The mechanical response and stability of one and two-row packing of monodisperse emulsion droplets are studied in quasi 2d microchannels under longitudinal compression. Depending on the choice of parameter, a considered droplet arrangement is either transformed continuously into another packing under longitudinal compression or becomes mechanically unstable and segregates into domains of higher and lower packing fraction. Our experimental results are compared to analytical calculations for 2d-droplet arrangements with good quantitative agreement. This study also predicts important consequences for the stability of droplet arrangements in flowing systems.

In the lateral confinement of a flat microfluidic channel, monodisperse emulsion droplets spontaneously self-organize in a variety of topologically different packings. The explicit construction of mechanically equilibrated arrangements of effectively two-dimensional congruent droplet shapes reveals the existence of multiple mechanical equilibria depending on channel width W, droplet area A{d}, and volume fraction φ of the dispersed phase. The corresponding boundaries of local or global stability are summarized in a packing diagram for congruent droplet shapes in terms of the dimensionless channel width w=W/sqrt[A_{d}] and φ. In agreement with experimental results, an increasingly strong hysteresis of the transition between single-row and two-row packings is observed during changes of w above a threshold volume fraction of φ≃0.813.

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