(353b) Universality in the Size and Spacing of Slugs Generated by Converging Immiscible Flows at Microfluidic Junctions

When two immiscible fluids such as water and oil flow in through either end of the horizontal arm of a T-shaped micro-channel network, a segmented flow is often observed at a sufficiently low Capillary number, wherein the fluid that does not wet the channel walls is broken up into slugs (ellipsoidal drops that span the lateral dimension of the channel), each separated by a bolus of the other (wetting) fluid. Such flows have been utilized in a large number of microfluidic systems to generate and subsequently keep isolated small volumes of reaction mixtures. Despite the wide use of these flows, we have not found any literature that studies the size and spacing of these drops as a function of the channel dimensions and/or flow rate ratios of the two phases.

Because of the large interfacial contact with the channel wall and the severe curvature on the thin side of a rectangular slot of large aspect ratio, we find the slug spacing dimensions are largely independent of viscous effects and can be estimated by purely interfacial energy arguments. When the laterally stratified two-phase configuration reaches a critical length from the junction, its interfacial energy is equal to the energy of the isolated slugs with the same spacing. A longer stratified configuration would be energetically unfavorable. This simple convective stability theory predicts that that the sum of the length the slugs of non-wetting liquid formed and their spacing is directly proportional to the transverse perimeter of the channel and is independent of all other physical parameters including the net flow rate, though the ratio of the lengths of the non-wetting slug and the bolus of wetting fluid is equal to the ratio of the flow-rates of the two fluids. This universal scaling is confirmed by detailed measurement via video microscopy for a wide range of flow rates, flow rate ratios, channel dimensions, channel material and liquid pairs. This simple scaling breaks down at extreme but universal flow ratios of ~ 0.2 and 0.9 when the static slug configurations cannot accommodate the small volume of the lesser phase. The theory correctly captures these two limiting flow rate ratios and, by determining the shortest slug spacing with the lowest energy that can accommodate both phases, slug spacing beyond these two limits can also be estimated. The length of the slugs, and their spacing in this instance are, however, flow rate ratio dependent.