(a) Sketch of the experimental setup for measurement of the effective hydrodynamic resistance to flow of a microchannel filled with n droplets, Rn . (b) Micrograph of water droplet flow in a microchannel filled with the ionic liquid, absence of contact lines indicates that the water droplets are completely encapsulated with an ionic liquid film. (c) Inset: The pressure drop across confined droplets in rectangular microchannels agrees reasonably well with the theory for inviscid bubbles. Here, and . (c) Comparison of the magnitudes of RD and . The effective change in the hydrodynamic resistance of microchannel caused by the presence of a single droplet is given by . Experimentally measured RD is less than and droplets therefore should act as discrete negative resistors when . (d) It is indeed seen that when the experimentally measured hydrodynamic resistance of a microchannel filled with n droplets, Rn is less than that of a microchannel devoid of droplets, R 0.
Schematic of repartition (a) and filter (b) regimes during droplet traffic through microfluidic loops. (c) Experimental measurements (symbols) of threshold capillary numbers for filtering droplets into the longer arm of a asymmetric loop, Caasym and in symmetric loops, Casym (inset) agree reasonably well with the theory (solid lines).
(a)–(d) Illustration of oscillatory droplet routing at a microfluidic junction; with the incoming droplet train filtering into arm i of the loop, a finite pulse of the continuous phase is injected into arm i to switch the filtering into the other arm. (enhanced online). (e)–(h) Plots tracking the trajectories of the droplet train at an asymmetric microfluidic loop, showing oscillatory routing; the arm into which the train is filtering into is plotted as solid black lines. The time dependent injection of the continuous phase to effect switching is represented by , which is plotted as dashed black lines. and −1 when the continuous phase at a flow rate of is injected exclusively into arms 1 and 2, respectively, and when there is no injection into either arm. [URL: http://dx.doi.org/10.1063/1.4819276.1] [URL: http://dx.doi.org/10.1063/1.4819276.2] [URL: http://dx.doi.org/10.1063/1.4819276.3] [URL: http://dx.doi.org/10.1063/1.4819276.4]doi: 10.1063/1.4819276.1.
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