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The breakup of droplets due to creeping motion in a confined microchannel geometry is studied using three-dimensional numerical simulations. Analogously to unconfined droplets, there exist two distinct breakup phases: (i) a quasi-steady droplet deformation driven by the externally applied flow; and (ii) a surface-tension-driven three-dimensional rapid pinching that is independent of the externally applied flow. In the first phase, the droplet relaxes back to its original shape if the externally applied flow stops; if the second phase is reached, the droplet will always break. Also analogously to unconfined droplets, there exist two distinct critical conditions: (i) one that determines whether the droplet reaches the second phase and breaks, or it reaches a steady shape and does not break; and (ii) one that determines when the rapid autonomous pinching starts. We analyse the second phase using stop-flow simulations, which reveal that the mechanism responsible for the autonomous breakup is similar to the end-pinching mechanism for unconfined droplets reported in the literature: the rapid pinching starts when, in the channel mid-plane, the curvature at the neck becomes larger than the curvature everywhere else. The same critical condition is observed in simulations in which we do not stop the flow: the breakup dynamics and the neck thickness corresponding to the crossover of curvatures are similar in both cases. This critical neck thickness depends strongly on the aspect ratio, and, unlike unconfined flows, depends only weakly on the capillary number and the viscosity contrast between the fluids inside and outside the droplet.

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We show experimentally, and explain theoretically, what velocity is needed to break an elongated droplet entering a microfluidic T-junction. Our experiments on short droplets confirm previous experimental and theoretical work that shows that the critical velocity for breakup scales with the inverse of the length of the droplet raised to the fifth power. For long elongated droplets that have a length about thrice the channel width, we reveal a drastically different scaling. Taking into account that a long droplet remains squeezed between the channel walls when it enters a T-junction, such that the gutters in the corners of the channel are the main route for the continuous phase to flow around the droplet, we developed a model that explains that the critical velocity for breakup is inversely proportional to the droplet length. This model for the transition between breaking and nonbreaking droplets is in excellent agreement with our experiments.

Abstract. Modeling of low-Capillary number segmented flows in microchannels is important for the design of microfluidic devices. We present numerical validations of microfluidic flow simulations using the volume-of-fluid (VOF) method as implemented in OpenFOAM. Two benchmark cases were investigated to ensure the reliability of OpenFOAM in modeling complex physical phenomena in microfluidics, viz. 1) the steady motion of bubbles in capillaries, and 2) the formation of bubbles in T-junctions. We found that it is crucial to reduce spurious currents and to apply local grid refinement to capture the relevant flow physics. With these, we obtain good agreement between our numerical simulations and previously published theoretical and experimental data.