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(a) The microfluidic flow-focusing device (top view). The cross sections of the channels are rectangular. The widths of the inlet channels were set to and for the liquid and gas, respectively. We used several widths of the orifice and of outlet channel . The actual dimensions did not differ from the designed ones by more than . All devices had the same height . (b) Illustration of a bubble in the outlet channel. Bubbles are squeezed between the top and bottom wall, and have a disc-like geometry. We approximate the volume of the bubble is , where is the radius of the bubble-wall interface.
Volume of the bubbles plotted against the product of the flow rate and viscosity of the liquid, and scaled to the units of pressure by multiplying by . All experiments were performed with and with following geometrical parameters: , , and . Symbols correspond to different viscosities and interfacial tensions , ; , ; , ; and , . The solid lines give the slope of a relation . The vertical line marks the transition from the period 1 to period 2. The inset shows scaling of the bubble size with pressure. Five series of data are shown for (, ) and five different flow rates: , , , , and . We multiplied by to leave only the dependence on pressure. The solid line gives the slope of a linear relation between and .
(a) Frequency of breakup plotted against the flow rate of the liquid. The pressure to flow-rate ratio was kept constant for all the data points. The solid line gives a fit . The dimensions of the channel are , . (b) The radius of the bubbles formed in the same experiment, the volume fraction of bubbles in the channel, and the volume fraction at which bubbles were formed . The arrows mark the data points for which snapshots of the system are shown as insets to plot (a).
Examples of the flowing lattices formed by the bubbles in the outlet channel. The outlet channel width is , the orifice width , and the pressure is set to a constant value of . The liquid flow rates were as follows: (a) 0.2, (b) 0.14, (c) 0.0278, (d) 0.0056, and (e) . Color stills have been converted to black and white images.
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