عنوان مقاله [English]
Due to recent advances in microfabrication techniques, it is possible to produce microchannels with positive, negative, or even neutral surface charges. Investigations of electroosmotic flow indicate that such a combination of charge patterns on the microchannel walls results in complex flow fields with circulation zones that are highly desirable for fluid mixing requirements, as in lab-on-a-chip devices. However, the mixing efficiency of such flows is not well-examined. The objective of this article is finding a proper mixing indicator among those which have been frequently used for evaluation of mixing, to examine the effect of wall heterogeneities on mixing efficiency. In general, for the numerical study of electro-osmotic flows, it is necessary to solve the electric potential field and the equations for ion transport, together with Navier-Stokes equations, which are numerically expensive and time-consuming, especially when heterogeneous channels are modeled. However, under certain conditions, the Helmholtz-Smoluchowski model can be used, which efficiently reduces numerical expense. In this model, the flow field is obtained by solving the Navier-Stokes equations with slip boundary conditions at walls, which comes from the Helmholtz-Smoluchowski slip velocity. Upon solving for the flow field, the concentration field can be obtained and the mixing efficiency can be evaluated. In most studies, the standard deviation of concentrations at any cross-section is considered the mixing indicator. Our investigations of the complex flow patterns with circulation zones show that this indicator is not well-behaved near the vortex area, such that some fluctuations in the mixing values occur. In order to have a more physically relevant mixing indicator, a weighted standard deviation is used to quantify the mixing performance, which is more consistent with vortex flows. Based on this indicator, some essential concepts for mixing, such as mixing performance, and channel efficiency, are introduced and the effects of step-wise heterogeneities are studied. Different zeta potential distributions associated with the single patch were examined, and it was found that the mixing performance of a non-continuous potential distribution is relatively similar to that of continuous counterparts, despite the slight differences in the flow field. The results for a single patch indicate that the channel efficiency of a channel with a single patch linearly increases with the size of the patch, such that for a channel with a patch size of channel height, the mixing efficiency increases 4\%, compared to its homogeneous channel. Also, the mixing performance is enhanced as the single patch is located closer to the channel inlet. The findings of the present study can be employed in the design of optimized micro-mixers.