be employed to optimize the performance of the devices according to the criteria chosen. In this work optimization of the cross-sectional area of a microchannel where EOF and heat transfer at the walls occur is employed to demonstrate how approaches based on the first or second law of thermodynamics may yield opposite results, which are strongly dependent on the peculiarities of EOF, i.e. the ratio of Joule heating to heat transfer at the walls.

Numerical Investigation of Thermally Developing and Fully Developed Electro-Osmotic Flow in Channels with Rounded Corners

“…Excluding simulations involving model verification and comparison with literature results, the values of the Debye-Hückel parameter and the nondimensional Stern potential were set to k D D h ≤ 9.77 and Ψ 0 ≤ 3.89 respectively for most of the parametric computations. As mentioned at the end of Section 2.1, these are determined by the choice of the wall and fluid inlet temperatures; the remaining quantities which compose the Debye-Hückel parameter and the Stern potential have the values of deionized, ultra-filtered water, and are often adopted in the literature [28,[30][31][32][33]44,45,50]. The highest values were considered for the GDA, while the channel cross section aspect ratio and the smoothing radius were set to β = 3/4 and γ = 1/2.…”

“…Optimization of the cross section can lead to improved performance in terms of increased heat transfer and decreased pressure drop and entropy production, and this can be achieved through smoothing of its corners, as demonstrated in [39,40]. Investigation has been extended to pressure-driven flows in microchannels with and without viscous dissipation [41][42][43], and to electro-osmotic flows in the fully developed and constant heat flux and perimeter temperature case [44,45], employing the results to carry out a first-law analysis based on performance evaluation criteria (PEC) [46].…”

Electro-osmotic non-isothermal flow in rectangular channels with smoothed corners

“…When the optimal radius of curvature of the cross-section is sought in terms of e.g. Performance Evaluation Criteria [41] or Entropy Generation Minimisation [43] one further geometry constraint must be applied [40,44], either on the reference side, crosssection, heated perimeter or hydraulic diameter, this is not the case for the computation of the Poiseuille and Nusselt numbers.…”