Investigation of alternating-flow mixing in microchannels

A number of different approaches to mixing liquids in microscale systems can be found in the literature. In the case of miscible liquids it is desirable to produce mixtures with residual non-uniformity in composition that is below some specified level. Yet very little quantitative information is available concerning the conditions required to produce a given level of mixture uniformity. A theoretical approach to this problem is described. Computational fluid dynamics and simple scaling are used to develop a quantitative understanding of the alternating flow method of mixing using pressure driven flow. In this approach, external flow control is used to produce alternating injection into a single microchannel of two or more solutions to be mixed. The resulting streamwise slugs of solution then mix by the stretching of the slugs into thin striations resulting from shear strain. The most challenging condition for mixing is where the Reynolds number is approaching zero and inertia effects are negligible, a common situation in microchannel flows, particularly where relatively high-viscosity liquids, for example ionic liquids, are involved. The scaling theory demonstrates that an initial time period of rapid mixing of fluid outside the core of the flow, scaling as Pe-2/3Pe-2/3, is followed by a far slower process of mixing in the core region, scaling as Pe-1/2Pe-1/2. An approximate correlation for the deviation from the perfectly mixed state as a function of time is found. This correlation applies over the range of Peclet number, slug length and solution mixture ratio that are of interest. The mixture uniformity produced is shown to be limited by the initial uniformity of each solution over the channel section resulting from the injection process.