Figure 1
(a) An optical micrograph of the FF bubble generator comprising a planar network of channels fabricated in poly(dimethylsiloxane) and having a uniform height of
. The relevant dimensions are plotted in the figure—the width of the inlet channel (
), the distance between the inlet channel and the orifice (
), the width of the orifice (
), and the length of the orifice (
). The original micrograph is shown in black; the gray lines extend the contours of the walls. (b) Bifurcation diagram showing the diameters of the bubbles as a function of the flow rate
of the liquid (
) for constant pressure (
) of gas. The first bifurcation occurs at
. It is followed by period halving at
. At
, the first of a cascade of period-doubling bifurcations occurs. The cascade leads to chaos which, upon further increase of
, gives way to a stable period-3 cycle. The solid line shows an outline of the bifurcation diagram (not to scale). The letters mark the rates of flow at which the micrographs of the period-1, period-2, period-4, and period-3 bubbling are shown in insets (c) to (f), respectively.
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