This paper reports an analysis of the parallelized production of bubbles in a microreactor based on the repeated break-up of bubbles at T-junctions linked in series. We address the question how to design and operate such a multi-junction device for the even distribution of bubbles over the exit channels. We study the influence of the three primary sources leading to the uneven distribution of bubbles: (1) nonuniformity in the size of bubbles fed to the distributor, (2) lack of bubble break-up, and (3) asymmetric bubble breakup caused by asymmetries in flow due to fabrication tolerances. Based on our theoretical and experimental analysis, we formulate two guidelines to operate the multi-junction bubble distributor. The device should be operated such that: (i) the capillary number exceeds a critical value at all junctions, Ca>CacritCa>Cacrit, to ensure that all bubbles break, and (ii) the parameter (ls/w)·Ca1/3(ls/w)·Ca1/3is sufficiently large, with ls/wls/w the distance between the bubbles normalized by the channel width. More quantitatively, (ls/w)·Ca1/3>2(ls/w)·Ca1/3>2 for fabrication tolerances below 2%, which are typical for devices made by soft lithography. Furthermore, we address the question whether including a bypass channel around the T-junctions reduces flow asymmetries and corresponding nonuniformities in bubble size. While bubble nonuniformities in devices with and without bypass channels are comparable for fabrication tolerances of a few percent, we find that incorporating a bypass channels does have a beneficial effect for larger fabrication tolerances. The results presented in this paper facilitate the scale-out of bubble-based microreactors.

Pag. R4-1 t/m R4-11 Abstract: 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.

Abstract We present an extensive analysis of the performance of the Volume of Fluid (VOF) method, as implemented in OpenFOAM, in modeling the flow of confined bubbles and droplets (¿segmented flows¿) in microfluidics. A criterion for having a sufficient grid solution to capture the thin lubricating film surrounding non-wetting bubbles or droplets, and the precise moment of breakup or coalescence is provided. We analyze and propose optimal computational settings to obtain a sharp fluid interface and small parasitic currents. To show the usability of our computational rules, numerical simulations are presented for three benchmark cases, viz. the steady motion of bubbles in a straight two-dimensional channel, the formation of bubbles in two- and three-dimensional T-junctions, and the breakup of droplets in three-dimensional T-junctions. An error analysis on the accuracy of the computations is presented to probe the efficacy of the VOF method. The results are in good agreement with published experimental data and experimentally-validated analytical solutions.